| # | ID | ODE | CAS classification |
Maple |
Mma |
Sympy |
time(sec) |
| \(1\) |
\begin{align*}
y^{\prime }&=x^{2}-y^{2} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✗ |
7.138 |
|
| \(2\) |
\begin{align*}
y^{\prime }&=x^{2}+y^{2}-1 \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_Riccati] |
✗ |
✓ |
✗ |
26.394 |
|
| \(3\) |
\begin{align*}
y y^{\prime \prime }&=6 x^{4} \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
0.424 |
|
| \(4\) |
\begin{align*}
x^{2} y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[_separable] |
✗ |
✓ |
✗ |
0.064 |
|
| \(5\) |
\begin{align*}
x^{3} y^{\prime }&=2 y \\
\end{align*} Series expansion around \(x=0\). |
[_separable] |
✗ |
✓ |
✗ |
0.075 |
|
| \(6\) |
\begin{align*}
x^{2} y^{\prime \prime }+\cos \left (x \right ) y^{\prime }+y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
0.158 |
|
| \(7\) |
\begin{align*}
3 x^{3} y^{\prime \prime }+2 x^{2} y^{\prime }+\left (-x^{2}+1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
0.106 |
|
| \(8\) |
\begin{align*}
x^{3} \left (1-x \right ) y^{\prime \prime }+\left (3 x +2\right ) y^{\prime }+y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
0.114 |
|
| \(9\) |
\begin{align*}
x^{2} y^{\prime \prime }+\left (3 x -1\right ) y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✗ |
✓ |
✗ |
0.154 |
|
| \(10\) |
\begin{align*}
x^{3} y^{\prime \prime }-y^{\prime } x +y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✗ |
✓ |
✗ |
0.098 |
|
| \(11\) |
\begin{align*}
y^{\prime }&=x^{2}+y^{2} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[[_Riccati, _special]] |
✓ |
✓ |
✗ |
8.039 |
|
| \(12\) |
\begin{align*}
x^{\prime }&=t x-{\mathrm e}^{t} y+\cos \left (t \right ) \\
y^{\prime }&={\mathrm e}^{-t} x+t^{2} y-\sin \left (t \right ) \\
\end{align*} |
system_of_ODEs |
✓ |
✗ |
✗ |
0.052 |
|
| \(13\) |
\begin{align*}
x^{\prime }&=t x-y+{\mathrm e}^{t} z \\
y^{\prime }&=2 x+t^{2} y-z \\
z^{\prime }&={\mathrm e}^{-t} x+3 t y+t^{3} z \\
\end{align*} |
system_of_ODEs |
✗ |
✗ |
✗ |
0.060 |
|
| \(14\) |
\begin{align*}
y^{\prime }&=1+x^{2}+y^{2}+x^{2} y^{4} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
1.198 |
|
| \(15\) |
\begin{align*}
x^{2} y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[_separable] |
✗ |
✓ |
✗ |
0.066 |
|
| \(16\) |
\begin{align*}
x^{3} y^{\prime }&=2 y \\
\end{align*} Series expansion around \(x=0\). |
[_separable] |
✗ |
✓ |
✗ |
0.077 |
|
| \(17\) |
\begin{align*}
y^{\prime }&=\frac {-{\mathrm e}^{-x}+x}{{\mathrm e}^{y}+x} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
2.216 |
|
| \(18\) |
\begin{align*}
{\mathrm e}^{x} \sin \left (y\right )+3 y-\left (3 x -{\mathrm e}^{x} \sin \left (y\right )\right ) y^{\prime }&=0 \\
\end{align*} |
[‘x=_G(y,y’)‘] |
✗ |
✗ |
✗ |
11.574 |
|
| \(19\) |
\begin{align*}
x \ln \left (x \right )+y x +\left (y \ln \left (x \right )+y x \right ) y^{\prime }&=0 \\
\end{align*} |
[[_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
74.067 |
|
| \(20\) |
\begin{align*}
u^{\prime \prime }+u^{\prime }+\frac {u^{3}}{5}&=\cos \left (t \right ) \\
u \left (0\right ) &= 2 \\
u^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[NONE] |
✗ |
✗ |
✗ |
0.639 |
|
| \(21\) |
\begin{align*}
t \left (t -1\right ) y^{\prime \prime \prime \prime }+{\mathrm e}^{t} y^{\prime \prime }+4 t^{2} y&=0 \\
\end{align*} |
[[_high_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
0.070 |
|
| \(22\) |
\begin{align*}
t y^{\prime \prime \prime }+2 y^{\prime \prime }-y^{\prime }+t y&=0 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.037 |
|
| \(23\) |
\begin{align*}
\left (2-t \right ) y^{\prime \prime \prime }+\left (2 t -3\right ) y^{\prime \prime }-y^{\prime } t +y&=0 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.063 |
|
| \(24\) |
\begin{align*}
t^{2} \left (t +3\right ) y^{\prime \prime \prime }-3 t \left (t +2\right ) y^{\prime \prime }+6 \left (1+t \right ) y^{\prime }-6 y&=0 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.072 |
|
| \(25\) |
\begin{align*}
y^{\prime }&=\frac {x^{2}+y^{2}}{\sin \left (x \right )} \\
\end{align*} |
[_Riccati] |
✗ |
✗ |
✗ |
22.558 |
|
| \(26\) |
\begin{align*}
y^{\prime }&=\frac {{\mathrm e}^{x}+y}{x^{2}+y^{2}} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
3.153 |
|
| \(27\) |
\begin{align*}
y^{\prime }&=\tan \left (y x \right ) \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✗ |
1.595 |
|
| \(28\) |
\begin{align*}
y^{\prime }&=\frac {x^{2}+y^{2}}{\ln \left (y x \right )} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
4.328 |
|
| \(29\) |
\begin{align*}
y^{\prime }&=\left (x^{2}+y^{2}\right ) y^{{1}/{3}} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
2.006 |
|
| \(30\) |
\begin{align*}
y^{\prime }&=\ln \left (1+x^{2}+y^{2}\right ) \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
1.531 |
|
| \(31\) |
\begin{align*}
y^{\prime }&=\sqrt {x^{2}+y^{2}} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
3.048 |
|
| \(32\) |
\begin{align*}
y^{\prime }&=\left (x^{2}+y^{2}\right )^{2} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
1.704 |
|
| \(33\) |
\begin{align*}
2 x^{2}+8 y x +y^{2}+\left (2 x^{2}+\frac {x y^{3}}{3}\right ) y^{\prime }&=0 \\
\end{align*} |
[_rational] |
✗ |
✗ |
✗ |
3.112 |
|
| \(34\) |
\begin{align*}
y \sin \left (y x \right )+x y^{2} \cos \left (y x \right )+\left (x \sin \left (y x \right )+x y^{2} \cos \left (y x \right )\right ) y^{\prime }&=0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
8.069 |
|
| \(35\) |
\begin{align*}
\left (3 x -1\right ) y^{\prime \prime }-\left (3 x +2\right ) y^{\prime }+\left (6 x -8\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
23.131 |
|
| \(36\) |
\begin{align*}
\left (2 x +1\right ) y^{\prime \prime }-2 \left (2 x^{2}-1\right ) y^{\prime }-4 \left (x +1\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✗ |
✗ |
34.219 |
|
| \(37\) |
\begin{align*}
y^{\prime }&=y^{2}+\cos \left (t^{2}\right ) \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_Riccati] |
✗ |
✗ |
✗ |
38.014 |
|
| \(38\) |
\begin{align*}
y^{\prime }&=1+y+y^{2} \cos \left (t \right ) \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_Riccati] |
✓ |
✗ |
✗ |
24.337 |
|
| \(39\) |
\begin{align*}
y^{\prime }&={\mathrm e}^{-t^{2}}+y^{2} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_Riccati] |
✗ |
✗ |
✗ |
35.513 |
|
| \(40\) |
\begin{align*}
y^{\prime }&={\mathrm e}^{-t^{2}}+y^{2} \\
y \left (1\right ) &= 0 \\
\end{align*} |
[_Riccati] |
✗ |
✗ |
✗ |
31.097 |
|
| \(41\) |
\begin{align*}
y^{\prime }&={\mathrm e}^{-t^{2}}+y^{2} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_Riccati] |
✗ |
✗ |
✗ |
32.331 |
|
| \(42\) |
\begin{align*}
y^{\prime }&=y+{\mathrm e}^{-y}+{\mathrm e}^{-t} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
5.938 |
|
| \(43\) |
\begin{align*}
y^{\prime }&=y^{3}+{\mathrm e}^{-5 t} \\
y \left (0\right ) &= {\frac {2}{5}} \\
\end{align*} |
[_Abel] |
✗ |
✗ |
✗ |
5.554 |
|
| \(44\) |
\begin{align*}
y^{\prime }&=\left (4 y+{\mathrm e}^{-t^{2}}\right ) {\mathrm e}^{2 y} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
6.049 |
|
| \(45\) |
\begin{align*}
y^{\prime }&={\mathrm e}^{-t}+\ln \left (1+y^{2}\right ) \\
y \left (0\right ) &= 0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
2.772 |
|
| \(46\) |
\begin{align*}
t \left (-2+t \right )^{2} y^{\prime \prime }+y^{\prime } t +y&=0 \\
\end{align*} Series expansion around \(t=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
0.217 |
|
| \(47\) |
\begin{align*}
\left (-t^{2}+1\right ) y^{\prime \prime }+\frac {y^{\prime }}{\sin \left (1+t \right )}+y&=0 \\
\end{align*} Series expansion around \(t=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
0.594 |
|
| \(48\) |
\begin{align*}
t^{3} y^{\prime \prime }-y^{\prime } t -\left (t^{2}+\frac {5}{4}\right ) y&=0 \\
\end{align*} Series expansion around \(t=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
0.126 |
|
| \(49\) |
\begin{align*}
2 t \cos \left (y\right )+3 t^{2} y+\left (2 y+2 t^{2}\right ) y^{\prime }&=0 \\
y \left (0\right ) &= 1 \\
\end{align*} |
[‘x=_G(y,y’)‘] |
✗ |
✗ |
✗ |
64.770 |
|
| \(50\) |
\begin{align*}
y^{\prime }&=t^{2}+y^{2} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[[_Riccati, _special]] |
✓ |
✓ |
✗ |
16.082 |
|
| \(51\) |
\begin{align*}
y^{\prime }&=1+y+y^{2} \cos \left (t \right ) \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_Riccati] |
✓ |
✗ |
✗ |
18.382 |
|
| \(52\) |
\begin{align*}
y^{\prime }&={\mathrm e}^{-t^{2}}+y^{2} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_Riccati] |
✗ |
✗ |
✗ |
29.951 |
|
| \(53\) |
\begin{align*}
y^{\prime }&={\mathrm e}^{-t^{2}}+y^{2} \\
y \left (1\right ) &= 0 \\
\end{align*} |
[_Riccati] |
✗ |
✗ |
✗ |
32.087 |
|
| \(54\) |
\begin{align*}
y^{\prime }&={\mathrm e}^{-t^{2}}+y^{2} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_Riccati] |
✗ |
✗ |
✗ |
33.151 |
|
| \(55\) |
\begin{align*}
y^{\prime }&=y+{\mathrm e}^{-y}+{\mathrm e}^{-t} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
6.067 |
|
| \(56\) |
\begin{align*}
y^{\prime }&=y^{3}+{\mathrm e}^{-5 t} \\
y \left (0\right ) &= {\frac {2}{5}} \\
\end{align*} |
[_Abel] |
✗ |
✗ |
✗ |
6.114 |
|
| \(57\) |
\begin{align*}
y^{\prime }&=\left (4 y+{\mathrm e}^{-t^{2}}\right ) {\mathrm e}^{2 y} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
6.433 |
|
| \(58\) |
\begin{align*}
y^{\prime }&={\mathrm e}^{-t}+\ln \left (1+y^{2}\right ) \\
y \left (0\right ) &= 0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
2.132 |
|
| \(59\) |
\begin{align*}
y^{\prime }&=y+{\mathrm e}^{-y}+2 t \\
y \left (0\right ) &= 0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
11.360 |
|
| \(60\) |
\begin{align*}
y^{\prime }&=\frac {t^{2}+y^{2}}{1+t +y^{2}} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_rational] |
✗ |
✗ |
✗ |
3.444 |
|
| \(61\) |
\begin{align*}
y^{\prime \prime }+p \left (t \right ) y^{\prime }+q \left (t \right ) y&=1+t \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
✗ |
✗ |
39.877 |
|
| \(62\) |
\begin{align*}
t \left (-2+t \right )^{2} y^{\prime \prime }+y^{\prime } t +y&=0 \\
\end{align*} Series expansion around \(t=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
0.443 |
|
| \(63\) |
\begin{align*}
\left (-t^{2}+1\right ) y^{\prime \prime }+\frac {y^{\prime }}{\sin \left (1+t \right )}+y&=0 \\
\end{align*} Series expansion around \(t=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
0.477 |
|
| \(64\) |
\begin{align*}
t^{2} y^{\prime \prime }+\left (-t^{2}+1\right ) y^{\prime }+4 t y&=0 \\
\end{align*} Series expansion around \(t=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
0.113 |
|
| \(65\) |
\begin{align*}
x^{\prime }&=x-x^{2}-2 x y \\
y^{\prime }&=2 y-2 y^{2}-3 x y \\
\end{align*} |
system_of_ODEs |
✗ |
✗ |
✗ |
0.037 |
|
| \(66\) |
\begin{align*}
x^{\prime }&=-b x y+m \\
y^{\prime }&=b x y-g y \\
\end{align*} |
system_of_ODEs |
✗ |
✗ |
✗ |
0.063 |
|
| \(67\) |
\begin{align*}
x^{\prime }&=a x-b x y \\
y^{\prime }&=-c y+d x y \\
z^{\prime }&=z+x^{2}+y^{2} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.049 |
|
| \(68\) |
\begin{align*}
x^{\prime }&=-x-x \,y^{2} \\
y^{\prime }&=-y-y \,x^{2} \\
z^{\prime }&=1-z+x^{2} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.044 |
|
| \(69\) |
\begin{align*}
x^{\prime }&=x \,y^{2}-x \\
y^{\prime }&=x \sin \left (\pi y\right ) \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.034 |
|
| \(70\) |
\begin{align*}
x^{\prime }&=\cos \left (y\right ) \\
y^{\prime }&=\sin \left (x\right )-1 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.035 |
|
| \(71\) |
\begin{align*}
x^{\prime }&=-1-y-{\mathrm e}^{x} \\
y^{\prime }&=x^{2}+y \left ({\mathrm e}^{x}-1\right ) \\
z^{\prime }&=x+\sin \left (z\right ) \\
\end{align*} |
system_of_ODEs |
✗ |
✗ |
✗ |
0.047 |
|
| \(72\) |
\begin{align*}
x^{\prime }&=x-y^{2} \\
y^{\prime }&=x^{2}-y \\
z^{\prime }&={\mathrm e}^{z}-x \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.124 |
|
| \(73\) |
\begin{align*}
x_{1}^{\prime }&=x_{2} \\
x_{2}^{\prime }&=-\frac {\left (x_{1}^{2}+\sqrt {x_{1}^{2}+4 x_{2}^{2}}\right ) x_{1}}{2} \\
\end{align*} |
system_of_ODEs |
✗ |
✗ |
✗ |
0.037 |
|
| \(74\) |
\begin{align*}
x^{\prime }&=x-x^{3}-x y \\
y^{\prime }&=2 y-y^{5}-y \,x^{4} \\
\end{align*} |
system_of_ODEs |
✗ |
✗ |
✗ |
0.038 |
|
| \(75\) |
\begin{align*}
x^{\prime }&=x^{2}+y^{2}+1 \\
y^{\prime }&=x^{2}-y^{2} \\
\end{align*} |
system_of_ODEs |
✗ |
✗ |
✗ |
0.033 |
|
| \(76\) |
\begin{align*}
x^{\prime }&=x^{2}+y^{2}-1 \\
y^{\prime }&=2 x y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.037 |
|
| \(77\) |
\begin{align*}
x^{\prime }&=6 x-6 x^{2}-2 x y \\
y^{\prime }&=4 y-4 y^{2}-2 x y \\
\end{align*} |
system_of_ODEs |
✗ |
✗ |
✗ |
0.038 |
|
| \(78\) |
\begin{align*}
x^{\prime }&=\tan \left (x+y\right ) \\
y^{\prime }&=x+x^{3} \\
\end{align*} |
system_of_ODEs |
✗ |
✗ |
✗ |
0.073 |
|
| \(79\) |
\begin{align*}
x^{\prime }&={\mathrm e}^{y}-x \\
y^{\prime }&={\mathrm e}^{x}+y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.063 |
|
| \(80\) |
\begin{align*}
x y^{2}+2 y+\left (2 y^{3}-x^{2} y+2 x \right ) y^{\prime }&=0 \\
\end{align*} |
[_rational] |
✗ |
✗ |
✗ |
29.108 |
|
| \(81\) |
\begin{align*}
y-x^{2} \sqrt {x^{2}-y^{2}}-y^{\prime } x&=0 \\
y \left (1\right ) &= 1 \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✗ |
✗ |
✗ |
34.513 |
|
| \(82\) |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime }+y x&=x \left (-x^{2}+1\right ) \sqrt {y} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✗ |
39.015 |
|
| \(83\) |
\begin{align*}
1+\left (2 y-x^{2}\right ) {y^{\prime }}^{2}-2 x^{2} y {y^{\prime }}^{2}&=0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
19.492 |
|
| \(84\) |
\begin{align*}
x y {y^{\prime }}^{2}+\left (y x -1\right ) y^{\prime }&=y \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
78.325 |
|
| \(85\) |
\begin{align*}
x^{3} \left (x^{2}+3\right ) y^{\prime \prime }+5 y^{\prime } x -\left (x +1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
0.148 |
|
| \(86\) |
\begin{align*}
-\frac {{y^{\prime }}^{2}}{y^{2}}+\frac {y^{\prime \prime }}{y}+\frac {2 a \coth \left (2 a x \right ) y^{\prime }}{y}&=2 a^{2} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✗ |
6.792 |
|
| \(87\) |
\begin{align*}
2 y y^{\prime \prime \prime }+2 \left (y+3 y^{\prime }\right ) y^{\prime \prime }+2 {y^{\prime }}^{2}&=\sin \left (x \right ) \\
\end{align*} |
[[_3rd_order, _exact, _nonlinear]] |
✓ |
✓ |
✗ |
0.049 |
|
| \(88\) |
\begin{align*}
y^{\prime \prime }+\frac {y}{z^{3}}&=0 \\
\end{align*} Series expansion around \(z=0\). |
[[_Emden, _Fowler]] |
✗ |
✓ |
✗ |
0.094 |
|
| \(89\) |
\begin{align*}
y^{\prime }+p \left (x \right ) y+q \left (x \right ) y^{2}&=r \left (x \right ) \\
\end{align*} |
[_Riccati] |
✗ |
✗ |
✗ |
37.091 |
|
| \(90\) |
\begin{align*}
y \,{\mathrm e}^{y x}+\left (2 y-x \,{\mathrm e}^{y x}\right ) y^{\prime }&=0 \\
\end{align*} |
[‘x=_G(y,y’)‘] |
✗ |
✗ |
✗ |
4.108 |
|
| \(91\) |
\begin{align*}
x_{1}^{\prime }&=-\tan \left (t \right ) x_{1}+3 \cos \left (t \right )^{2} \\
x_{2}^{\prime }&=x_{1}+\tan \left (t \right ) x_{2}+2 \sin \left (t \right ) \\
\end{align*} With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 4 \\
x_{2} \left (0\right ) &= 0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.056 |
|
| \(92\) |
\begin{align*}
x_{1}^{\prime }&=\frac {x_{1}}{t} \\
x_{2}^{\prime }&=x_{2} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.037 |
|
| \(93\) |
\begin{align*}
x_{1}^{\prime }&=\frac {x_{1}}{t}+t x_{2} \\
x_{2}^{\prime }&=-\frac {x_{1}}{t} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.076 |
|
| \(94\) |
\begin{align*}
x_{1}^{\prime }&=\left (2 t -1\right ) x_{1} \\
x_{2}^{\prime }&={\mathrm e}^{-t^{2}+t} x_{1}+x_{2} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.072 |
|
| \(95\) |
\begin{align*}
x_{1}^{\prime }&=t \cot \left (t^{2}\right ) x_{1}+\frac {t \cos \left (t^{2}\right ) x_{3}}{2} \\
x_{2}^{\prime }&=\frac {x_{2}}{t}-x_{3}+2-t \sin \left (t \right ) \\
x_{3}^{\prime }&=\csc \left (t^{2}\right ) x_{1}+x_{2}-x_{3}+1-t \cos \left (t \right ) \\
\end{align*} |
system_of_ODEs |
✗ |
✗ |
✗ |
0.064 |
|
| \(96\) |
\begin{align*}
y^{\prime \prime }+\frac {2 y^{\prime }}{x \left (x -3\right )}-\frac {y}{x^{3} \left (x +3\right )}&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
0.127 |
|
| \(97\) |
\begin{align*}
y^{2} \left (x^{2}+1\right )+y+\left (2 y x +1\right ) y^{\prime }&=0 \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
23.108 |
|
| \(98\) |
\begin{align*}
2 y^{2}-4 x +5&=\left (4-2 y+4 y x \right ) y^{\prime } \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
32.527 |
|
| \(99\) |
\begin{align*}
x^{2}+y^{3}+y+\left (x^{3}+y^{2}-x \right ) y^{\prime }&=0 \\
\end{align*} |
[_rational] |
✗ |
✗ |
✗ |
4.329 |
|
| \(100\) |
\begin{align*}
x^{\prime \prime }+x^{\prime }+y^{\prime }-2 y&=0 \\
x^{\prime }+x-y^{\prime }&=0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.046 |
|
| \(101\) |
\begin{align*}
x^{\prime \prime }-3 x-4 y&=0 \\
x+y^{\prime \prime }+y&=0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.036 |
|
| \(102\) |
\begin{align*}
x^{\prime }+4 x+2 y&=\frac {2}{{\mathrm e}^{t}-1} \\
6 x-y^{\prime }+3 y&=\frac {3}{{\mathrm e}^{t}-1} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.045 |
|
| \(103\) |
\begin{align*}
x^{\prime \prime }+x^{\prime }+y^{\prime }-2 y&=40 \,{\mathrm e}^{3 t} \\
x^{\prime }+x-y^{\prime }&=36 \,{\mathrm e}^{t} \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 3 \\
x^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.033 |
|
| \(104\) |
\begin{align*}
x^{\prime \prime }+2 x-2 y^{\prime }&=0 \\
3 x^{\prime }+y^{\prime \prime }-8 y&=240 \,{\mathrm e}^{t} \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.029 |
|
| \(105\) |
\begin{align*}
x_{1}^{\prime }&=-x_{1}+2 x_{2} \\
x_{2}^{\prime }&=-3 x_{1}+4 x_{2}+\frac {{\mathrm e}^{3 t}}{1+{\mathrm e}^{2 t}} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.044 |
|
| \(106\) |
\begin{align*}
x_{1}^{\prime }&=-4 x_{1}-2 x_{2}+\frac {2}{{\mathrm e}^{t}-1} \\
x_{2}^{\prime }&=6 x_{1}+3 x_{2}-\frac {3}{{\mathrm e}^{t}-1} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.050 |
|
| \(107\) |
\begin{align*}
y^{\prime }&=f \left (x \right )+a y+b y^{2} \\
\end{align*} |
[_Riccati] |
✗ |
✗ |
✗ |
8.082 |
|
| \(108\) |
\begin{align*}
y^{\prime }&=f \left (x \right )+g \left (x \right ) y+a y^{2} \\
\end{align*} |
[_Riccati] |
✗ |
✗ |
✗ |
9.877 |
|
| \(109\) |
\begin{align*}
y^{\prime }&=f \left (x \right )+g \left (x \right ) y+h \left (x \right ) y^{2} \\
\end{align*} |
[_Riccati] |
✗ |
✗ |
✗ |
20.739 |
|
| \(110\) |
\begin{align*}
y^{\prime }+\left (a x +y\right ) y^{2}&=0 \\
\end{align*} |
[_Abel] |
✓ |
✓ |
✗ |
11.542 |
|
| \(111\) |
\begin{align*}
y^{\prime }&=\left (a \,{\mathrm e}^{x}+y\right ) y^{2} \\
\end{align*} |
[_Abel] |
✓ |
✓ |
✗ |
9.601 |
|
| \(112\) |
\begin{align*}
y^{\prime }+3 a \left (2 x +y\right ) y^{2}&=0 \\
\end{align*} |
[_Abel] |
✓ |
✓ |
✗ |
12.080 |
|
| \(113\) |
\begin{align*}
y^{\prime }&=f \left (x \right )+g \left (x \right ) y+h \left (x \right ) y^{n} \\
\end{align*} |
[_Chini] |
✗ |
✗ |
✗ |
4.914 |
|
| \(114\) |
\begin{align*}
y^{\prime }&=\tan \left (x \right ) \left (\tan \left (y\right )+\sec \left (x \right ) \sec \left (y\right )\right ) \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✓ |
11.228 |
|
| \(115\) |
\begin{align*}
y^{\prime }&=\left (1+\cos \left (x \right ) \sin \left (y\right )\right ) \tan \left (y\right ) \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✓ |
✓ |
8.635 |
|
| \(116\) |
\begin{align*}
y^{\prime }&=x^{m -1} y^{1-n} f \left (a \,x^{m}+b y^{n}\right ) \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
✗ |
11.283 |
|
| \(117\) |
\begin{align*}
2 y^{\prime }&=2 \sin \left (y\right )^{2} \tan \left (y\right )-x \sin \left (2 y\right ) \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✓ |
✗ |
55.503 |
|
| \(118\) |
\begin{align*}
y^{\prime } x&=y-x \left (x -y\right ) \sqrt {x^{2}+y^{2}} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✗ |
13.752 |
|
| \(119\) |
\begin{align*}
y^{\prime } x&=\sin \left (x -y\right ) \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
348.601 |
|
| \(120\) |
\begin{align*}
y^{\prime } x +n y&=f \left (x \right ) g \left (x^{n} y\right ) \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✗ |
5.192 |
|
| \(121\) |
\begin{align*}
x^{2} y^{\prime }&=a \,x^{2} y^{2}-a y^{3} \\
\end{align*} |
[_rational, _Abel] |
✓ |
✓ |
✗ |
3.073 |
|
| \(122\) |
\begin{align*}
x^{2} y^{\prime }+a y^{2}+b \,x^{2} y^{3}&=0 \\
\end{align*} |
[_rational, _Abel] |
✓ |
✓ |
✗ |
4.345 |
|
| \(123\) |
\begin{align*}
x^{2} y^{\prime }&=\sec \left (y\right )+3 x \tan \left (y\right ) \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✗ |
16.397 |
|
| \(124\) |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime }&=n \left (1-2 y x +y^{2}\right ) \\
\end{align*} |
[_rational, _Riccati] |
✓ |
✓ |
✗ |
3.912 |
|
| \(125\) |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime }&=1+y^{2}-2 x y \left (1+y^{2}\right ) \\
\end{align*} |
[_rational, _Abel] |
✓ |
✓ |
✗ |
50.275 |
|
| \(126\) |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime }+x \sin \left (y\right ) \cos \left (y\right )&=x \left (x^{2}+1\right ) \cos \left (y\right )^{2} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✗ |
29.431 |
|
| \(127\) |
\begin{align*}
\left (b x +a \right )^{2} y^{\prime }+c y^{2}+\left (b x +a \right ) y^{3}&=0 \\
\end{align*} |
[_rational, _Abel] |
✓ |
✓ |
✗ |
16.318 |
|
| \(128\) |
\begin{align*}
x^{7} y^{\prime }+5 x^{3} y^{2}+2 \left (x^{2}+1\right ) y^{3}&=0 \\
\end{align*} |
[_rational, _Abel] |
✓ |
✓ |
✗ |
33.129 |
|
| \(129\) |
\begin{align*}
x^{k} y^{\prime }&=a \,x^{m}+b y^{n} \\
\end{align*} |
[_Chini] |
✗ |
✗ |
✗ |
3.085 |
|
| \(130\) |
\begin{align*}
y y^{\prime }+x^{3}+y&=0 \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
✗ |
✗ |
7.563 |
|
| \(131\) |
\begin{align*}
y y^{\prime }+f \left (x \right )&=g \left (x \right ) y \\
\end{align*} |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
✗ |
✗ |
8.970 |
|
| \(132\) |
\begin{align*}
y y^{\prime }+x +f \left (x^{2}+y^{2}\right ) g \left (x \right )&=0 \\
\end{align*} |
[NONE] |
✓ |
✓ |
✗ |
9.638 |
|
| \(133\) |
\begin{align*}
\left (x +4 x^{3}+5 y\right ) y^{\prime }+7 x^{3}+3 x^{2} y+4 y&=0 \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✗ |
25.069 |
|
| \(134\) |
\begin{align*}
x \left (a +y\right ) y^{\prime }+b x +c y&=0 \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
16.684 |
|
| \(135\) |
\begin{align*}
\left (a +x \left (x +y\right )\right ) y^{\prime }&=b \left (x +y\right ) y \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
28.648 |
|
| \(136\) |
\begin{align*}
\left (1-x^{2} y\right ) y^{\prime }-1+x y^{2}&=0 \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✗ |
61.339 |
|
| \(137\) |
\begin{align*}
x^{7} y y^{\prime }&=2 x^{2}+2+5 x^{3} y \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✗ |
31.460 |
|
| \(138\) |
\begin{align*}
\left (x +2 y+y^{2}\right ) y^{\prime }+y \left (1+y\right )+\left (x +y\right )^{2} y^{2}&=0 \\
\end{align*} |
[_rational] |
✓ |
✓ |
✗ |
7.292 |
|
| \(139\) |
\begin{align*}
\left (\cot \left (x \right )-2 y^{2}\right ) y^{\prime }&=y^{3} \csc \left (x \right ) \sec \left (x \right ) \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✗ |
47.950 |
|
| \(140\) |
\begin{align*}
\left (x^{2}-x^{3}+3 x y^{2}+2 y^{3}\right ) y^{\prime }+2 x^{3}+3 x^{2} y+y^{2}-y^{3}&=0 \\
\end{align*} |
[_rational] |
✓ |
✓ |
✗ |
5.737 |
|
| \(141\) |
\begin{align*}
f \left (x \right ) y^{m} y^{\prime }+g \left (x \right ) y^{m +1}+h \left (x \right ) y^{n}&=0 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✗ |
9.582 |
|
| \(142\) |
\begin{align*}
{y^{\prime }}^{2}&=f \left (x \right )^{2} \left (y-u \left (x \right )\right )^{2} \left (y-a \right ) \left (y-b \right ) \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
17.803 |
|
| \(143\) |
\begin{align*}
x^{2} {y^{\prime }}^{2}+x \left (x^{2}+y x -2 y\right ) y^{\prime }+\left (1-x \right ) \left (x^{2}-y\right ) y&=0 \\
\end{align*} |
[_rational] |
✗ |
✗ |
✗ |
77.511 |
|
| \(144\) |
\begin{align*}
x \left (-x^{2}+1\right ) {y^{\prime }}^{2}-2 \left (-x^{2}+1\right ) y y^{\prime }+x \left (1-y^{2}\right )&=0 \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✗ |
29.223 |
|
| \(145\) |
\begin{align*}
x y^{2} {y^{\prime }}^{2}+\left (a -x^{3}-y^{3}\right ) y^{\prime }+x^{2} y&=0 \\
\end{align*} |
[_rational] |
✓ |
✓ |
✗ |
213.986 |
|
| \(146\) |
\begin{align*}
x y^{2} {y^{\prime }}^{3}-y^{3} {y^{\prime }}^{2}+x \left (x^{2}+1\right ) y^{\prime }-x^{2} y&=0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✓ |
✗ |
497.112 |
|
| \(147\) |
\begin{align*}
{y^{\prime }}^{6}+f \left (x \right ) \left (y-a \right )^{4} \left (y-b \right )^{3}&=0 \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
34.794 |
|
| \(148\) |
\begin{align*}
{y^{\prime }}^{6}+f \left (x \right ) \left (y-a \right )^{5} \left (y-b \right )^{3}&=0 \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
37.089 |
|
| \(149\) |
\begin{align*}
{y^{\prime }}^{6}+f \left (x \right ) \left (y-a \right )^{5} \left (y-b \right )^{4}&=0 \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
37.614 |
|
| \(150\) |
\begin{align*}
x^{2} \left ({y^{\prime }}^{6}+3 y^{4}+3 y^{2}+1\right )&=a^{2} \\
\end{align*} |
[_rational] |
✗ |
✗ |
✗ |
1.040 |
|
| \(151\) |
\begin{align*}
\left (x^{2}+a \right ) y+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
5.365 |
|
| \(152\) |
\begin{align*}
\left (-x^{2}+a \right ) y+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
5.084 |
|
| \(153\) |
\begin{align*}
y^{\prime \prime }&=\left (x^{2}+a \right ) y \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
4.933 |
|
| \(154\) |
\begin{align*}
\left (b^{2} x^{2}+a \right ) y+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
5.356 |
|
| \(155\) |
\begin{align*}
\left (c \,x^{2}+b x +a \right ) y+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
4.262 |
|
| \(156\) |
\begin{align*}
\left (x^{4}+\operatorname {a1} \,x^{2}+\operatorname {a0} \right ) y+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
19.668 |
|
| \(157\) |
\begin{align*}
\left (a +b \cos \left (2 x \right )\right ) y+y^{\prime \prime }&=0 \\
\end{align*} |
[_ellipsoidal] |
✓ |
✓ |
✗ |
5.710 |
|
| \(158\) |
\begin{align*}
\left (a +b \cos \left (2 x \right )+k \cos \left (4 x \right )\right ) y+y^{\prime \prime }&=0 \\
\end{align*} |
[_ellipsoidal] |
✓ |
✗ |
✗ |
8.223 |
|
| \(159\) |
\begin{align*}
a \csc \left (x \right )^{2} y+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
6.779 |
|
| \(160\) |
\begin{align*}
\left (\operatorname {a0} +\operatorname {a1} \cos \left (x \right )^{2}+\operatorname {a2} \csc \left (x \right )^{2}\right ) y+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✗ |
✗ |
9.695 |
|
| \(161\) |
\begin{align*}
y^{\prime \prime }&=\left (a^{2}+\left (-1+p \right ) p \csc \left (x \right )^{2}+\left (-1+q \right ) q \sec \left (x \right )^{2}\right ) y \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
10.684 |
|
| \(162\) |
\begin{align*}
\left (a +b \sin \left (x \right )^{2}\right ) y+y^{\prime \prime }&=0 \\
\end{align*} |
[_ellipsoidal] |
✓ |
✓ |
✗ |
6.036 |
|
| \(163\) |
\begin{align*}
\left (a +b \,{\mathrm e}^{x}+c \,{\mathrm e}^{2 x}\right ) y+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
2.655 |
|
| \(164\) |
\begin{align*}
\left (a +b \cosh \left (x \right )^{2}\right ) y+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
6.556 |
|
| \(165\) |
\begin{align*}
\left (a +b \sinh \left (x \right )^{2}\right ) y+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
7.217 |
|
| \(166\) |
\begin{align*}
\left (a +b \sin \left (x \right )^{2}\right ) y+y^{\prime \prime }&=0 \\
\end{align*} |
[_ellipsoidal] |
✓ |
✓ |
✗ |
5.674 |
|
| \(167\) |
\begin{align*}
\left (c \,x^{2}+b \right ) y+a y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
9.474 |
|
| \(168\) |
\begin{align*}
n y-y^{\prime } x +y^{\prime \prime }&=0 \\
\end{align*} |
[_Hermite] |
✓ |
✓ |
✗ |
9.259 |
|
| \(169\) |
\begin{align*}
-a y-y^{\prime } x +y^{\prime \prime }&=0 \\
\end{align*} |
[_Hermite] |
✓ |
✓ |
✗ |
6.885 |
|
| \(170\) |
\begin{align*}
2 n y-2 y^{\prime } x +y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
9.250 |
|
| \(171\) |
\begin{align*}
b y+a x y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
9.708 |
|
| \(172\) |
\begin{align*}
c y+\left (b x +a \right ) y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
9.135 |
|
| \(173\) |
\begin{align*}
\left (\operatorname {b1} x +\operatorname {a1} \right ) y+\left (\operatorname {b0} x +\operatorname {a0} \right ) y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
10.579 |
|
| \(174\) |
\begin{align*}
\left (\operatorname {c1} \,x^{2}+\operatorname {b1} x +\operatorname {a1} \right ) y+\left (\operatorname {b0} x +\operatorname {a0} \right ) y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
10.910 |
|
| \(175\) |
\begin{align*}
b \,x^{-1+k} y+a \,x^{k} y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
8.335 |
|
| \(176\) |
\begin{align*}
k \left (1+k \right ) y+\cot \left (x \right ) y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
7.634 |
|
| \(177\) |
\begin{align*}
\left (p \left (1+p \right )-k^{2} \csc \left (x \right )^{2}\right ) y+\cot \left (x \right ) y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
9.144 |
|
| \(178\) |
\begin{align*}
\left (\operatorname {a0} -\operatorname {a2} \csc \left (x \right )^{2}+4 \operatorname {a1} \sin \left (x \right )^{2}\right ) y+\cot \left (x \right ) y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
13.671 |
|
| \(179\) |
\begin{align*}
\left (b +k^{2} \cos \left (x \right )^{2}\right ) y+a \cot \left (x \right ) y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✗ |
✗ |
10.846 |
|
| \(180\) |
\begin{align*}
\left (a \cot \left (x \right )^{2}+b \cot \left (x \right ) \csc \left (x \right )+c \csc \left (x \right )^{2}\right ) y+k \cot \left (x \right ) y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
9.885 |
|
| \(181\) |
\begin{align*}
c y+a \cot \left (b x \right ) y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✗ |
✗ |
23.900 |
|
| \(182\) |
\begin{align*}
\csc \left (x \right )^{2} \left (2+\sin \left (x \right )^{2}\right ) y-\csc \left (2 x \right ) y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
128.109 |
|
| \(183\) |
\begin{align*}
-a \left (1+a \right ) \csc \left (x \right )^{2} y-\tan \left (x \right ) y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
11.252 |
|
| \(184\) |
\begin{align*}
b y+a \tan \left (x \right ) y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
10.124 |
|
| \(185\) |
\begin{align*}
\left (\operatorname {a0} -\operatorname {a2} \operatorname {csch}\left (x \right )^{2}+4 \operatorname {a1} \sinh \left (x \right )^{2}\right ) y+\coth \left (x \right ) y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✗ |
✗ |
55.243 |
|
| \(186\) |
\begin{align*}
\left (\operatorname {a0} +4 \operatorname {a1} \cosh \left (x \right )^{2}-\operatorname {a2} \operatorname {sech}\left (x \right )^{2}\right ) y+\tanh \left (x \right ) y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✗ |
✗ |
46.343 |
|
| \(187\) |
\begin{align*}
b y+a \tanh \left (x \right ) y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
18.457 |
|
| \(188\) |
\begin{align*}
a k \,x^{-1+k} y+2 a \,x^{k} y^{\prime }+2 y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
6.545 |
|
| \(189\) |
\begin{align*}
4 y^{\prime \prime }&=\left (x^{2}+a \right ) y \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
5.629 |
|
| \(190\) |
\begin{align*}
\left (-x^{2}+4 a +2\right ) y+4 y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
5.947 |
|
| \(191\) |
\begin{align*}
\left (a +x \right ) y+y^{\prime \prime } x&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
4.509 |
|
| \(192\) |
\begin{align*}
\left ({\mathrm e}^{x^{2}}-k^{2}\right ) x^{3} y-y^{\prime }+y^{\prime \prime } x&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
9.747 |
|
| \(193\) |
\begin{align*}
y+\left (1+a \right ) y^{\prime }+y^{\prime \prime } x&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✗ |
8.303 |
|
| \(194\) |
\begin{align*}
y+\left (1-a \right ) y^{\prime }+y^{\prime \prime } x&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✗ |
8.190 |
|
| \(195\) |
\begin{align*}
-y+\left (1+a \right ) y^{\prime }+y^{\prime \prime } x&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✗ |
6.313 |
|
| \(196\) |
\begin{align*}
\left (\operatorname {b2} x +\operatorname {b1} \right ) y+a y^{\prime }+y^{\prime \prime } x&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
11.302 |
|
| \(197\) |
\begin{align*}
\left (\operatorname {c1} \,x^{2}+\operatorname {b1} x +\operatorname {a1} \right ) y+a y^{\prime }+y^{\prime \prime } x&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
7.786 |
|
| \(198\) |
\begin{align*}
n y+\left (1-x \right ) y^{\prime }+y^{\prime \prime } x&=0 \\
\end{align*} |
[_Laguerre] |
✓ |
✓ |
✗ |
9.962 |
|
| \(199\) |
\begin{align*}
n y+\left (1+k -x \right ) y^{\prime }+y^{\prime \prime } x&=0 \\
\end{align*} |
[_Laguerre] |
✓ |
✓ |
✗ |
11.898 |
|
| \(200\) |
\begin{align*}
b y+\left (a +x \right ) y^{\prime }+y^{\prime \prime } x&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
11.588 |
|
| \(201\) |
\begin{align*}
-a y+\left (c -x \right ) y^{\prime }+y^{\prime \prime } x&=0 \\
\end{align*} |
[_Laguerre] |
✓ |
✓ |
✗ |
11.454 |
|
| \(202\) |
\begin{align*}
c y+\left (b x +a \right ) y^{\prime }+y^{\prime \prime } x&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
12.303 |
|
| \(203\) |
\begin{align*}
\left (\operatorname {b2} x +\operatorname {a2} \right ) y+\left (\operatorname {b1} x +\operatorname {a1} \right ) y^{\prime }+y^{\prime \prime } x&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
13.539 |
|
| \(204\) |
\begin{align*}
\left (b x +2 a \right ) y-2 \left (b x +a \right ) y^{\prime }+y^{\prime \prime } x&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
13.365 |
|
| \(205\) |
\begin{align*}
\left (a b x +a n +b m \right ) y+\left (m +n +\left (a +b \right ) x \right ) y^{\prime }+y^{\prime \prime } x&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
16.466 |
|
| \(206\) |
\begin{align*}
\left (\operatorname {b2} x +\operatorname {a2} \right ) y+\left (\operatorname {b1} x +\operatorname {a1} \right ) y^{\prime }+\left (a +x \right ) y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
37.574 |
|
| \(207\) |
\begin{align*}
\left (b x +a \right ) y+y^{\prime }+2 y^{\prime \prime } x&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
12.108 |
|
| \(208\) |
\begin{align*}
y+4 \coth \left (x \right ) y^{\prime }+4 y^{\prime \prime } x&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✗ |
✗ |
✗ |
56.562 |
|
| \(209\) |
\begin{align*}
\left (b x +a \right ) y+8 y^{\prime }+16 y^{\prime \prime } x&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
9.319 |
|
| \(210\) |
\begin{align*}
\left (\operatorname {b2} x +\operatorname {a2} \right ) y+\left (\operatorname {b1} x +\operatorname {a1} \right ) y^{\prime }+\left (\operatorname {b0} x +\operatorname {a0} \right ) y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
43.325 |
|
| \(211\) |
\begin{align*}
\left (c \,x^{2}+b x +a \right ) y+x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
6.598 |
|
| \(212\) |
\begin{align*}
x^{k} \left (a +b \,x^{k}\right ) y+x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
3.408 |
|
| \(213\) |
\begin{align*}
-\left (c \,x^{2}+b x +a \right ) y+y^{\prime } x +x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
39.572 |
|
| \(214\) |
\begin{align*}
-\left (-x^{4}+4 a \,x^{2}+n^{2}\right ) y+y^{\prime } x +x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
61.727 |
|
| \(215\) |
\begin{align*}
-\left (c^{2} x^{4}+b^{2} x^{2}+a^{2}\right ) y+y^{\prime } x +x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
39.898 |
|
| \(216\) |
\begin{align*}
\left (m +1\right ) x^{m} a \left (m \right ) y+y^{\prime } x +x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
32.151 |
|
| \(217\) |
\begin{align*}
a y-2 \left (1-x \right ) y^{\prime }+x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
39.863 |
|
| \(218\) |
\begin{align*}
\left (\operatorname {c2} \,x^{2}+\operatorname {b2} x +\operatorname {a2} \right ) y+\operatorname {a1} x y^{\prime }+x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
29.509 |
|
| \(219\) |
\begin{align*}
x^{2} \left (\operatorname {b1} \,x^{2}+\operatorname {a1} \right ) y+a x y^{\prime }+x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
31.824 |
|
| \(220\) |
\begin{align*}
c y+\left (b x +a \right ) y^{\prime }+x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
32.496 |
|
| \(221\) |
\begin{align*}
\left (b \,x^{2}+a \right ) y+x^{2} y^{\prime }+x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
11.484 |
|
| \(222\) |
\begin{align*}
-y+x \left (x +3\right ) y^{\prime }+x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
35.107 |
|
| \(223\) |
\begin{align*}
\left (\operatorname {c2} \,x^{2}+\operatorname {b2} x +\operatorname {a2} \right ) y+x \left (\operatorname {b1} x +\operatorname {a1} \right ) y^{\prime }+x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
35.086 |
|
| \(224\) |
\begin{align*}
\left (\operatorname {a1} +\operatorname {b1} \,x^{k}+\operatorname {c1} \,x^{2 k}\right ) y+x \left (\operatorname {a0} +\operatorname {b0} \,x^{k}\right ) y^{\prime }+x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
47.306 |
|
| \(225\) |
\begin{align*}
a y+2 x^{2} \cot \left (x \right ) y^{\prime }+x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
7.813 |
|
| \(226\) |
\begin{align*}
-\left (a -x \cot \left (x \right )\right ) y+x \left (1+2 x \cot \left (x \right )\right ) y^{\prime }+x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
42.294 |
|
| \(227\) |
\begin{align*}
a y-2 x^{2} \tan \left (x \right ) y^{\prime }+x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
8.558 |
|
| \(228\) |
\begin{align*}
-\left (a +x \tan \left (x \right )\right ) y+x \left (1-2 x \tan \left (x \right )\right ) y^{\prime }+x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
26.123 |
|
| \(229\) |
\begin{align*}
y \left (\operatorname {a2} +\operatorname {b2} \,x^{k}+\operatorname {c2} \,x^{2 k}+\left (-1+\operatorname {a1} +\operatorname {b1} \,x^{k}\right ) f \left (x \right )+f \left (x \right )^{2}+f^{\prime }\left (x \right )\right )+x \left (\operatorname {a1} +\operatorname {b1} \,x^{k}+2 f \left (x \right )\right ) y^{\prime }+x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
87.694 |
|
| \(230\) |
\begin{align*}
\left (b \,x^{2}+a \right ) y-y^{\prime } x +\left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
55.470 |
|
| \(231\) |
\begin{align*}
n \left (n +1\right ) y-2 y^{\prime } x +\left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
[_Gegenbauer] |
✓ |
✓ |
✗ |
119.397 |
|
| \(232\) |
\begin{align*}
n \left (n +1\right ) y-2 y^{\prime } x +\left (-x^{2}+1\right ) y^{\prime \prime }&=\frac {2 \left (-1-n \right ) x \operatorname {LegendreP}\left (n , x\right )+2 \left (n +1\right ) \operatorname {LegendreP}\left (n +1, x\right )}{x^{2}-1} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✗ |
100.523 |
|
| \(233\) |
\begin{align*}
-p \left (1+p \right ) y+2 y^{\prime } x +\left (x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
56.213 |
|
| \(234\) |
\begin{align*}
p \left (1+p \right ) y-2 y^{\prime } x +\left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
[_Gegenbauer] |
✓ |
✓ |
✗ |
93.210 |
|
| \(235\) |
\begin{align*}
n \left (1+a +b +n \right ) y+\left (-a +b -\left (2+a +b \right ) x \right ) y^{\prime }+\left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
155.711 |
|
| \(236\) |
\begin{align*}
p \left (2 k +p \right ) y-\left (1+2 k \right ) x y^{\prime }+\left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
[_Gegenbauer] |
✓ |
✓ |
✗ |
85.859 |
|
| \(237\) |
\begin{align*}
p \left (1+2 k +p \right ) y-2 \left (1+k \right ) x y^{\prime }+\left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
[_Gegenbauer] |
✓ |
✓ |
✗ |
88.786 |
|
| \(238\) |
\begin{align*}
-\left (k -p \right ) \left (1+k +p \right ) y-2 \left (1+k \right ) x y^{\prime }+\left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
[_Gegenbauer] |
✓ |
✓ |
✗ |
66.722 |
|
| \(239\) |
\begin{align*}
b y+a x y^{\prime }+\left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
[_Gegenbauer] |
✓ |
✓ |
✗ |
120.460 |
|
| \(240\) |
\begin{align*}
\left (\operatorname {c0} \,x^{2}+\operatorname {b0} x +\operatorname {a0} \right ) y+a x y^{\prime }+\left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
64.362 |
|
| \(241\) |
\begin{align*}
c y+\left (b x +a \right ) y^{\prime }+\left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
149.006 |
|
| \(242\) |
\begin{align*}
\left (c^{2} x^{2}+b^{2}\right ) y-y^{\prime } x +\left (a^{2}-x^{2}\right ) y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
81.515 |
|
| \(243\) |
\begin{align*}
y+2 y^{\prime }+\left (1-x \right ) x y^{\prime \prime }&=0 \\
\end{align*} |
[_Jacobi] |
✓ |
✓ |
✗ |
41.931 |
|
| \(244\) |
\begin{align*}
p \left (1+p \right ) y+\left (1-2 x \right ) y^{\prime }+\left (1-x \right ) x y^{\prime \prime }&=0 \\
\end{align*} |
[_Jacobi] |
✓ |
✓ |
✗ |
62.126 |
|
| \(245\) |
\begin{align*}
2 y+\left (1-x \right ) y^{\prime }+\left (1-x \right ) x y^{\prime \prime }&=0 \\
\end{align*} |
[_Jacobi] |
✓ |
✓ |
✗ |
71.779 |
|
| \(246\) |
\begin{align*}
\left (-k +p \right ) \left (1+k +p \right ) y+\left (1+k \right ) \left (1-2 x \right ) y^{\prime }+\left (1-x \right ) x y^{\prime \prime }&=0 \\
\end{align*} |
[_Jacobi] |
✓ |
✓ |
✗ |
127.283 |
|
| \(247\) |
\begin{align*}
n \left (a +n \right ) y+\left (c -\left (1+a \right ) x \right ) y^{\prime }+\left (1-x \right ) x y^{\prime \prime }&=0 \\
\end{align*} |
[_Jacobi] |
✓ |
✓ |
✗ |
139.115 |
|
| \(248\) |
\begin{align*}
c y+\left (b x +a \right ) y^{\prime }+x \left (x +1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
108.114 |
|
| \(249\) |
\begin{align*}
-a b y+\left (c -\left (a +b +1\right ) x \right ) y^{\prime }+\left (1-x \right ) x y^{\prime \prime }&=0 \\
\end{align*} |
[_Jacobi] |
✓ |
✓ |
✗ |
170.306 |
|
| \(250\) |
\begin{align*}
c y+\left (b x +a \right ) y^{\prime }+\left (1-x \right ) x y^{\prime \prime }&=0 \\
\end{align*} |
[_Jacobi] |
✓ |
✓ |
✗ |
110.605 |
|
| \(251\) |
\begin{align*}
\operatorname {a2} y+\left (\operatorname {b1} x +\operatorname {a1} \right ) y^{\prime }+x \left (\operatorname {a0} +x \right ) y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
37.071 |
|
| \(252\) |
\begin{align*}
2 a^{2} y-y^{\prime } x +2 \left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
93.423 |
|
| \(253\) |
\begin{align*}
a y-\left (1-2 x \right ) y^{\prime }+2 \left (1-x \right ) x y^{\prime \prime }&=0 \\
\end{align*} |
[_Jacobi] |
✓ |
✓ |
✗ |
178.493 |
|
| \(254\) |
\begin{align*}
\left (b x +a \right ) y+\left (1-2 x \right ) y^{\prime }+2 \left (1-x \right ) x y^{\prime \prime }&=0 \\
\end{align*} |
[_Jacobi] |
✓ |
✓ |
✗ |
92.082 |
|
| \(255\) |
\begin{align*}
2 a \left (1+a \right ) y-\left (1+3 x \right ) y^{\prime }+2 \left (1-x \right ) x y^{\prime \prime }&=0 \\
\end{align*} |
[_Jacobi] |
✓ |
✓ |
✗ |
93.892 |
|
| \(256\) |
\begin{align*}
\left (4 k x -4 p^{2}-x^{2}+1\right ) y+4 x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
6.304 |
|
| \(257\) |
\begin{align*}
-y-8 y^{\prime } x +4 \left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
49.908 |
|
| \(258\) |
\begin{align*}
-\left (4 p^{2}+1\right ) y-8 y^{\prime } x +4 \left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
73.475 |
|
| \(259\) |
\begin{align*}
y+2 \left (1-x \right ) y^{\prime }+4 \left (1-x \right ) x y^{\prime \prime }&=0 \\
\end{align*} |
[_Jacobi] |
✓ |
✓ |
✗ |
54.642 |
|
| \(260\) |
\begin{align*}
\left (b x +a \right ) y+2 \left (1-2 x \right ) y^{\prime }+4 \left (1-x \right ) x y^{\prime \prime }&=0 \\
\end{align*} |
[_Jacobi] |
✓ |
✗ |
✗ |
68.017 |
|
| \(261\) |
\begin{align*}
\left (c \,x^{2}+b x +a \right ) y+2 \left (1-2 x \right ) y^{\prime }+4 \left (1-x \right ) x y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✗ |
✗ |
55.786 |
|
| \(262\) |
\begin{align*}
-\left (k -p \right ) \left (1+k +p \right ) y+2 \left (1-\left (3-2 k \right ) x \right ) y^{\prime }+4 \left (1-x \right ) x y^{\prime \prime }&=0 \\
\end{align*} |
[_Jacobi] |
✓ |
✓ |
✗ |
147.464 |
|
| \(263\) |
\begin{align*}
\left (k^{2} x +b \right ) y+2 \left (a x +1\right ) y^{\prime }+4 \left (1-x \right ) x y^{\prime \prime }&=0 \\
\end{align*} |
[_Jacobi] |
✓ |
✗ |
✗ |
111.316 |
|
| \(264\) |
\begin{align*}
c y+b x y^{\prime }+\left (a \,x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
612.651 |
|
| \(265\) |
\begin{align*}
2 \operatorname {a2} y+\left (\operatorname {b1} x +\operatorname {a1} \right ) y^{\prime }+\left (\operatorname {c0} \,x^{2}+\operatorname {b0} x +\operatorname {a0} \right ) y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
117.792 |
|
| \(266\) |
\begin{align*}
-y+2 y^{\prime } x +x^{3} y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
31.553 |
|
| \(267\) |
\begin{align*}
\left (\operatorname {b2} x +\operatorname {a2} \right ) y+\operatorname {a1} x y^{\prime }+x^{3} y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
29.920 |
|
| \(268\) |
\begin{align*}
\left (c \,x^{2}+b x +a \right ) y+x^{2} y^{\prime }+x^{3} y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✗ |
✗ |
64.072 |
|
| \(269\) |
\begin{align*}
\operatorname {a2} x y+\left (\operatorname {b1} \,x^{2}+\operatorname {a1} \right ) y^{\prime }+x^{3} y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
88.924 |
|
| \(270\) |
\begin{align*}
\operatorname {a2} y+x \left (\operatorname {b1} x +\operatorname {a1} \right ) y^{\prime }+x^{3} y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
90.431 |
|
| \(271\) |
\begin{align*}
\left (\operatorname {b2} x +\operatorname {a2} \right ) y+x \left (\operatorname {b1} x +\operatorname {a1} \right ) y^{\prime }+x^{3} y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
64.577 |
|
| \(272\) |
\begin{align*}
c x y+\left (b \,x^{2}+a \right ) y^{\prime }+x \left (x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
147.461 |
|
| \(273\) |
\begin{align*}
2 \left (1-b \right ) x y+\left (b \,x^{2}+a \right ) y^{\prime }+x \left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
134.286 |
|
| \(274\) |
\begin{align*}
c x y+\left (a -\left (1+a \right ) x^{2}\right ) y^{\prime }+x \left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
140.369 |
|
| \(275\) |
\begin{align*}
c x y+\left (b \,x^{2}+a \right ) y^{\prime }+x \left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
127.708 |
|
| \(276\) |
\begin{align*}
\operatorname {a2} x y+\left (\operatorname {b1} \,x^{2}+\operatorname {a1} \right ) y^{\prime }+x \left (x^{2}+\operatorname {a0} \right ) y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
37.428 |
|
| \(277\) |
\begin{align*}
\left (\operatorname {b2} x +\operatorname {a2} \right ) y+x \left (\operatorname {b1} x +\operatorname {a1} \right ) y^{\prime }+\left (1-x \right ) x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
152.365 |
|
| \(278\) |
\begin{align*}
\left (\operatorname {b2} x +\operatorname {a2} \right ) y+x \left (\operatorname {b1} x +\operatorname {a1} \right ) y^{\prime }+x^{2} \left (\operatorname {a0} +x \right ) y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
44.460 |
|
| \(279\) |
\begin{align*}
y+x \left (x +1\right ) y^{\prime }+x \left (x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✗ |
✗ |
103.122 |
|
| \(280\) |
\begin{align*}
\left (\operatorname {c1} x +\operatorname {c0} \right ) y+\left (\operatorname {b2} \,x^{2}+\operatorname {b1} x +\operatorname {b0} \right ) y^{\prime }+\left (\operatorname {a1} -x \right ) \left (\operatorname {a2} -x \right ) \left (\operatorname {a3} -x \right ) y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
478.043 |
|
| \(281\) |
\begin{align*}
\left (b x +a \right ) y+2 \left (1-3 x \right ) \left (1-x \right ) y^{\prime }+4 \left (1-x \right ) x y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
108.589 |
|
| \(282\) |
\begin{align*}
\left (\operatorname {b1} \,x^{2}+\operatorname {b0} \right ) y+\left (\operatorname {a2} \,x^{2}+\operatorname {a1} x +\operatorname {a0} \right ) y^{\prime }+4 \left (1-x \right ) x \left (-a x +1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
242.399 |
|
| \(283\) |
\begin{align*}
\left (-a^{2}+{\mathrm e}^{\frac {2}{x}}\right ) y+x^{4} y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
4.951 |
|
| \(284\) |
\begin{align*}
\left (c \,x^{4}+b \,x^{2}+a \right ) y+x^{3} y^{\prime }+x^{4} y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✗ |
✗ |
54.741 |
|
| \(285\) |
\begin{align*}
y+x \left (x^{2}+1\right ) y^{\prime }+x^{4} y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
51.672 |
|
| \(286\) |
\begin{align*}
a \left (1+a \right ) y-2 x^{3} y^{\prime }+x^{2} \left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
112.111 |
|
| \(287\) |
\begin{align*}
-a^{2} y-2 x \left (-x^{2}+1\right ) y^{\prime }+\left (x^{2}+1\right )^{2} y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✗ |
✗ |
70.671 |
|
| \(288\) |
\begin{align*}
-\left (m^{2}-n \left (n +1\right ) \left (-x^{2}+1\right )\right ) y-2 x \left (-x^{2}+1\right ) y^{\prime }+\left (-x^{2}+1\right )^{2} y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
93.378 |
|
| \(289\) |
\begin{align*}
-\left (k^{2}-p \left (1+p \right ) \left (-x^{2}+1\right )\right ) y-2 x \left (-x^{2}+1\right ) y^{\prime }+\left (-x^{2}+1\right )^{2} y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
83.155 |
|
| \(290\) |
\begin{align*}
-\left (a^{2}-k \left (-x^{2}+1\right )\right ) y-2 x \left (-x^{2}+1\right ) y^{\prime }+\left (-x^{2}+1\right )^{2} y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
71.511 |
|
| \(291\) |
\begin{align*}
\left (\operatorname {a4} \,x^{4}+\operatorname {a2} \,x^{2}+\operatorname {a0} \right ) y-2 x \left (-x^{2}+1\right ) y^{\prime }+\left (-x^{2}+1\right )^{2} y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
80.089 |
|
| \(292\) |
\begin{align*}
b y+a x \left (-x^{2}+1\right ) y^{\prime }+\left (x^{2}+1\right )^{2} y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✗ |
✗ |
99.941 |
|
| \(293\) |
\begin{align*}
\left (\operatorname {c2} \,x^{2}+\operatorname {b2} x +\operatorname {a2} \right ) y+\operatorname {a1} x \left (-x^{2}+1\right ) y^{\prime }+\left (-x^{2}+1\right )^{2} y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
112.284 |
|
| \(294\) |
\begin{align*}
b^{2} y+x \left (a^{2}+2 x^{2}\right ) y^{\prime }+x^{2} \left (a^{2}+x^{2}\right )^{2} y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✗ |
✗ |
162.494 |
|
| \(295\) |
\begin{align*}
-\left (\operatorname {a4} \,x^{4}+\operatorname {a2} \,x^{2}+\operatorname {a0} \right ) y+2 x \left (a^{2}+2 x^{2}\right ) y^{\prime }+\left (a^{2}+x^{2}\right )^{2} y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
132.448 |
|
| \(296\) |
\begin{align*}
\left (\operatorname {a4} \,x^{4}+\operatorname {a2} \,x^{2}+\operatorname {a0} \right ) y-2 x \left (a^{2}-x^{2}\right ) y^{\prime }+\left (a^{2}-x^{2}\right )^{2} y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✗ |
✗ |
132.211 |
|
| \(297\) |
\begin{align*}
\left (\operatorname {b1} \,x^{2}+\operatorname {a1} \right ) y+x \left (\operatorname {b0} \,x^{2}+\operatorname {a0} \right ) y^{\prime }+\left (a^{2}+x^{2}\right )^{2} \left (b^{2}+x^{2}\right ) y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
309.523 |
|
| \(298\) |
\begin{align*}
\left (\operatorname {c1} \,x^{4}+\operatorname {b1} \,x^{2}+\operatorname {a1} \right ) y+x \left (\operatorname {b0} \,x^{2}+\operatorname {a0} \right ) y^{\prime }+\left (a^{2}-x^{2}\right )^{2} \left (b^{2}-x^{2}\right ) y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
387.141 |
|
| \(299\) |
\begin{align*}
\left (c \,x^{2}+b x +a \right ) y+\left (1-x \right )^{2} x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
14.263 |
|
| \(300\) |
\begin{align*}
\left (\operatorname {c2} \,x^{2}+\operatorname {b2} x +\operatorname {a2} \right ) y+\left (1-x \right ) x \left (\operatorname {b2} x +\operatorname {a1} \right ) y^{\prime }+\left (1-x \right )^{2} x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
258.536 |
|
| \(301\) |
\begin{align*}
-\left (4 k^{2}+\left (4 p^{2}+1\right ) \left (-x^{2}+1\right )\right ) y-8 x \left (-x^{2}+1\right ) y^{\prime }+4 \left (-x^{2}+1\right )^{2} y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
74.813 |
|
| \(302\) |
\begin{align*}
-\left (4 k^{2}+\left (-4 p^{2}+1\right ) \left (-x^{2}+1\right )\right ) y-8 x \left (-x^{2}+1\right ) y^{\prime }+4 \left (-x^{2}+1\right )^{2} y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
74.178 |
|
| \(303\) |
\begin{align*}
-\left (a \left (1+a \right ) \left (1-x \right )+b^{2} x \right ) y+2 \left (1-3 x \right ) \left (1-x \right ) x y^{\prime }+4 x^{2} \left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✗ |
✗ |
304.095 |
|
| \(304\) |
\begin{align*}
\left (\operatorname {c2} \,x^{2}+\operatorname {b2} x +\operatorname {a2} \right ) y+\left (a -x \right ) \left (b -x \right ) \left (c -x \right ) \left (\operatorname {c1} \,x^{2}+\operatorname {b1} x +\operatorname {a1} \right ) y^{\prime }+\left (a -x \right )^{2} \left (b -x \right )^{2} \left (c -x \right )^{2} y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
1450.929 |
|
| \(305\) |
\begin{align*}
\left (\operatorname {a2} +\operatorname {b2} \,x^{k}\right ) y+x \left (\operatorname {a1} +\operatorname {b1} \,x^{k}\right ) y^{\prime }+x^{2} \left (\operatorname {a0} +\operatorname {b0} \,x^{k}\right ) y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
54.867 |
|
| \(306\) |
\begin{align*}
\left (\operatorname {a1} \cos \left (x \right )^{2}+\operatorname {a0} \right ) y+a^{2} \cos \left (x \right ) \sin \left (x \right ) y^{\prime }+\left (1-a^{2} \cos \left (x \right )^{2}\right ) y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✗ |
✗ |
46.447 |
|
| \(307\) |
\begin{align*}
-\left (4 k^{2}-\left (-p^{2}+1\right ) \sinh \left (x \right )^{2}\right ) y+4 \cosh \left (x \right ) \sinh \left (x \right ) y^{\prime }+4 \sinh \left (x \right )^{2} y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
45.316 |
|
| \(308\) |
\begin{align*}
y^{\prime \prime }&=x +6 y^{2} \\
\end{align*} |
[[_Painleve, ‘1st‘]] |
✗ |
✗ |
✗ |
0.550 |
|
| \(309\) |
\begin{align*}
y^{\prime \prime }&=a +b x +c y^{2} \\
\end{align*} |
[NONE] |
✗ |
✗ |
✗ |
0.586 |
|
| \(310\) |
\begin{align*}
y^{\prime \prime }&=a +y x +2 y^{3} \\
\end{align*} |
[[_Painleve, ‘2nd‘]] |
✗ |
✗ |
✗ |
0.563 |
|
| \(311\) |
\begin{align*}
y^{\prime \prime }&=f \left (x \right )+g \left (x \right ) y+2 y^{3} \\
\end{align*} |
[NONE] |
✗ |
✗ |
✗ |
1.906 |
|
| \(312\) |
\begin{align*}
y^{\prime \prime }&=a -2 a b x y+2 b^{2} y^{3} \\
\end{align*} |
[NONE] |
✗ |
✗ |
✗ |
0.602 |
|
| \(313\) |
\begin{align*}
y^{\prime \prime }&=\operatorname {a0} +\operatorname {a2} y+\operatorname {a1} x y+\operatorname {a3} y^{3} \\
\end{align*} |
[NONE] |
✗ |
✗ |
✗ |
0.593 |
|
| \(314\) |
\begin{align*}
a \,x^{r} y^{s}+y^{\prime \prime }&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
0.746 |
|
| \(315\) |
\begin{align*}
y \left (2 f \left (x \right )^{2}+f^{\prime }\left (x \right )\right )+3 f \left (x \right ) y^{\prime }+y^{\prime \prime }&=2 y^{3} \\
\end{align*} |
[NONE] |
✗ |
✗ |
✗ |
3.721 |
|
| \(316\) |
\begin{align*}
a y+y y^{\prime }+y^{\prime \prime }&=y^{3} \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✗ |
833.285 |
|
| \(317\) |
\begin{align*}
y y^{\prime }+y^{\prime \prime }&=-12 f \left (x \right ) y+y^{3}+12 f^{\prime }\left (x \right ) \\
\end{align*} |
[NONE] |
✗ |
✗ |
✗ |
3.829 |
|
| \(318\) |
\begin{align*}
2 a^{2} y+a y^{2}+\left (3 a +y\right ) y^{\prime }+y^{\prime \prime }&=y^{3} \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✗ |
105.847 |
|
| \(319\) |
\begin{align*}
y^{\prime \prime }&=f \left (x \right ) y^{2}+y^{3}+y \left (-2 f \left (x \right )^{2}+f^{\prime }\left (x \right )\right )+\left (3 f \left (x \right )-y\right ) y^{\prime } \\
\end{align*} |
[NONE] |
✓ |
✗ |
✗ |
4.807 |
|
| \(320\) |
\begin{align*}
y^{\prime \prime }&=\operatorname {f2} \left (x \right )+\operatorname {f3} \left (x \right ) y+\operatorname {f1} \left (x \right ) y^{2}+y^{3}+\left (3 \operatorname {f1} \left (x \right )-y\right ) y^{\prime } \\
\end{align*} |
[NONE] |
✗ |
✗ |
✗ |
5.855 |
|
| \(321\) |
\begin{align*}
y^{\prime \prime }&=\operatorname {g3} \left (x \right )+\operatorname {g2} \left (x \right ) y+\operatorname {g1} \left (x \right ) y^{2}+\operatorname {g0} \left (x \right ) y^{3}+\left (\operatorname {f1} \left (x \right )+\operatorname {f0} \left (x \right ) y\right ) y^{\prime } \\
\end{align*} |
[NONE] |
✗ |
✗ |
✗ |
7.816 |
|
| \(322\) |
\begin{align*}
y^{\prime \prime }&=y f^{\prime }\left (x \right )+\left (f \left (x \right )-2 y\right ) y^{\prime } \\
\end{align*} |
[[_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_xy]] |
✗ |
✗ |
✗ |
23.438 |
|
| \(323\) |
\begin{align*}
y^{\prime \prime }&=g \left (x \right )+f \left (x \right ) y^{2}+\left (f \left (x \right )-2 y\right ) y^{\prime } \\
\end{align*} |
[[_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✗ |
✗ |
✗ |
4.688 |
|
| \(324\) |
\begin{align*}
y^{\prime \prime }&=\operatorname {f3} \left (x \right )+\operatorname {f2} \left (x \right ) y^{2}+\left (\operatorname {f1} \left (x \right )-2 y\right ) y^{\prime } \\
\end{align*} |
[NONE] |
✗ |
✗ |
✗ |
5.339 |
|
| \(325\) |
\begin{align*}
y^{\prime \prime }&=\operatorname {f4} \left (x \right )+\operatorname {f3} \left (x \right ) y+\operatorname {f2} \left (x \right ) y^{2}+\left (\operatorname {f1} \left (x \right )-2 y\right ) y^{\prime } \\
\end{align*} |
[NONE] |
✗ |
✗ |
✗ |
6.407 |
|
| \(326\) |
\begin{align*}
y^{\prime \prime }&=a +4 b^{2} y+3 b y^{2}+3 y y^{\prime } \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✗ |
93.708 |
|
| \(327\) |
\begin{align*}
3 y y^{\prime }+y^{\prime \prime }&=f \left (x \right )+g \left (x \right ) y-y^{3} \\
\end{align*} |
[NONE] |
✗ |
✗ |
✗ |
4.942 |
|
| \(328\) |
\begin{align*}
y^{\prime \prime }&=f \left (x \right ) y^{2}-y^{3}+\left (f \left (x \right )-3 y\right ) y^{\prime } \\
\end{align*} |
[[_2nd_order, _with_potential_symmetries]] |
✓ |
✗ |
✗ |
4.118 |
|
| \(329\) |
\begin{align*}
y^{\prime \prime }&=a \left (1+2 y y^{\prime }\right ) \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✗ |
204.639 |
|
| \(330\) |
\begin{align*}
b y+a \left (-1+y^{2}\right ) y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✗ |
✗ |
✗ |
68.565 |
|
| \(331\) |
\begin{align*}
g \left (x , y\right )+f \left (x , y\right ) y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
[NONE] |
✗ |
✗ |
✗ |
1.123 |
|
| \(332\) |
\begin{align*}
c y+b y^{\prime }+a {y^{\prime }}^{2}+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✗ |
✗ |
✗ |
114.581 |
|
| \(333\) |
\begin{align*}
h \left (y\right )+f \left (y\right ) y^{\prime }+g \left (y\right ) {y^{\prime }}^{2}+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✗ |
✗ |
✗ |
17.626 |
|
| \(334\) |
\begin{align*}
y^{\prime \prime }&=a \left (-y+y^{\prime } x \right )^{k} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
1.452 |
|
| \(335\) |
\begin{align*}
y^{\prime \prime }&=A \,x^{a} y^{b} {y^{\prime }}^{c} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
0.868 |
|
| \(336\) |
\begin{align*}
y^{\prime \prime }&=a \sqrt {b y^{2}+{y^{\prime }}^{2}} \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✗ |
938.819 |
|
| \(337\) |
\begin{align*}
y^{\prime \prime }&=a \left (b +c x +y\right ) \left (1+{y^{\prime }}^{2}\right )^{{3}/{2}} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
✓ |
✗ |
0.755 |
|
| \(338\) |
\begin{align*}
y^{\prime \prime }&=f \left (a x +b y, y^{\prime }\right ) \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
0.356 |
|
| \(339\) |
\begin{align*}
y^{\prime \prime }&=f \left (x , \frac {y^{\prime }}{y}\right ) y \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
0.325 |
|
| \(340\) |
\begin{align*}
y^{\prime \prime }&=x^{-2+n} f \left (y x^{-n}, x^{1-n} y^{\prime }\right ) \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
0.532 |
|
| \(341\) |
\begin{align*}
a \,{\mathrm e}^{y} x +y^{\prime }+y^{\prime \prime } x&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
✗ |
0.506 |
|
| \(342\) |
\begin{align*}
x y^{5}+2 y^{\prime }+y^{\prime \prime } x&=0 \\
\end{align*} |
[_Emden, [_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.452 |
|
| \(343\) |
\begin{align*}
x y^{n}+2 y^{\prime }+y^{\prime \prime } x&=0 \\
\end{align*} |
[_Emden, [_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
0.498 |
|
| \(344\) |
\begin{align*}
x^{m} y^{n}+2 y^{\prime }+y^{\prime \prime } x&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
0.494 |
|
| \(345\) |
\begin{align*}
a \,x^{m} y^{n}+2 y^{\prime }+y^{\prime \prime } x&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
0.512 |
|
| \(346\) |
\begin{align*}
b \,{\mathrm e}^{y} x +a y^{\prime }+y^{\prime \prime } x&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
0.507 |
|
| \(347\) |
\begin{align*}
y^{\prime \prime } x&=-y^{2}-2 y^{\prime }+x^{2} {y^{\prime }}^{2} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✗ |
0.559 |
|
| \(348\) |
\begin{align*}
\left (-y+a x y^{\prime }\right )^{2}+y^{\prime \prime } x&=b \\
\end{align*} |
[NONE] |
✗ |
✗ |
✗ |
0.574 |
|
| \(349\) |
\begin{align*}
a y \left (1-y^{n}\right )+x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
0.411 |
|
| \(350\) |
\begin{align*}
a \,{\mathrm e}^{-1+y}+x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
0.409 |
|
| \(351\) |
\begin{align*}
\left (1+a \right ) x y^{\prime }+x^{2} y^{\prime \prime }&=x^{k} f \left (x^{k} y, k y+y^{\prime } x \right ) \\
\end{align*} |
[NONE] |
✗ |
✗ |
✗ |
1.069 |
|
| \(352\) |
\begin{align*}
x^{2} y^{\prime \prime }&=6 y-4 y^{2} x^{2}+x^{4} {y^{\prime }}^{2} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✗ |
0.863 |
|
| \(353\) |
\begin{align*}
a \left (-y+y^{\prime } x \right )^{2}+x^{2} y^{\prime \prime }&=b \,x^{2} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.697 |
|
| \(354\) |
\begin{align*}
2 y x +a \,x^{4} {y^{\prime }}^{2}+x^{2} y^{\prime \prime }&=b \\
\end{align*} |
[NONE] |
✗ |
✗ |
✗ |
0.603 |
|
| \(355\) |
\begin{align*}
b x +a y {y^{\prime }}^{2}+x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
0.386 |
|
| \(356\) |
\begin{align*}
x^{2} y^{\prime \prime }&=\sqrt {b y^{2}+a \,x^{2} {y^{\prime }}^{2}} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✗ |
✗ |
0.929 |
|
| \(357\) |
\begin{align*}
x^{2} y^{\prime \prime }&=f \left (\frac {x y^{\prime }}{y}\right ) y \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✗ |
✗ |
23.257 |
|
| \(358\) |
\begin{align*}
2 y+a y^{3}+9 x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.414 |
|
| \(359\) |
\begin{align*}
24+12 y x +x^{3} \left (-y^{3}+y y^{\prime }+y^{\prime \prime }\right )&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
0.988 |
|
| \(360\) |
\begin{align*}
x^{3} y^{\prime \prime }&=a \left (-y+y^{\prime } x \right )^{2} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✗ |
0.775 |
|
| \(361\) |
\begin{align*}
-6+x y \left (12+3 y x -2 y^{2} x^{2}\right )+x^{2} \left (9+2 y x \right ) y^{\prime }+2 x^{3} y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
1.223 |
|
| \(362\) |
\begin{align*}
x^{4} y^{\prime \prime }&=-4 y^{2}+x \left (x^{2}+2 y\right ) y^{\prime } \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✗ |
0.924 |
|
| \(363\) |
\begin{align*}
x^{4} y^{\prime \prime }&=-4 y^{2}+x^{2} y^{\prime } \left (x +y^{\prime }\right ) \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✗ |
1.223 |
|
| \(364\) |
\begin{align*}
\left (-y+y^{\prime } x \right )^{3}+x^{4} y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
1.434 |
|
| \(365\) |
\begin{align*}
y^{b}+x^{a} y^{\prime \prime }&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
0.332 |
|
| \(366\) |
\begin{align*}
24-48 y x +\left (-12 x^{2}+1\right ) \left (y^{2}+3 y^{\prime }\right )+2 x \left (-4 x^{2}+1\right ) \left (-y^{3}+y y^{\prime }+y^{\prime \prime }\right )&=0 \\
\end{align*} |
[NONE] |
✗ |
✗ |
✗ |
1.783 |
|
| \(367\) |
\begin{align*}
b +a x y-\left (-12 x^{2}+k \,x^{-1+k}\right ) \left (y^{2}+3 y^{\prime }\right )+2 \left (-4 x^{3}+x^{k}\right ) \left (-y^{3}+y y^{\prime }+y^{\prime \prime }\right )&=0 \\
\end{align*} |
[NONE] |
✗ |
✗ |
✗ |
2.797 |
|
| \(368\) |
\begin{align*}
\sqrt {x}\, y^{\prime \prime }&=y^{{3}/{2}} \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
0.344 |
|
| \(369\) |
\begin{align*}
x^{{3}/{2}} y^{\prime \prime }&=f \left (\frac {y}{\sqrt {x}}\right ) \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
18.396 |
|
| \(370\) |
\begin{align*}
f \left (x \right ) f^{\prime }\left (x \right ) y^{\prime }+f \left (x \right )^{2} y^{\prime \prime }&=g \left (y, f \left (x \right ) y^{\prime }\right ) \\
\end{align*} |
[NONE] |
✗ |
✗ |
✗ |
0.750 |
|
| \(371\) |
\begin{align*}
f \left (x \right )^{2} y^{\prime \prime }&=-24 f \left (x \right )^{4}+\left (3 f \left (x \right )^{3}-f \left (x \right )^{2} y+3 f \left (x \right ) f^{\prime }\left (x \right )\right ) y^{\prime } \\
\end{align*} |
[NONE] |
✗ |
✗ |
✗ |
1.031 |
|
| \(372\) |
\begin{align*}
2 f \left (x \right )^{2} y^{\prime \prime }&=2 f \left (x \right )^{2} y^{3}+f \left (x \right ) y^{2} f^{\prime }\left (x \right )+f \left (x \right ) \left (-2 f \left (x \right ) y+3 f^{\prime }\left (x \right )\right ) y^{\prime }+y \left (-2 f \left (x \right )^{3}-2 {f^{\prime }\left (x \right )}^{2}+f \left (x \right ) f^{\prime \prime }\left (x \right )\right ) \\
\end{align*} |
[NONE] |
✓ |
✗ |
✗ |
1.226 |
|
| \(373\) |
\begin{align*}
y y^{\prime \prime }&={\mathrm e}^{x} y \left (\operatorname {a0} +\operatorname {a1} y^{2}\right )+{\mathrm e}^{2 x} \left (\operatorname {a2} +\operatorname {a3} y^{4}\right )+{y^{\prime }}^{2} \\
\end{align*} |
[NONE] |
✗ |
✗ |
✗ |
0.610 |
|
| \(374\) |
\begin{align*}
y y^{\prime \prime }&=-y^{2} x^{2}+\ln \left (y\right ) y^{2}+{y^{\prime }}^{2} \\
\end{align*} |
[[_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✗ |
0.396 |
|
| \(375\) |
\begin{align*}
y y^{\prime \prime }&=y^{2} \left (f \left (x \right ) y+g^{\prime }\left (x \right )\right )+y^{\prime }+{y^{\prime }}^{2} \\
\end{align*} |
[NONE] |
✗ |
✗ |
✗ |
1.174 |
|
| \(376\) |
\begin{align*}
y-y^{\prime } x +{y^{\prime }}^{2}+y y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
0.508 |
|
| \(377\) |
\begin{align*}
a x y^{\prime }+{y^{\prime }}^{2}+y y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
0.457 |
|
| \(378\) |
\begin{align*}
y y^{\prime \prime }&=y^{3}-y f^{\prime }\left (x \right )+f \left (x \right ) y^{\prime }+{y^{\prime }}^{2} \\
\end{align*} |
[NONE] |
✗ |
✓ |
✗ |
1.184 |
|
| \(379\) |
\begin{align*}
y y^{\prime \prime }&=-f \left (x \right ) y^{3}+y^{4}-f \left (x \right ) y^{\prime }+{y^{\prime }}^{2}+y f^{\prime \prime }\left (x \right ) \\
\end{align*} |
[NONE] |
✗ |
✓ |
✗ |
1.466 |
|
| \(380\) |
\begin{align*}
y y^{\prime \prime }&=b y^{2}+y^{3}+a y y^{\prime }+{y^{\prime }}^{2} \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✗ |
✗ |
✗ |
27.273 |
|
| \(381\) |
\begin{align*}
y y^{\prime \prime }&=g \left (x \right ) y^{2}+f \left (x \right ) y y^{\prime }+{y^{\prime }}^{2} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✗ |
1.355 |
|
| \(382\) |
\begin{align*}
y y^{\prime \prime }&=-y \left (f^{\prime }\left (x \right )-y^{2} g^{\prime }\left (x \right )\right )+\left (f \left (x \right )+g \left (x \right ) y^{2}\right ) y^{\prime }+{y^{\prime }}^{2} \\
\end{align*} |
[[_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_xy]] |
✗ |
✗ |
✗ |
1.616 |
|
| \(383\) |
\begin{align*}
y y^{\prime \prime }&=\operatorname {a2} y^{2}+\operatorname {a3} y^{1+a}+\operatorname {a1} y y^{\prime }+a {y^{\prime }}^{2} \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✗ |
232.433 |
|
| \(384\) |
\begin{align*}
g \left (x \right ) y^{2}+f \left (x \right ) y y^{\prime }+a {y^{\prime }}^{2}+y y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
1.417 |
|
| \(385\) |
\begin{align*}
2 y^{\prime } \left (1+y^{\prime }\right )+\left (x -y\right ) y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
✓ |
✗ |
0.561 |
|
| \(386\) |
\begin{align*}
\left (x -y\right ) y^{\prime \prime }&=\left (1+y^{\prime }\right ) \left (1+{y^{\prime }}^{2}\right ) \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
✓ |
✗ |
0.700 |
|
| \(387\) |
\begin{align*}
\left (x -y\right ) y^{\prime \prime }&=f \left (y^{\prime }\right ) \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
✓ |
✗ |
1.894 |
|
| \(388\) |
\begin{align*}
2 y y^{\prime \prime }&=4 y^{2} \left (x +2 y\right )+{y^{\prime }}^{2} \\
\end{align*} |
[NONE] |
✗ |
✗ |
✗ |
0.368 |
|
| \(389\) |
\begin{align*}
2 y y^{\prime \prime }&=-1-2 x y^{2}+a y^{3}+{y^{\prime }}^{2} \\
\end{align*} |
[NONE] |
✗ |
✗ |
✗ |
0.361 |
|
| \(390\) |
\begin{align*}
2 y y^{\prime \prime }&=y^{2} \left (a x +b y\right )+{y^{\prime }}^{2} \\
\end{align*} |
[NONE] |
✗ |
✗ |
✗ |
0.346 |
|
| \(391\) |
\begin{align*}
2 y y^{\prime \prime }&=-a^{2}-4 \left (-x^{2}+b \right ) y^{2}+8 x y^{3}+3 y^{4}+{y^{\prime }}^{2} \\
\end{align*} |
[[_Painleve, ‘4th‘]] |
✗ |
✗ |
✗ |
0.453 |
|
| \(392\) |
\begin{align*}
2 y y^{\prime \prime }&=8 y^{3}-2 y^{2} \left (f \left (x \right )^{2}+f^{\prime }\left (x \right )\right )-3 f \left (x \right ) y y^{\prime }+{y^{\prime }}^{2} \\
\end{align*} |
[NONE] |
✗ |
✗ |
✗ |
1.099 |
|
| \(393\) |
\begin{align*}
2 y y^{\prime \prime }&=-1+2 x f \left (x \right ) y^{2}-y^{4}-4 y^{2} y^{\prime }+{y^{\prime }}^{2} \\
\end{align*} |
[NONE] |
✗ |
✗ |
✗ |
0.942 |
|
| \(394\) |
\begin{align*}
2 y y^{\prime \prime }&=f \left (x \right ) y^{2}+3 {y^{\prime }}^{2} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
0.600 |
|
| \(395\) |
\begin{align*}
a \left (2+a \right )^{2} y y^{\prime \prime }&=-a^{2} f \left (x \right )^{2} y^{4}+a^{2} \left (2+a \right ) y^{3} f^{\prime }\left (x \right )+a \left (2+a \right )^{2} f \left (x \right ) y^{2} y^{\prime }+\left (-1+a \right ) \left (2+a \right )^{2} {y^{\prime }}^{2} \\
\end{align*} |
[NONE] |
✗ |
✓ |
✗ |
1.724 |
|
| \(396\) |
\begin{align*}
x y y^{\prime \prime }&=y \left (\operatorname {a2} +\operatorname {a3} y^{2}\right )+x \left (\operatorname {a0} +\operatorname {a1} y^{4}\right )-y y^{\prime }+x {y^{\prime }}^{2} \\
\end{align*} |
[[_Painleve, ‘3rd‘]] |
✗ |
✗ |
✗ |
0.672 |
|
| \(397\) |
\begin{align*}
f \left (x \right )+a y y^{\prime }+x {y^{\prime }}^{2}+x y y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✗ |
1.252 |
|
| \(398\) |
\begin{align*}
x y y^{\prime \prime }&=x y^{3}+a y y^{\prime }+x {y^{\prime }}^{2} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
0.574 |
|
| \(399\) |
\begin{align*}
x y y^{\prime \prime }&=b^{2} x y^{3}+a y y^{\prime }+x {y^{\prime }}^{2} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
0.573 |
|
| \(400\) |
\begin{align*}
x y y^{\prime \prime }&=-\left (1+y\right ) y^{\prime }+2 x {y^{\prime }}^{2} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✗ |
0.609 |
|
| \(401\) |
\begin{align*}
\left (-y+y^{\prime } x \right )^{2}+x^{2} y y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✗ |
0.648 |
|
| \(402\) |
\begin{align*}
x^{2} y y^{\prime \prime }&=a y^{2}+a x y y^{\prime }+2 x^{2} {y^{\prime }}^{2} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✗ |
0.713 |
|
| \(403\) |
\begin{align*}
c y^{2}+b x y y^{\prime }+a \,x^{2} {y^{\prime }}^{2}+x^{2} y y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✗ |
0.683 |
|
| \(404\) |
\begin{align*}
2 \left (1-y\right )^{2} y-2 x \left (1-y\right ) y^{\prime }+2 x^{2} {y^{\prime }}^{2}+x^{2} \left (1-y\right ) y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✗ |
1.849 |
|
| \(405\) |
\begin{align*}
x^{2} \left (x -y\right ) y^{\prime \prime }&=\left (-y+y^{\prime } x \right )^{2} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✗ |
1.005 |
|
| \(406\) |
\begin{align*}
\left (-y+y^{\prime } x \right )^{2}+x^{2} \left (x -y\right ) y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✗ |
0.888 |
|
| \(407\) |
\begin{align*}
x^{2} \left (x -y\right ) y^{\prime \prime }&=a \left (-y+y^{\prime } x \right )^{2} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✗ |
1.017 |
|
| \(408\) |
\begin{align*}
2 x^{2} y y^{\prime \prime }&=-y^{2}+x^{2} {y^{\prime }}^{2} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✗ |
0.491 |
|
| \(409\) |
\begin{align*}
2 x^{2} y y^{\prime \prime }&=-4 y^{2}+2 y y^{\prime } x +x^{2} {y^{\prime }}^{2} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✗ |
0.689 |
|
| \(410\) |
\begin{align*}
x \left (x +1\right )^{2} y y^{\prime \prime }&=a \left (2+x \right ) y^{2}-2 \left (x^{2}+1\right ) y y^{\prime }+x \left (x +1\right )^{2} {y^{\prime }}^{2} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✗ |
1.061 |
|
| \(411\) |
\begin{align*}
3 x y^{2}-12 x^{2} y y^{\prime }+4 \left (-x^{3}+1\right ) {y^{\prime }}^{2}+8 \left (-x^{3}+1\right ) y y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✗ |
1.013 |
|
| \(412\) |
\begin{align*}
\sqrt {a^{2}-x^{2}}\, \left (-y y^{\prime }-x {y^{\prime }}^{2}+x y y^{\prime \prime }\right )&=b x {y^{\prime }}^{2} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
1.288 |
|
| \(413\) |
\begin{align*}
\operatorname {f3} \left (x \right ) y^{2}+\operatorname {f2} \left (x \right ) y y^{\prime }+\operatorname {f1} \left (x \right ) {y^{\prime }}^{2}+\operatorname {f0} \left (x \right ) y y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
1.722 |
|
| \(414\) |
\begin{align*}
4 f \left (x \right ) y y^{\prime \prime }&=4 f \left (x \right )^{2} y+3 f \left (x \right ) g \left (x \right ) y^{2}-f \left (x \right ) y^{4}+2 y^{3} f^{\prime }\left (x \right )+\left (-6 f \left (x \right ) y^{2}+2 f^{\prime }\left (x \right )\right ) y^{\prime }+3 f \left (x \right ) {y^{\prime }}^{2} \\
\end{align*} |
[NONE] |
✗ |
✗ |
✗ |
1.407 |
|
| \(415\) |
\begin{align*}
a x +y {y^{\prime }}^{2}+y^{2} y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✗ |
✗ |
0.341 |
|
| \(416\) |
\begin{align*}
y {y^{\prime }}^{2}+y^{2} y^{\prime \prime }&=b x +a \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
0.341 |
|
| \(417\) |
\begin{align*}
\left (x +y^{2}\right ) y^{\prime \prime }&=2 \left (x -y^{2}\right ) {y^{\prime }}^{3}-y^{\prime } \left (1+4 y y^{\prime }\right ) \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
✓ |
✗ |
0.886 |
|
| \(418\) |
\begin{align*}
\left (x^{2}+y^{2}\right ) y^{\prime \prime }&=\left (1+y^{2}\right ) \left (-y+y^{\prime } x \right ) \\
\end{align*} |
[NONE] |
✗ |
✗ |
✗ |
0.778 |
|
| \(419\) |
\begin{align*}
\left (x^{2}+y^{2}\right ) y^{\prime \prime }&=2 \left (1+y^{2}\right ) \left (-y+y^{\prime } x \right ) \\
\end{align*} |
[NONE] |
✗ |
✗ |
✗ |
0.782 |
|
| \(420\) |
\begin{align*}
2 \left (1-y\right ) y y^{\prime \prime }&=f \left (x \right ) \left (1-y\right ) y y^{\prime }+\left (1-2 y\right ) {y^{\prime }}^{2} \\
\end{align*} |
[_Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✗ |
1.143 |
|
| \(421\) |
\begin{align*}
2 \left (1-y\right ) y y^{\prime \prime }&=4 y \left (f \left (x \right )+g \left (x \right ) y\right ) y^{\prime }+\left (1-3 y\right ) {y^{\prime }}^{2} \\
\end{align*} |
[NONE] |
✗ |
✗ |
✗ |
1.462 |
|
| \(422\) |
\begin{align*}
2 \left (1-y\right ) y y^{\prime \prime }&=-\left (1-y\right )^{3} \left (\operatorname {F0} \left (x \right )^{2}-\operatorname {G0} \left (x \right )^{2} y^{2}\right )-4 \left (1-y\right ) y^{2} \left (f \left (x \right )^{2}-g \left (x \right )^{2}+f^{\prime }\left (x \right )+g^{\prime }\left (x \right )\right )-4 y \left (f \left (x \right )+g \left (x \right ) y\right ) y^{\prime }+\left (1-3 y\right ) {y^{\prime }}^{2} \\
\end{align*} |
[NONE] |
✗ |
✗ |
✗ |
2.787 |
|
| \(423\) |
\begin{align*}
x y^{2} y^{\prime \prime }&=a \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.361 |
|
| \(424\) |
\begin{align*}
x y^{2} y^{\prime \prime }&=\left (a -y^{2}\right ) y^{\prime }+x y {y^{\prime }}^{2} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✗ |
0.621 |
|
| \(425\) |
\begin{align*}
x^{2} y^{2} y^{\prime \prime }&=\left (x^{2}+y^{2}\right ) \left (-y+y^{\prime } x \right ) \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✗ |
0.946 |
|
| \(426\) |
\begin{align*}
\left (a^{2}-x^{2}\right ) y {y^{\prime }}^{2}+\left (a^{2}-x^{2}\right ) \left (a^{2}-y^{2}\right ) y^{\prime \prime }&=x \left (a^{2}-y^{2}\right ) y^{\prime } \\
\end{align*} |
[_Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✗ |
1.858 |
|
| \(427\) |
\begin{align*}
\operatorname {a2} x \left (1-y\right ) y^{2}+\operatorname {a3} \,x^{3} y^{2} \left (1+y\right )+\left (1-y\right )^{3} \left (\operatorname {a0} +\operatorname {a1} y^{2}\right )+2 x \left (1-y\right ) y y^{\prime }-x^{2} \left (1-3 y\right ) {y^{\prime }}^{2}+2 x^{2} \left (1-y\right ) y y^{\prime \prime }&=0 \\
\end{align*} |
[NONE] |
✗ |
✗ |
✗ |
3.405 |
|
| \(428\) |
\begin{align*}
\left (x +y\right ) \left (-y+y^{\prime } x \right )^{3}+x^{3} y^{2} y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
2.333 |
|
| \(429\) |
\begin{align*}
2 \left (1-x \right ) x \left (1-y\right ) \left (x -y\right ) y y^{\prime \prime }&=-y^{2} \left (1-y^{2}\right )+2 \left (1-y\right ) y \left (x^{2}+y-2 y x \right ) y^{\prime }+\left (1-x \right ) x \left (x -2 y-2 y x +3 y^{2}\right ) {y^{\prime }}^{2} \\
\end{align*} |
[NONE] |
✗ |
✗ |
✗ |
2.633 |
|
| \(430\) |
\begin{align*}
2 \left (1-x \right ) x \left (1-y\right ) \left (x -y\right ) y y^{\prime \prime }&=f \left (x \right ) \left (\left (1-y\right ) \left (x -y\right ) y\right )^{{3}/{2}}-y^{2} \left (1-y^{2}\right )+2 \left (1-y\right ) y \left (x^{2}+y-2 y x \right ) y^{\prime }+\left (1-x \right ) x \left (x -2 y-2 y x +3 y^{2}\right ) {y^{\prime }}^{2} \\
\end{align*} |
unknown |
✗ |
✗ |
✗ |
3.519 |
|
| \(431\) |
\begin{align*}
2 \left (1-x \right )^{2} x^{2} \left (1-y\right ) \left (x -y\right ) y y^{\prime \prime }&=\operatorname {a0} x \left (1-y\right )^{2} \left (x -y\right )^{2}+\left (-1+\operatorname {a2} \right ) \left (1-x \right ) x \left (1-y\right )^{2} y^{2}+\operatorname {a1} \left (1-x \right ) \left (x -y\right )^{2} y^{2}+\operatorname {a3} \left (1-y\right )^{2} \left (x -y\right )^{2} y^{2}+2 \left (1-x \right ) x \left (1-y\right )^{2} y \left (x^{2}+y-2 y x \right ) y^{\prime }+\left (1-x \right )^{2} x^{2} \left (x -2 y-2 y x +3 y^{2}\right ) {y^{\prime }}^{2} \\
\end{align*} |
[NONE] |
✗ |
✗ |
✗ |
5.725 |
|
| \(432\) |
\begin{align*}
a^{2} y+\left (x^{2}+y^{2}\right )^{2} y^{\prime \prime }&=0 \\
\end{align*} |
[NONE] |
✓ |
✗ |
✗ |
0.598 |
|
| \(433\) |
\begin{align*}
A y+\left (a +2 b x +c \,x^{2}+y^{2}\right )^{2} y^{\prime \prime }&=0 \\
\end{align*} |
[NONE] |
✓ |
✓ |
✗ |
0.752 |
|
| \(434\) |
\begin{align*}
\operatorname {f3} \left (y\right )+\operatorname {f2} \left (y\right ) y^{\prime }+\operatorname {f1} \left (y\right ) {y^{\prime }}^{2}+\operatorname {f0} \left (y\right ) y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✗ |
✗ |
✗ |
7.633 |
|
| \(435\) |
\begin{align*}
\sqrt {y}\, y^{\prime \prime }&=2 b x +2 a \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✗ |
✗ |
0.357 |
|
| \(436\) |
\begin{align*}
X \left (x , y\right )^{3} y^{\prime \prime }&=1 \\
\end{align*} |
[NONE] |
✗ |
✗ |
✗ |
0.296 |
|
| \(437\) |
\begin{align*}
y^{\prime } y^{\prime \prime }&=x y^{2}+x^{2} y y^{\prime } \\
\end{align*} |
[[_2nd_order, _exact, _nonlinear], [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_poly_yn]] |
✗ |
✗ |
✗ |
13.479 |
|
| \(438\) |
\begin{align*}
a y^{2}+x^{3} y^{\prime } y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✗ |
✗ |
1.133 |
|
| \(439\) |
\begin{align*}
\left ({y^{\prime }}^{2}+a \left (-y+y^{\prime } x \right )\right ) y^{\prime \prime }&=b \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.903 |
|
| \(440\) |
\begin{align*}
h \left (x \right )+g \left (y\right ) y^{\prime }+f \left (y^{\prime }\right ) y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1]] |
✗ |
✗ |
✗ |
2.700 |
|
| \(441\) |
\begin{align*}
{y^{\prime \prime }}^{2}&=a +b y \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
✗ |
0.050 |
|
| \(442\) |
\begin{align*}
2 \left (x -y^{\prime }\right ) y^{\prime }-x \left (x +4 y^{\prime }\right ) y^{\prime \prime }+2 \left (x^{2}+1\right ) {y^{\prime \prime }}^{2}&=2 y \\
\end{align*} |
[NONE] |
✗ |
✗ |
✗ |
0.048 |
|
| \(443\) |
\begin{align*}
4 {y^{\prime }}^{2}-2 \left (y+3 y^{\prime } x \right ) y^{\prime \prime }+3 x^{2} {y^{\prime \prime }}^{2}&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
5.134 |
|
| \(444\) |
\begin{align*}
6 y y^{\prime \prime }-6 \left (1-6 x \right ) x y^{\prime } y^{\prime \prime }+\left (2-9 x \right ) x^{2} {y^{\prime \prime }}^{2}&=36 x {y^{\prime }}^{2} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
32.533 |
|
| \(445\) |
\begin{align*}
h y^{2}+\operatorname {g1} y y^{\prime }+\operatorname {g0} {y^{\prime }}^{2}+\operatorname {f2} y y^{\prime \prime }+\operatorname {f1} y^{\prime } y^{\prime \prime }+\operatorname {f0} {y^{\prime \prime }}^{2}&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✗ |
✗ |
0.045 |
|
| \(446\) |
\begin{align*}
\left (y^{2}-x^{2} {y^{\prime }}^{2}+x^{2} y y^{\prime \prime }\right )^{2}&=4 x y \left (-y+y^{\prime } x \right )^{3} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
0.058 |
|
| \(447\) |
\begin{align*}
f \left (y^{\prime \prime }, y^{\prime }-y^{\prime \prime } x , y-y^{\prime } x +\frac {x^{2} y^{\prime \prime }}{2}\right )&=0 \\
\end{align*} |
[NONE] |
✓ |
✗ |
✗ |
21.491 |
|
| \(448\) |
\begin{align*}
y^{\prime \prime \prime }&=y x \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.028 |
|
| \(449\) |
\begin{align*}
y+2 y^{\prime } x +y^{\prime \prime \prime }&=0 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.034 |
|
| \(450\) |
\begin{align*}
a y+2 a x y^{\prime }+y^{\prime \prime \prime }&=0 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.033 |
|
| \(451\) |
\begin{align*}
y f^{\prime }\left (x \right )+2 f \left (x \right ) y^{\prime }+y^{\prime \prime \prime }&=0 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
0.043 |
|
| \(452\) |
\begin{align*}
-8 a x y-2 \left (-4 x^{2}-2 a +1\right ) y^{\prime }-6 y^{\prime \prime } x +y^{\prime \prime \prime }&=0 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.043 |
|
| \(453\) |
\begin{align*}
a^{3} x^{3} y+3 a^{2} x^{2} y^{\prime }+3 a x y^{\prime \prime }+y^{\prime \prime \prime }&=0 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.042 |
|
| \(454\) |
\begin{align*}
-2 y+2 y^{\prime } x -x^{2} y^{\prime \prime }+y^{\prime \prime \prime }&=0 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.039 |
|
| \(455\) |
\begin{align*}
-y^{\prime }+\left (2 \cot \left (x \right )+\csc \left (x \right )\right ) y^{\prime \prime }+y^{\prime \prime \prime }&=\cot \left (x \right ) \\
\end{align*} |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
✗ |
4.066 |
|
| \(456\) |
\begin{align*}
2 y \left (2 f \left (x \right ) g \left (x \right )+g^{\prime }\left (x \right )\right )+\left (4 g \left (x \right )+f^{\prime }\left (x \right )+2 {f^{\prime }\left (x \right )}^{2}\right ) y^{\prime }+3 f \left (x \right ) y^{\prime \prime }+y^{\prime \prime \prime }&=0 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
0.066 |
|
| \(457\) |
\begin{align*}
f \left (x \right ) y+y^{\prime }+f \left (x \right ) y^{\prime \prime }+y^{\prime \prime \prime }&=0 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.038 |
|
| \(458\) |
\begin{align*}
y x +3 y^{\prime }+x y^{\prime \prime \prime }&=0 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✗ |
✗ |
0.034 |
|
| \(459\) |
\begin{align*}
-y+y^{\prime } x -y^{\prime \prime }+x y^{\prime \prime \prime }&=0 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.038 |
|
| \(460\) |
\begin{align*}
y-y^{\prime } x -y^{\prime \prime }+x y^{\prime \prime \prime }&=0 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.036 |
|
| \(461\) |
\begin{align*}
y-y^{\prime } x -y^{\prime \prime }+x y^{\prime \prime \prime }&=-x^{2}+1 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.042 |
|
| \(462\) |
\begin{align*}
-x^{2} y+3 y^{\prime \prime }+x y^{\prime \prime \prime }&=0 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.040 |
|
| \(463\) |
\begin{align*}
a \,x^{2} y-6 y^{\prime }+x^{2} y^{\prime \prime \prime }&=0 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.042 |
|
| \(464\) |
\begin{align*}
3 y x +\left (x^{2}+2\right ) y^{\prime }+4 y^{\prime \prime } x +x^{2} y^{\prime \prime \prime }&=f \left (x \right ) \\
\end{align*} |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✗ |
0.046 |
|
| \(465\) |
\begin{align*}
a \,x^{2} y+6 y^{\prime }+6 y^{\prime \prime } x +x^{2} y^{\prime \prime \prime }&=0 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.041 |
|
| \(466\) |
\begin{align*}
2 x^{3} y+\left (-2 x^{3}+6\right ) y^{\prime }+x \left (-x^{2}+6\right ) y^{\prime \prime }+x^{2} y^{\prime \prime \prime }&=0 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
0.052 |
|
| \(467\) |
\begin{align*}
10 y^{\prime }+8 y^{\prime } x +\left (x^{2}+1\right ) y^{\prime \prime \prime }&=0 \\
\end{align*} |
[[_3rd_order, _missing_y]] |
✓ |
✗ |
✗ |
0.619 |
|
| \(468\) |
\begin{align*}
-2 y x +\left (x^{2}+2\right ) y^{\prime }-2 y^{\prime \prime } x +\left (x^{2}+2\right ) y^{\prime \prime \prime }&=0 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.041 |
|
| \(469\) |
\begin{align*}
-2 y+2 y^{\prime } x -x^{2} y^{\prime \prime }+\left (x^{2}-2 x +2\right ) y^{\prime \prime \prime }&=0 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.043 |
|
| \(470\) |
\begin{align*}
y+y^{\prime } x +\left (\operatorname {b1} x +\operatorname {a1} \right ) y^{\prime \prime }+x \left (\operatorname {b0} x +\operatorname {a0} \right ) y^{\prime \prime \prime }&=f \left (x \right ) \\
\end{align*} |
[[_3rd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✗ |
1.490 |
|
| \(471\) |
\begin{align*}
-2 \left (x^{2}+4\right ) y+x \left (x^{2}+8\right ) y^{\prime }-4 x^{2} y^{\prime \prime }+x^{3} y^{\prime \prime \prime }&=0 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.046 |
|
| \(472\) |
\begin{align*}
-y+2 y^{\prime } x +x^{2} \ln \left (x \right ) y^{\prime \prime }+x^{3} y^{\prime \prime \prime }&=2 x^{3} \\
\end{align*} |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✗ |
1.427 |
|
| \(473\) |
\begin{align*}
-12 y+3 \left (2 x^{2}+1\right ) y^{\prime \prime }+x \left (x^{2}+1\right ) y^{\prime \prime \prime }&=0 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.042 |
|
| \(474\) |
\begin{align*}
-8 y+3 \left (x +1\right ) y^{\prime }+\left (x +1\right )^{2} y^{\prime \prime }+\left (x +1\right )^{3} y^{\prime \prime \prime }&=0 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.055 |
|
| \(475\) |
\begin{align*}
-6 y+6 \left (x +1\right ) y^{\prime }-3 x \left (2+x \right ) y^{\prime \prime }+x^{2} \left (3+y\right ) y^{\prime \prime \prime }&=0 \\
\end{align*} |
[NONE] |
✗ |
✗ |
✗ |
0.041 |
|
| \(476\) |
\begin{align*}
2 y+\left (1-2 x \right ) y^{\prime }+\left (1-2 x \right )^{3} y^{\prime \prime \prime }&=0 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.040 |
|
| \(477\) |
\begin{align*}
-4 \left (1+3 x \right ) y+2 x \left (2+5 x \right ) y^{\prime }-2 x^{2} \left (2 x +1\right ) y^{\prime \prime }+x^{3} \left (x +1\right ) y^{\prime \prime \prime }&=0 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.051 |
|
| \(478\) |
\begin{align*}
-4 \left (3 x^{2}+1\right ) y+2 x \left (5 x^{2}+2\right ) y^{\prime }-2 x^{2} \left (2 x^{2}+1\right ) y^{\prime \prime }+x^{3} \left (x^{2}+1\right ) y^{\prime \prime \prime }&=0 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.050 |
|
| \(479\) |
\begin{align*}
\left (a -x \right )^{3} \left (b -x \right )^{3} y^{\prime \prime \prime }&=c y \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.044 |
|
| \(480\) |
\begin{align*}
10 f^{\prime }\left (x \right ) y^{\prime }+3 y \left (3 f \left (x \right )^{2}+f^{\prime \prime }\left (x \right )\right )+10 f \left (x \right ) y^{\prime \prime }+y^{\prime \prime \prime \prime }&=0 \\
\end{align*} |
[[_high_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
0.057 |
|
| \(481\) |
\begin{align*}
y^{2}-2 y^{\prime \prime \prime }+y^{\prime \prime \prime \prime }&=0 \\
\end{align*} |
[[_high_order, _missing_x], [_high_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
0.034 |
|
| \(482\) |
\begin{align*}
y^{2}-2 y^{\prime \prime \prime }+y^{\prime \prime \prime \prime }&=x^{3} \\
\end{align*} |
[NONE] |
✗ |
✗ |
✗ |
0.034 |
|
| \(483\) |
\begin{align*}
a^{4} x^{4} y+4 a^{3} x^{3} y^{\prime }+6 a^{2} x^{2} y^{\prime \prime }+4 a x y^{\prime \prime \prime }+y^{\prime \prime \prime \prime }&=0 \\
\end{align*} |
[[_high_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.054 |
|
| \(484\) |
\begin{align*}
-a^{2} y+12 y^{\prime \prime }+8 x y^{\prime \prime \prime }+x^{2} y^{\prime \prime \prime \prime }&=0 \\
\end{align*} |
[[_high_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.043 |
|
| \(485\) |
\begin{align*}
-c^{4} y+16 \left (1+a -b \right ) \left (2+a -b \right ) y^{\prime \prime }+32 \left (2+a -b \right ) x y^{\prime \prime \prime }+16 x^{2} y^{\prime \prime \prime \prime }&=0 \\
\end{align*} |
[[_high_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.049 |
|
| \(486\) |
\begin{align*}
-a^{4} x^{3} y-y^{\prime \prime } x +2 x^{2} y^{\prime \prime \prime }+x^{3} y^{\prime \prime \prime \prime }&=0 \\
\end{align*} |
[[_high_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.047 |
|
| \(487\) |
\begin{align*}
-k y-\left (-a b c +x \right ) y^{\prime }+\left (a b +a c +b c +a +b +c +1\right ) x y^{\prime \prime }+\left (3+a +b +c \right ) x^{2} y^{\prime \prime \prime }+x^{3} y^{\prime \prime \prime \prime }&=0 \\
\end{align*} |
[[_high_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.058 |
|
| \(488\) |
\begin{align*}
-b^{4} x^{\frac {2}{a}} y+16 \left (-2 a +1\right ) \left (1-a \right ) a^{2} x^{2} y^{\prime \prime }-32 \left (-2 a +1\right ) a^{2} x^{3} y^{\prime \prime \prime }+16 a^{4} x^{4} y^{\prime \prime \prime \prime }&=0 \\
\end{align*} |
[[_high_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.063 |
|
| \(489\) |
\begin{align*}
-y y^{\prime }+{y^{\prime }}^{2}+y^{\prime \prime \prime }&=0 \\
\end{align*} |
[[_3rd_order, _missing_x], [_3rd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
0.031 |
|
| \(490\) |
\begin{align*}
a y y^{\prime \prime }+y^{\prime \prime \prime }&=0 \\
\end{align*} |
[[_3rd_order, _missing_x], [_3rd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
0.029 |
|
| \(491\) |
\begin{align*}
y^{2}-\left (1-2 y x \right ) y^{\prime }+y^{\prime \prime } x +x^{2} y^{\prime \prime \prime }&=f \left (x \right ) \\
\end{align*} |
[[_3rd_order, _exact, _nonlinear]] |
✗ |
✗ |
✗ |
0.040 |
|
| \(492\) |
\begin{align*}
\left (1-y\right ) y^{\prime }+x {y^{\prime }}^{2}-x \left (1-y\right ) y^{\prime \prime }+x^{2} y^{\prime \prime \prime }&=0 \\
\end{align*} |
[[_3rd_order, _exact, _nonlinear], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2]] |
✓ |
✓ |
✗ |
0.041 |
|
| \(493\) |
\begin{align*}
y^{3} y^{\prime }-y^{\prime } y^{\prime \prime }+y y^{\prime \prime \prime }&=0 \\
\end{align*} |
[[_3rd_order, _missing_x], [_3rd_order, _exact, _nonlinear], [_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.040 |
|
| \(494\) |
\begin{align*}
3 y^{\prime } y^{\prime \prime }+\left (a +y\right ) y^{\prime \prime \prime }&=0 \\
\end{align*} |
[[_3rd_order, _missing_x], [_3rd_order, _exact, _nonlinear], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2], [_3rd_order, _reducible, _mu_poly_yn]] |
✓ |
✓ |
✗ |
0.035 |
|
| \(495\) |
\begin{align*}
3 y^{2}+18 y y^{\prime } x +9 x^{2} {y^{\prime }}^{2}+9 x^{2} y y^{\prime \prime }+3 x^{3} y^{\prime } y^{\prime \prime }+x^{3} y y^{\prime \prime \prime }&=0 \\
\end{align*} |
[[_3rd_order, _exact, _nonlinear], [_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.049 |
|
| \(496\) |
\begin{align*}
2 {y^{\prime }}^{3}+3 y^{\prime \prime }+6 y y^{\prime } y^{\prime \prime }+\left (x +y^{2}\right ) y^{\prime \prime \prime }&=0 \\
\end{align*} |
[[_3rd_order, _exact, _nonlinear], [_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.044 |
|
| \(497\) |
\begin{align*}
15 {y^{\prime }}^{3}-18 y y^{\prime } y^{\prime \prime }+4 y^{2} y^{\prime \prime \prime }&=0 \\
\end{align*} |
[[_3rd_order, _missing_x], [_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.041 |
|
| \(498\) |
\begin{align*}
40 {y^{\prime }}^{3}-45 y y^{\prime } y^{\prime \prime }+9 y^{2} y^{\prime \prime \prime }&=0 \\
\end{align*} |
[[_3rd_order, _missing_x], [_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.037 |
|
| \(499\) |
\begin{align*}
y^{\prime } y^{\prime \prime }&=a x {y^{\prime }}^{5}+3 {y^{\prime \prime }}^{2} \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✗ |
✗ |
✗ |
319.585 |
|
| \(500\) |
\begin{align*}
40 {y^{\prime \prime \prime }}^{3}-45 y^{\prime \prime } y^{\prime \prime \prime } y^{\prime \prime \prime \prime }+9 {y^{\prime \prime }}^{2} y^{\left (5\right )}&=0 \\
\end{align*} |
[[_high_order, _missing_x], [_high_order, _missing_y], [_high_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.095 |
|
| \(501\) |
\begin{align*}
\left (x y \sqrt {x^{2}-y^{2}}+x \right ) y^{\prime }&=y-x^{2} \sqrt {x^{2}-y^{2}} \\
\end{align*} |
[NONE] |
✓ |
✓ |
✗ |
32.454 |
|
| \(502\) |
\begin{align*}
x y y^{\prime \prime }-2 x {y^{\prime }}^{2}+\left (1+y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✗ |
0.355 |
|
| \(503\) |
\begin{align*}
y^{\prime }-\left (y-f \left (x \right )\right ) \left (y-g \left (x \right )\right ) \left (y-\frac {a f \left (x \right )+b g \left (x \right )}{a +b}\right ) h \left (x \right )-\frac {f^{\prime }\left (x \right ) \left (y-g \left (x \right )\right )}{f \left (x \right )-g \left (x \right )}-\frac {g^{\prime }\left (x \right ) \left (y-f \left (x \right )\right )}{g \left (x \right )-f \left (x \right )}&=0 \\
\end{align*} |
[_Abel] |
✓ |
✓ |
✗ |
12.608 |
|
| \(504\) |
\begin{align*}
x^{2} y^{\prime }+x y^{3}+a y^{2}&=0 \\
\end{align*} |
[_rational, _Abel] |
✓ |
✓ |
✗ |
15.813 |
|
| \(505\) |
\begin{align*}
\left (a x +b \right )^{2} y^{\prime }+\left (a x +b \right ) y^{3}+c y^{2}&=0 \\
\end{align*} |
[_rational, _Abel] |
✓ |
✓ |
✗ |
23.926 |
|
| \(506\) |
\begin{align*}
x^{4} y^{\prime \prime }+y^{\prime } x +y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
0.219 |
|
| \(507\) |
\begin{align*}
x^{3} y^{\prime \prime }-\left (2 x -1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
0.078 |
|
| \(508\) |
\begin{align*}
y^{\prime \prime }+\frac {a y}{x^{{3}/{2}}}&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_Emden, _Fowler]] |
✗ |
✓ |
✗ |
0.175 |
|
| \(509\) |
\begin{align*}
x^{3} y^{\prime \prime }+y&=x^{{3}/{2}} \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
✓ |
✗ |
0.097 |
|
| \(510\) |
\begin{align*}
2 x^{2} y^{\prime \prime }-\left (3 x +2\right ) y^{\prime }+\frac {\left (2 x -1\right ) y}{x}&=\sqrt {x} \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
✓ |
✗ |
0.109 |
|
| \(511\) |
\begin{align*}
s^{\prime }&=t \ln \left (s^{2 t}\right )+8 t^{2} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✓ |
✗ |
17.939 |
|
| \(512\) |
\begin{align*}
s^{2}+s^{\prime }&=\frac {s+1}{s t} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class C‘]] |
✗ |
✗ |
✗ |
40.321 |
|
| \(513\) |
\begin{align*}
x^{\prime }+t x&={\mathrm e}^{x} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
11.135 |
|
| \(514\) |
\begin{align*}
x x^{\prime }+t^{2} x&=\sin \left (t \right ) \\
\end{align*} |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
✗ |
✗ |
87.843 |
|
| \(515\) |
\begin{align*}
5 x^{2} y+6 x^{3} y^{2}+4 x y^{2}+\left (2 x^{3}+3 x^{4} y+3 x^{2} y\right ) y^{\prime }&=0 \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✗ |
26.966 |
|
| \(516\) |
\begin{align*}
2 x +2 y+2 x^{3} y+4 y^{2} x^{2}+\left (2 x +x^{4}+2 x^{3} y\right ) y^{\prime }&=0 \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✗ |
20.729 |
|
| \(517\) |
\begin{align*}
1+\frac {1}{1+x^{2}+4 y x +y^{2}}+\left (\frac {1}{\sqrt {y}}+\frac {1}{1+x^{2}+2 y x +y^{2}}\right ) y^{\prime }&=0 \\
\end{align*} |
[_rational] |
✗ |
✗ |
✗ |
53.391 |
|
| \(518\) |
\begin{align*}
\sqrt {\frac {y}{x}}+\cos \left (x \right )+\left (\sqrt {\frac {x}{y}}+\sin \left (y\right )\right ) y^{\prime }&=0 \\
\end{align*} |
[NONE] |
✗ |
✓ |
✗ |
61.469 |
|
| \(519\) |
\begin{align*}
y^{\prime \prime }+y&=0 \\
y \left (0\right ) &= 2 \\
y \left (\pi \right ) &= 0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✗ |
✗ |
✗ |
7.178 |
|
| \(520\) |
\begin{align*}
x^{2} y^{\prime \prime }+3 y^{\prime }-y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
0.182 |
|
| \(521\) |
\begin{align*}
y^{\prime \prime } x +\left (1-x \right ) y^{\prime }+m y&=0 \\
\end{align*} |
[_Laguerre] |
✓ |
✓ |
✗ |
7.803 |
|
| \(522\) |
\begin{align*}
x^{3} y^{\prime \prime }+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_Emden, _Fowler]] |
✗ |
✓ |
✗ |
0.081 |
|
| \(523\) |
\begin{align*}
\left (2 x -3\right ) y^{\prime \prime \prime }-\left (6 x -7\right ) y^{\prime \prime }+4 y^{\prime } x -4 y&=8 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.043 |
|
| \(524\) |
\begin{align*}
\left (1+2 y+3 y^{2}\right ) y^{\prime \prime \prime }+6 y^{\prime } \left (y^{\prime \prime }+{y^{\prime }}^{2}+3 y y^{\prime \prime }\right )&=x \\
\end{align*} |
[[_3rd_order, _exact, _nonlinear]] |
✓ |
✗ |
✗ |
0.046 |
|
| \(525\) |
\begin{align*}
3 x \left (y^{2} y^{\prime \prime \prime }+6 y y^{\prime } y^{\prime \prime }+2 {y^{\prime }}^{3}\right )-3 y \left (y y^{\prime \prime }+2 {y^{\prime }}^{2}\right )&=-\frac {2}{x} \\
\end{align*} |
[[_3rd_order, _exact, _nonlinear], [_3rd_order, _with_linear_symmetries]] |
✓ |
✗ |
✗ |
0.070 |
|
| \(526\) |
\begin{align*}
y y^{\prime \prime \prime }+3 y^{\prime } y^{\prime \prime }-2 y y^{\prime \prime }-2 {y^{\prime }}^{2}+y y^{\prime }&={\mathrm e}^{2 x} \\
\end{align*} |
[[_3rd_order, _exact, _nonlinear], [_3rd_order, _with_linear_symmetries]] |
✓ |
✗ |
✗ |
0.051 |
|
| \(527\) |
\begin{align*}
x^{3} \left (x +1\right ) y^{\prime \prime \prime }-\left (2+4 x \right ) x^{2} y^{\prime \prime }+\left (4+10 x \right ) x y^{\prime }-\left (4+12 x \right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.031 |
|
| \(528\) |
\begin{align*}
x^{3} \left (x^{2}+1\right ) y^{\prime \prime \prime }-\left (4 x^{2}+2\right ) x^{2} y^{\prime \prime }+\left (10 x^{2}+4\right ) x y^{\prime }-\left (12 x^{2}+4\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.033 |
|
| \(529\) |
\begin{align*}
x^{3} y^{\prime \prime }+y&=\frac {1}{x^{4}} \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
✓ |
✗ |
0.065 |
|
| \(530\) |
\begin{align*}
y^{\prime \prime } x -2 y^{\prime }+y&=\cos \left (x \right ) \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
✓ |
✗ |
27.134 |
|
| \(531\) |
\begin{align*}
y^{\prime }-\frac {y}{x}&=\cos \left (x \right ) \\
\end{align*} Series expansion around \(x=0\). |
[_linear] |
✗ |
✓ |
✗ |
0.222 |
|
| \(532\) |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
0.123 |
|
| \(533\) |
\begin{align*}
x^{3} y^{\prime \prime }+\left (x +1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
0.074 |
|
| \(534\) |
\begin{align*}
\left (1-x \right ) y^{\prime \prime }-4 y^{\prime } x +5 y&=\cos \left (x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✗ |
10.606 |
|
| \(535\) |
\begin{align*}
x y^{\prime \prime \prime }-{y^{\prime }}^{4}+y&=0 \\
\end{align*} |
[NONE] |
✗ |
✗ |
✗ |
0.031 |
|
| \(536\) |
\begin{align*}
t^{5} y^{\prime \prime \prime \prime }-t^{3} y^{\prime \prime }+6 y&=0 \\
\end{align*} |
[[_high_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
0.041 |
|
| \(537\) |
\begin{align*}
u^{\prime \prime }+u^{\prime }+u&=\cos \left (r +u\right ) \\
\end{align*} |
[NONE] |
✗ |
✗ |
✗ |
1.327 |
|
| \(538\) |
\begin{align*}
x^{\prime \prime }-\left (1-\frac {{x^{\prime }}^{2}}{3}\right ) x^{\prime }+x&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✗ |
✗ |
✗ |
47.860 |
|
| \(539\) |
\begin{align*}
\sin \left (x^{\prime }\right )+y^{3} x&=\sin \left (y \right ) \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
24.251 |
|
| \(540\) |
\begin{align*}
x^{\prime \prime }&=4 y+{\mathrm e}^{t} \\
y^{\prime \prime }&=4 x-{\mathrm e}^{t} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.061 |
|
| \(541\) |
\begin{align*}
y^{\prime \prime }+4 y&=0 \\
y^{\prime }\left (\frac {\pi }{2}\right ) &= 1 \\
y^{\prime }\left (\pi \right ) &= 0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✗ |
✗ |
✗ |
5.372 |
|
| \(542\) |
\begin{align*}
y^{\prime }&=x^{2}+y^{2} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[[_Riccati, _special]] |
✓ |
✓ |
✗ |
15.993 |
|
| \(543\) |
\begin{align*}
y^{\prime }&=6 \sqrt {y}+5 x^{3} \\
y \left (-1\right ) &= 4 \\
\end{align*} |
[_Chini] |
✗ |
✗ |
✗ |
3.626 |
|
| \(544\) |
\begin{align*}
y^{\prime }&=x^{2}-y^{2} \\
y \left (0\right ) &= 2 \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✗ |
13.153 |
|
| \(545\) |
\begin{align*}
y^{\prime }&={\mathrm e}^{-\frac {x y^{2}}{100}} \\
y \left (-6\right ) &= 0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
1.232 |
|
| \(546\) |
\begin{align*}
y^{\prime }&={\mathrm e}^{-\frac {x y^{2}}{100}} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
1.009 |
|
| \(547\) |
\begin{align*}
y^{\prime }&={\mathrm e}^{-\frac {x y^{2}}{100}} \\
y \left (0\right ) &= -4 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
1.022 |
|
| \(548\) |
\begin{align*}
y^{\prime }&={\mathrm e}^{-\frac {x y^{2}}{100}} \\
y \left (8\right ) &= -4 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
1.011 |
|
| \(549\) |
\begin{align*}
y^{\prime } x -4 y&=x^{6} {\mathrm e}^{x} \\
y \left (0\right ) &= y_{0} \\
\end{align*} |
[_linear] |
✗ |
✗ |
✗ |
3.221 |
|
| \(550\) |
\begin{align*}
x^{3} y^{\prime \prime }+4 x^{2} y^{\prime }+3 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_Emden, _Fowler]] |
✗ |
✓ |
✗ |
0.085 |
|
| \(551\) |
\begin{align*}
x^{3} \left (x^{2}-25\right ) \left (x -2\right )^{2} y^{\prime \prime }+3 x \left (x -2\right ) y^{\prime }+7 \left (x +5\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
0.117 |
|
| \(552\) |
\begin{align*}
x^{4} y^{\prime \prime }+\lambda y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_Emden, _Fowler]] |
✗ |
✓ |
✗ |
0.099 |
|
| \(553\) |
\begin{align*}
x^{3} y^{\prime \prime }+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_Emden, _Fowler]] |
✗ |
✓ |
✗ |
0.066 |
|
| \(554\) |
\begin{align*}
x^{2} y^{\prime \prime }+\left (3 x -1\right ) y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✗ |
✓ |
✗ |
0.134 |
|
| \(555\) |
\begin{align*}
y^{\prime \prime }-\cot \left (x \right ) y^{\prime }+\cos \left (x \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✗ |
✗ |
3.181 |
|
| \(556\) |
\begin{align*}
y^{\prime \prime \prime }-2 y^{\prime \prime } x +4 x^{2} y^{\prime }+8 x^{3} y&=0 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
0.043 |
|
| \(557\) |
\begin{align*}
y^{\prime \prime }+x \left (1-x \right ) y^{\prime }+{\mathrm e}^{x} y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
6.248 |
|
| \(558\) |
\begin{align*}
x^{2} \left (x +1\right ) y^{\prime \prime }+x \left (4 x +3\right ) y^{\prime }-y&=x +\frac {1}{x} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✗ |
85.936 |
|
| \(559\) |
\begin{align*}
\left (\cos \left (x \right )-\sin \left (x \right )\right ) y^{\prime \prime }-2 \sin \left (x \right ) y^{\prime }+\left (\cos \left (x \right )+\sin \left (x \right )\right ) y&=\left (\cos \left (x \right )-\sin \left (x \right )\right )^{2} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✗ |
12.784 |
|
| \(560\) |
\begin{align*}
x^{2} y y^{\prime \prime }&=-y^{2}+x^{2} {y^{\prime }}^{2} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✗ |
0.488 |
|
| \(561\) |
\begin{align*}
\left (-x^{2}+1\right ) z^{\prime \prime }+\left (1-3 x \right ) z^{\prime }+k z&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
93.900 |
|
| \(562\) |
\begin{align*}
\left (-x^{2}+1\right ) \eta ^{\prime \prime }-\left (x +1\right ) \eta ^{\prime }+\left (1+k \right ) \eta &=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
91.459 |
|
| \(563\) |
\begin{align*}
y^{\prime \prime \prime }-y x&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
y^{\prime \prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.045 |
|
| \(564\) |
\begin{align*}
y^{\prime \prime }-2 y^{\prime } x +2 \alpha y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
6.029 |
|
| \(565\) |
\begin{align*}
x^{2} y^{\prime \prime }-5 y^{\prime }+3 x^{2} y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
0.117 |
|
| \(566\) |
\begin{align*}
y_{1}^{\prime }&=3 y_{1}+x y_{3} \\
y_{2}^{\prime }&=y_{2}+x^{3} y_{3} \\
y_{3}^{\prime }&=2 x y_{1}-y_{2}+{\mathrm e}^{x} y_{3} \\
\end{align*} |
system_of_ODEs |
✗ |
✗ |
✗ |
0.041 |
|
| \(567\) |
\begin{align*}
x \ln \left (x \right ) y^{\prime }+y&=3 x^{3} \\
y \left (1\right ) &= 0 \\
\end{align*} |
[_linear] |
✗ |
✗ |
✓ |
2.008 |
|
| \(568\) |
\begin{align*}
2 y^{2}-4 x +5&=\left (4-2 y+4 y x \right ) y^{\prime } \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
22.060 |
|
| \(569\) |
\begin{align*}
x y y^{\prime \prime }&=y^{\prime }+{y^{\prime }}^{3} \\
\end{align*} |
[NONE] |
✗ |
✓ |
✗ |
0.798 |
|
| \(570\) |
\begin{align*}
x^{2} y^{\prime }&=y \\
\end{align*} Series expansion around \(x=0\). |
[_separable] |
✗ |
✓ |
✗ |
0.050 |
|
| \(571\) |
\begin{align*}
x^{3} \left (x -1\right ) y^{\prime \prime }-2 \left (x -1\right ) y^{\prime }+3 y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
0.088 |
|
| \(572\) |
\begin{align*}
x^{2} y^{\prime \prime }+\left (-x +2\right ) y^{\prime }&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _missing_y]] |
✗ |
✓ |
✗ |
0.087 |
|
| \(573\) |
\begin{align*}
x^{4} y^{\prime \prime }+\sin \left (x \right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
0.081 |
|
| \(574\) |
\begin{align*}
y^{\prime \prime }+\frac {y^{\prime }}{x^{2}}-\frac {y}{x^{3}}&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✗ |
✓ |
✗ |
0.092 |
|
| \(575\) |
\begin{align*}
x^{2} y^{\prime \prime }+\left (3 x -1\right ) y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✗ |
✓ |
✗ |
0.119 |
|
| \(576\) |
\begin{align*}
x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }+\left (x^{2}+x \right ) y^{\prime }+y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.023 |
|
| \(577\) |
\begin{align*}
x^{3} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }-3 y^{\prime } x +\left (x -1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.023 |
|
| \(578\) |
\begin{align*}
x^{3} y^{\prime \prime \prime }-2 x^{2} y^{\prime \prime }+\left (x^{2}+2 x \right ) y^{\prime }-y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.024 |
|
| \(579\) |
\begin{align*}
x^{3} y^{\prime \prime \prime }+\left (2 x^{3}-x^{2}\right ) y^{\prime \prime }-y^{\prime } x +y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.023 |
|
| \(580\) |
\begin{align*}
x^{\prime }&=x y+1 \\
y^{\prime }&=-x+y \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 2 \\
y \left (0\right ) &= -1 \\
\end{align*} |
system_of_ODEs |
✗ |
✗ |
✗ |
0.035 |
|
| \(581\) |
\begin{align*}
x^{\prime }&=t y+1 \\
y^{\prime }&=-t x+y \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= -1 \\
\end{align*} |
system_of_ODEs |
✗ |
✗ |
✗ |
0.031 |
|
| \(582\) |
\begin{align*}
y^{\prime }&=y+x \,{\mathrm e}^{y} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
7.973 |
|
| \(583\) |
\begin{align*}
y^{\prime \prime }+5 y^{\prime } x +\sqrt {x}\, y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
0.451 |
|
| \(584\) |
\begin{align*}
x^{3} y^{\prime \prime }+4 x^{2} y^{\prime }+3 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_Emden, _Fowler]] |
✗ |
✓ |
✗ |
0.093 |
|
| \(585\) |
\begin{align*}
x^{3} \left (x^{2}-25\right ) \left (x -2\right )^{2} y^{\prime \prime }+3 x \left (x -2\right ) y^{\prime }+7 \left (x +5\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
0.114 |
|
| \(586\) |
\begin{align*}
x^{3} y^{\prime \prime }+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_Emden, _Fowler]] |
✗ |
✓ |
✗ |
0.063 |
|
| \(587\) |
\begin{align*}
x^{2} y^{\prime \prime }+\left (3 x -1\right ) y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✗ |
✓ |
✗ |
0.148 |
|
| \(588\) |
\begin{align*}
y^{\prime }&=\sqrt {1-x^{2}-y^{2}} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
4.373 |
|
| \(589\) |
\begin{align*}
y^{\prime \prime }+\frac {\left (t^{2}-1\right ) y^{\prime }}{t}+\frac {t^{2} y}{\left (1+{\mathrm e}^{\frac {t^{2}}{2}}\right )^{2}}&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
28.191 |
|
| \(590\) |
\begin{align*}
y y^{\prime \prime }&=x \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
0.270 |
|
| \(591\) |
\begin{align*}
y^{2} y^{\prime \prime }&=x \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _with_linear_symmetries]] |
✓ |
✗ |
✗ |
0.285 |
|
| \(592\) |
\begin{align*}
3 y y^{\prime \prime }&=\sin \left (x \right ) \\
\end{align*} |
[NONE] |
✗ |
✗ |
✗ |
0.416 |
|
| \(593\) |
\begin{align*}
y^{\prime \prime }-y y^{\prime }&=2 x \\
\end{align*} |
[[_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✗ |
133.504 |
|
| \(594\) |
\begin{align*}
y^{\prime \prime }-a x y^{\prime }-b x y-c x&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
6.374 |
|
| \(595\) |
\begin{align*}
y^{\prime \prime }-a x y^{\prime }-b x y-c \,x^{2}&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
4.477 |
|
| \(596\) |
\begin{align*}
y^{\prime \prime }-a x y^{\prime }-b x y-c \,x^{3}&=0 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✗ |
4.558 |
|
| \(597\) |
\begin{align*}
y^{\prime \prime }-x^{2} y^{\prime }-x^{2} y-x^{2}&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✗ |
✗ |
7.107 |
|
| \(598\) |
\begin{align*}
y^{\prime \prime }-x^{3} y^{\prime }-x^{3} y-x^{3}&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
19.169 |
|
| \(599\) |
\begin{align*}
y^{\prime \prime }-x^{2} y^{\prime }-y x -x^{2}&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
14.543 |
|
| \(600\) |
\begin{align*}
y^{\prime \prime }-x^{2} y^{\prime }-x^{2} y-x^{3}-x^{2}&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✗ |
✗ |
5.179 |
|
| \(601\) |
\begin{align*}
y^{\prime \prime }-x^{2} y^{\prime }-x^{3} y-x^{4}-x^{2}&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✗ |
✗ |
5.750 |
|
| \(602\) |
\begin{align*}
y^{\prime \prime }-\frac {y^{\prime }}{x}-y x -x^{2}-\frac {1}{x}&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
40.981 |
|
| \(603\) |
\begin{align*}
y^{\prime \prime }-\frac {y^{\prime }}{x}-x^{3} y-x^{4}-\frac {1}{x}&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
241.305 |
|
| \(604\) |
\begin{align*}
y^{\prime \prime }-x^{3} y^{\prime }-y x -x^{3}-x^{2}&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
10.431 |
|
| \(605\) |
\begin{align*}
y^{\prime \prime }-x^{3} y^{\prime }-x^{2} y-x^{3}&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
8.972 |
|
| \(606\) |
\begin{align*}
y^{\prime \prime }-x^{3} y^{\prime }-x^{3} y-x^{4}-x^{3}&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
6.833 |
|
| \(607\) |
\begin{align*}
y^{\prime \prime \prime }-x^{3} y^{\prime }-x^{2} y-x^{3}&=0 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.042 |
|
| \(608\) |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime \prime }+1+{y^{\prime }}^{2}&=x \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✗ |
✗ |
240.529 |
|
| \(609\) |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime \prime }+y {y^{\prime }}^{2}&=0 \\
\end{align*} |
[NONE] |
✗ |
✗ |
✗ |
0.487 |
|
| \(610\) |
\begin{align*}
2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (-x^{2}+1\right ) y&=x +1 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
✓ |
✗ |
0.706 |
|
| \(611\) |
\begin{align*}
2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (-x^{2}+1\right ) y&=x \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
✓ |
✗ |
0.587 |
|
| \(612\) |
\begin{align*}
2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (-x^{2}+1\right ) y&=x^{2}+x +1 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
✓ |
✗ |
0.596 |
|
| \(613\) |
\begin{align*}
2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (-x^{2}+1\right ) y&=\sin \left (x \right ) \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
✓ |
✗ |
0.549 |
|
| \(614\) |
\begin{align*}
2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (-x^{2}+1\right ) y&=1+\sin \left (x \right ) \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
✓ |
✗ |
0.594 |
|
| \(615\) |
\begin{align*}
2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (-x^{2}+1\right ) y&=\cos \left (x \right )+\sin \left (x \right ) \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
✓ |
✗ |
0.602 |
|
| \(616\) |
\begin{align*}
2 x^{2} y^{\prime \prime }+2 y^{\prime } x -y x&=1 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
✓ |
✗ |
0.517 |
|
| \(617\) |
\begin{align*}
{y^{\prime }}^{2}+y^{2}&=\sec \left (x \right )^{4} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
57.778 |
|
| \(618\) |
\begin{align*}
\frac {x y^{\prime \prime }}{1-x}+y&=\frac {1}{1-x} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✗ |
3.809 |
|
| \(619\) |
\begin{align*}
\frac {x y^{\prime \prime }}{1-x}+y&=\cos \left (x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✗ |
3.702 |
|
| \(620\) |
\begin{align*}
\frac {x y^{\prime \prime }}{-x^{2}+1}+y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
3.072 |
|
| \(621\) |
\begin{align*}
y^{\prime }+y&=\frac {1}{x} \\
\end{align*} Series expansion around \(x=0\). |
[[_linear, ‘class A‘]] |
✗ |
✓ |
✗ |
0.251 |
|
| \(622\) |
\begin{align*}
y^{\prime }+y&=\frac {1}{x^{2}} \\
\end{align*} Series expansion around \(x=0\). |
[[_linear, ‘class A‘]] |
✗ |
✓ |
✗ |
0.280 |
|
| \(623\) |
\begin{align*}
y^{\prime }&=\frac {1}{x} \\
\end{align*} Series expansion around \(x=0\). |
[_quadrature] |
✗ |
✓ |
✗ |
0.125 |
|
| \(624\) |
\begin{align*}
y^{\prime \prime }&=\frac {1}{x} \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _quadrature]] |
✗ |
✓ |
✗ |
0.403 |
|
| \(625\) |
\begin{align*}
y^{\prime \prime }+y^{\prime }&=\frac {1}{x} \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _missing_y]] |
✗ |
✓ |
✗ |
0.574 |
|
| \(626\) |
\begin{align*}
y^{\prime \prime }+y&=\frac {1}{x} \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
✓ |
✗ |
0.484 |
|
| \(627\) |
\begin{align*}
y^{\prime \prime }+y^{\prime }+y&=\frac {1}{x} \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
✓ |
✗ |
0.531 |
|
| \(628\) |
\begin{align*}
y^{\prime }&=\frac {y x +3 x -2 y+6}{y x -3 x -2 y+6} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
25.872 |
|
| \(629\) |
\begin{align*}
y^{\prime }&=\cos \left (x \right )+\frac {y^{2}}{x} \\
\end{align*} |
[_Riccati] |
✗ |
✗ |
✗ |
8.647 |
|
| \(630\) |
\begin{align*}
y^{\prime } x +y&=0 \\
y \left (0\right ) &= 1 \\
\end{align*} Series expansion around \(x=0\). |
[_separable] |
✗ |
✗ |
✗ |
0.193 |
|
| \(631\) |
\begin{align*}
{y^{\prime \prime }}^{2}+y^{\prime }+y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✗ |
✗ |
✗ |
0.072 |
|
| \(632\) |
\begin{align*}
y^{\prime \prime }+\left (1-x \right ) y^{\prime }+y^{2} {y^{\prime }}^{2}&=0 \\
\end{align*} |
[_Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✗ |
0.820 |
|
| \(633\) |
\begin{align*}
y^{\prime \prime }+\left (\sin \left (x \right )+2 x \right ) y^{\prime }+\cos \left (y\right ) y {y^{\prime }}^{2}&=0 \\
\end{align*} |
[_Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✗ |
2.085 |
|
| \(634\) |
\begin{align*}
y^{\prime \prime }+\left (x +3\right ) y^{\prime }+\left (3+y^{2}\right ) {y^{\prime }}^{2}&=0 \\
\end{align*} |
[_Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✗ |
0.835 |
|
| \(635\) |
\begin{align*}
10 y^{\prime \prime }+\left ({\mathrm e}^{x}+3 x \right ) y^{\prime }+\frac {3 \,{\mathrm e}^{y} {y^{\prime }}^{2}}{\sin \left (y\right )}&=0 \\
\end{align*} |
[_Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✗ |
2.800 |
|
| \(636\) |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime \prime }+\left (x +1\right ) y^{\prime }+y&=4 \cos \left (\ln \left (x +1\right )\right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✗ |
✗ |
53.730 |
|
| \(637\) |
\begin{align*}
x^{2} y^{\prime \prime }+\left (-y+y^{\prime } x \right )^{2}&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✗ |
✗ |
0.813 |
|
| \(638\) |
\begin{align*}
y^{\prime \prime \prime }-y x&=0 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.039 |
|
| \(639\) |
\begin{align*}
y^{\prime }-\frac {y^{2} f^{\prime }\left (x \right )}{g \left (x \right )}+\frac {g^{\prime }\left (x \right )}{f \left (x \right )}&=0 \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✗ |
7.143 |
|
| \(640\) |
\begin{align*}
y^{\prime }+y^{3}+a x y^{2}&=0 \\
\end{align*} |
[_Abel] |
✓ |
✓ |
✗ |
12.699 |
|
| \(641\) |
\begin{align*}
y^{\prime }-y^{3}-a \,{\mathrm e}^{x} y^{2}&=0 \\
\end{align*} |
[_Abel] |
✓ |
✓ |
✗ |
9.464 |
|
| \(642\) |
\begin{align*}
y^{\prime }+3 a y^{3}+6 a x y^{2}&=0 \\
\end{align*} |
[_Abel] |
✓ |
✓ |
✗ |
13.180 |
|
| \(643\) |
\begin{align*}
y^{\prime }-x \left (2+x \right ) y^{3}-\left (x +3\right ) y^{2}&=0 \\
\end{align*} |
[_Abel] |
✓ |
✓ |
✗ |
11.586 |
|
| \(644\) |
\begin{align*}
y^{\prime }+\left (4 a^{2} x +3 a \,x^{2}+b \right ) y^{3}+3 x y^{2}&=0 \\
\end{align*} |
[_Abel] |
✓ |
✓ |
✗ |
21.092 |
|
| \(645\) |
\begin{align*}
y^{\prime }+2 \left (a^{2} x^{3}-b^{2} x \right ) y^{3}+3 b y^{2}&=0 \\
\end{align*} |
[_Abel] |
✓ |
✓ |
✗ |
14.583 |
|
| \(646\) |
\begin{align*}
y^{\prime }-a \left (x^{n}-x \right ) y^{3}-y^{2}&=0 \\
\end{align*} |
[_Abel] |
✗ |
✗ |
✗ |
43.690 |
|
| \(647\) |
\begin{align*}
y^{\prime }-\left (a \,x^{n}+b x \right ) y^{3}-c y^{2}&=0 \\
\end{align*} |
[_Abel] |
✗ |
✗ |
✗ |
43.068 |
|
| \(648\) |
\begin{align*}
y^{\prime }-f_{3} \left (x \right ) y^{3}-f_{2} \left (x \right ) y^{2}-f_{1} \left (x \right ) y-f_{0} \left (x \right )&=0 \\
\end{align*} |
[_Abel] |
✗ |
✗ |
✗ |
9.438 |
|
| \(649\) |
\begin{align*}
y^{\prime }-\left (y-f \left (x \right )\right ) \left (y-g \left (x \right )\right ) \left (y-\frac {a f \left (x \right )+b g \left (x \right )}{a +b}\right ) h \left (x \right )-\frac {f^{\prime }\left (x \right ) \left (y-g \left (x \right )\right )}{f \left (x \right )-g \left (x \right )}-\frac {g^{\prime }\left (x \right ) \left (y-f \left (x \right )\right )}{g \left (x \right )-f \left (x \right )}&=0 \\
\end{align*} |
[_Abel] |
✓ |
✓ |
✗ |
12.258 |
|
| \(650\) |
\begin{align*}
y^{\prime }-f \left (x \right ) y^{n}-g \left (x \right ) y-h \left (x \right )&=0 \\
\end{align*} |
[_Chini] |
✗ |
✗ |
✗ |
5.871 |
|
| \(651\) |
\begin{align*}
y^{\prime }-f \left (x \right ) y^{a}-g \left (x \right ) y^{b}&=0 \\
\end{align*} |
[NONE] |
✗ |
✗ |
✗ |
5.252 |
|
| \(652\) |
\begin{align*}
y^{\prime }-\frac {y-x^{2} \sqrt {x^{2}-y^{2}}}{x y \sqrt {x^{2}-y^{2}}+x}&=0 \\
\end{align*} |
[NONE] |
✓ |
✓ |
✗ |
34.823 |
|
| \(653\) |
\begin{align*}
y^{\prime }-f \left (x \right ) \left (y-g \left (x \right )\right ) \sqrt {\left (y-a \right ) \left (y-b \right )}&=0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
10.764 |
|
| \(654\) |
\begin{align*}
y^{\prime }+f \left (x \right ) \cos \left (a y\right )+g \left (x \right ) \sin \left (a y\right )+h \left (x \right )&=0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
6.195 |
|
| \(655\) |
\begin{align*}
y^{\prime }+f \left (x \right ) \sin \left (y\right )+\left (1-f^{\prime }\left (x \right )\right ) \cos \left (y\right )-f^{\prime }\left (x \right )-1&=0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✗ |
2.741 |
|
| \(656\) |
\begin{align*}
y^{\prime }+2 \tan \left (y\right ) \tan \left (x \right )-1&=0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✗ |
4.303 |
|
| \(657\) |
\begin{align*}
y^{\prime }-a \left (1+\tan \left (y\right )^{2}\right )+\tan \left (y\right ) \tan \left (x \right )&=0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
7.987 |
|
| \(658\) |
\begin{align*}
y^{\prime }-\tan \left (y x \right )&=0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✗ |
✗ |
2.145 |
|
| \(659\) |
\begin{align*}
y^{\prime }-x^{-1+a} y^{1-b} f \left (\frac {x^{a}}{a}+\frac {y^{b}}{b}\right )&=0 \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
✗ |
11.960 |
|
| \(660\) |
\begin{align*}
2 y^{\prime }-3 y^{2}-4 a y-b -c \,{\mathrm e}^{-2 a x}&=0 \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✗ |
46.167 |
|
| \(661\) |
\begin{align*}
y^{\prime } x +y^{3}+3 x y^{2}&=0 \\
\end{align*} |
[_rational, _Abel] |
✓ |
✓ |
✗ |
17.117 |
|
| \(662\) |
\begin{align*}
y^{\prime } x -x \left (-x +y\right ) \sqrt {x^{2}+y^{2}}-y&=0 \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✗ |
13.844 |
|
| \(663\) |
\begin{align*}
y^{\prime } x -\sin \left (x -y\right )&=0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
358.699 |
|
| \(664\) |
\begin{align*}
y^{\prime } x +a y-f \left (x \right ) g \left (x^{a} y\right )&=0 \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✗ |
10.477 |
|
| \(665\) |
\begin{align*}
x^{2} y^{\prime }+a y^{3}-a \,x^{2} y^{2}&=0 \\
\end{align*} |
[_rational, _Abel] |
✓ |
✓ |
✗ |
9.260 |
|
| \(666\) |
\begin{align*}
x^{2} y^{\prime }+x y^{3}+a y^{2}&=0 \\
\end{align*} |
[_rational, _Abel] |
✓ |
✓ |
✗ |
19.594 |
|
| \(667\) |
\begin{align*}
x^{2} y^{\prime }+y^{3} a \,x^{2}+b y^{2}&=0 \\
\end{align*} |
[_rational, _Abel] |
✓ |
✓ |
✗ |
11.012 |
|
| \(668\) |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime }+\left (1+y^{2}\right ) \left (2 y x -1\right )&=0 \\
\end{align*} |
[_rational, _Abel] |
✓ |
✓ |
✗ |
64.220 |
|
| \(669\) |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime }+x \sin \left (y\right ) \cos \left (y\right )-x \left (x^{2}+1\right ) \cos \left (y\right )^{2}&=0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✗ |
35.448 |
|
| \(670\) |
\begin{align*}
\left (x^{2}-1\right ) y^{\prime }+a \left (1-2 y x +y^{2}\right )&=0 \\
\end{align*} |
[_rational, _Riccati] |
✓ |
✓ |
✗ |
15.403 |
|
| \(671\) |
\begin{align*}
\left (a x +b \right )^{2} y^{\prime }+\left (a x +b \right ) y^{3}+c y^{2}&=0 \\
\end{align*} |
[_rational, _Abel] |
✓ |
✓ |
✗ |
28.377 |
|
| \(672\) |
\begin{align*}
x^{7} y^{\prime }+5 x^{3} y^{2}+2 \left (x^{2}+1\right ) y^{3}&=0 \\
\end{align*} |
[_rational, _Abel] |
✓ |
✓ |
✗ |
38.171 |
|
| \(673\) |
\begin{align*}
y y^{\prime }+x^{3}+y&=0 \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
✗ |
✗ |
21.471 |
|
| \(674\) |
\begin{align*}
y y^{\prime }+a y+\frac {\left (a^{2}-1\right ) x}{4}+b \,x^{n}&=0 \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
✗ |
✗ |
112.961 |
|
| \(675\) |
\begin{align*}
y y^{\prime }+a y+b \,{\mathrm e}^{x}-2 a&=0 \\
\end{align*} |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
✗ |
✗ |
38.619 |
|
| \(676\) |
\begin{align*}
y y^{\prime }+x +f \left (x^{2}+y^{2}\right ) g \left (x \right )&=0 \\
\end{align*} |
[NONE] |
✓ |
✓ |
✗ |
15.823 |
|
| \(677\) |
\begin{align*}
y y^{\prime } x -y^{2}+y x +x^{3}-2 x^{2}&=0 \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
46.394 |
|
| \(678\) |
\begin{align*}
x \left (a +y\right ) y^{\prime }+b y+c x&=0 \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
31.928 |
|
| \(679\) |
\begin{align*}
\left (x^{2} y-1\right ) y^{\prime }-x y^{2}+1&=0 \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✗ |
74.262 |
|
| \(680\) |
\begin{align*}
\left (x^{2} y-1\right ) y^{\prime }+8 x y^{2}-8&=0 \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
84.398 |
|
| \(681\) |
\begin{align*}
x \left (y x +x^{4}-1\right ) y^{\prime }-y \left (y x -x^{4}-1\right )&=0 \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✗ |
40.876 |
|
| \(682\) |
\begin{align*}
\left (x +2 y+y^{2}\right ) y^{\prime }+y \left (1+y\right )+\left (x +y\right )^{2} y^{2}&=0 \\
\end{align*} |
[_rational] |
✓ |
✓ |
✗ |
15.910 |
|
| \(683\) |
\begin{align*}
\left (2 a y^{3}+3 a x y^{2}-b \,x^{3}+c \,x^{2}\right ) y^{\prime }-a y^{3}+c y^{2}+3 b \,x^{2} y+2 b \,x^{3}&=0 \\
\end{align*} |
[_rational] |
✓ |
✓ |
✗ |
9.641 |
|
| \(684\) |
\begin{align*}
y^{\prime } \cos \left (y\right )-\cos \left (x \right ) \sin \left (y\right )^{2}-\sin \left (y\right )&=0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✓ |
38.916 |
|
| \(685\) |
\begin{align*}
y^{\prime } \cos \left (y\right )+x \sin \left (y\right ) \cos \left (y\right )^{2}-\sin \left (y\right )^{3}&=0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✓ |
66.856 |
|
| \(686\) |
\begin{align*}
x y^{\prime } \ln \left (x \right ) \sin \left (y\right )+\cos \left (y\right ) \left (1-x \cos \left (y\right )\right )&=0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✓ |
54.082 |
|
| \(687\) |
\begin{align*}
\left (2 x^{2}+1\right ) {y^{\prime }}^{2}+\left (y^{2}+2 y x +x^{2}+2\right ) y^{\prime }+2 y^{2}+1&=0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✓ |
✗ |
74.300 |
|
| \(688\) |
\begin{align*}
x \left (x^{2}-1\right ) {y^{\prime }}^{2}+2 \left (-x^{2}+1\right ) y y^{\prime }+x y^{2}-x&=0 \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✗ |
44.222 |
|
| \(689\) |
\begin{align*}
\left ({y^{\prime }}^{2}+y^{2}\right ) \cos \left (x \right )^{4}-a^{2}&=0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
67.407 |
|
| \(690\) |
\begin{align*}
\left (a y-x^{2}\right ) {y^{\prime }}^{2}+2 x y {y^{\prime }}^{2}-y^{2}&=0 \\
\end{align*} |
[_rational] |
✗ |
✗ |
✗ |
17.719 |
|
| \(691\) |
\begin{align*}
x y {y^{\prime }}^{2}+\left (x^{22}-y^{2}+a \right ) y^{\prime }-y x&=0 \\
\end{align*} |
[_rational] |
✗ |
✗ |
✗ |
80.402 |
|
| \(692\) |
\begin{align*}
\left (a y^{2}+b x +c \right ) {y^{\prime }}^{2}-b y y^{\prime }+d y^{2}&=0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✓ |
✗ |
279.247 |
|
| \(693\) |
\begin{align*}
x y^{2} {y^{\prime }}^{2}-\left (y^{3}+x^{3}-a \right ) y^{\prime }+x^{2} y&=0 \\
\end{align*} |
[_rational] |
✓ |
✓ |
✗ |
249.883 |
|
| \(694\) |
\begin{align*}
x^{2} \left (x y^{2}-1\right ) {y^{\prime }}^{2}+2 x^{2} y^{2} \left (-x +y\right ) y^{\prime }-y^{2} \left (x^{2} y-1\right )&=0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
80.594 |
|
| \(695\) |
\begin{align*}
\left (y^{4}-a^{2} x^{2}\right ) {y^{\prime }}^{2}+2 a^{2} x y y^{\prime }+y^{2} \left (y^{2}-a^{2}\right )&=0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
59.683 |
|
| \(696\) |
\begin{align*}
x^{2} \left (x^{2} y^{4}-1\right ) {y^{\prime }}^{2}+2 x^{3} y^{3} \left (y^{2}-x^{2}\right ) y^{\prime }-y^{2} \left (y^{2} x^{4}-1\right )&=0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
42.177 |
|
| \(697\) |
\begin{align*}
\left (a^{2} \sqrt {x^{2}+y^{2}}-x^{2}\right ) {y^{\prime }}^{2}+2 y y^{\prime } x +a^{2} \sqrt {x^{2}+y^{2}}-y^{2}&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
148.701 |
|
| \(698\) |
\begin{align*}
\left (a \left (x^{2}+y^{2}\right )^{{3}/{2}}-x^{2}\right ) {y^{\prime }}^{2}+2 y y^{\prime } x +a \left (x^{2}+y^{2}\right )^{{3}/{2}}-y^{2}&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
114.850 |
|
| \(699\) |
\begin{align*}
f \left (x^{2}+y^{2}\right ) \left (1+{y^{\prime }}^{2}\right )-\left (-y+y^{\prime } x \right )^{2}&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
48.232 |
|
| \(700\) |
\begin{align*}
{y^{\prime }}^{2}-\left (y^{4}+x y^{2}+x^{2}\right ) {y^{\prime }}^{2}+\left (x y^{6}+x^{2} y^{4}+x^{3} y^{2}\right ) y^{\prime }-x^{3} y^{6}&=0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
137.434 |
|
| \(701\) |
\begin{align*}
x y^{2} {y^{\prime }}^{3}-y^{3} {y^{\prime }}^{2}+x \left (x^{2}+1\right ) y^{\prime }-x^{2} y&=0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✓ |
✗ |
400.057 |
|
| \(702\) |
\begin{align*}
x^{n -1} {y^{\prime }}^{n}-n x y^{\prime }+y&=0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✗ |
8.643 |
|
| \(703\) |
\begin{align*}
y \sqrt {1+{y^{\prime }}^{2}}-a y y^{\prime }-a x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✗ |
0.136 |
|
| \(704\) |
\begin{align*}
f \left (x^{2}+y^{2}\right ) \sqrt {1+{y^{\prime }}^{2}}-y^{\prime } x +y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
66.588 |
|
| \(705\) |
\begin{align*}
a \,x^{n} f \left (y^{\prime }\right )+y^{\prime } x -y&=0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✗ |
5.777 |
|
| \(706\) |
\begin{align*}
f \left (x {y^{\prime }}^{2}\right )+2 y^{\prime } x -y&=0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✗ |
2.916 |
|
| \(707\) |
\begin{align*}
f \left (x -\frac {3 {y^{\prime }}^{2}}{2}\right )+{y^{\prime }}^{3}-y&=0 \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
✗ |
6.257 |
|
| \(708\) |
\begin{align*}
y^{\prime }&=\frac {1+2 F \left (\frac {4 x^{2} y+1}{4 x^{2}}\right ) x}{2 x^{3}} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
✓ |
✗ |
9.155 |
|
| \(709\) |
\begin{align*}
y^{\prime }&=\frac {1+F \left (\frac {a x y+1}{a x}\right ) a \,x^{2}}{a \,x^{2}} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
✗ |
9.177 |
|
| \(710\) |
\begin{align*}
y^{\prime }&=F \left (\ln \left (\ln \left (y\right )\right )-\ln \left (x \right )\right ) y \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
✗ |
55.231 |
|
| \(711\) |
\begin{align*}
y^{\prime }&=\frac {\left (x^{{3}/{2}}+2 F \left (y-\frac {x^{3}}{6}\right )\right ) \sqrt {x}}{2} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
✓ |
✗ |
10.985 |
|
| \(712\) |
\begin{align*}
y^{\prime }&=\frac {6 x^{3}+5 \sqrt {x}+5 F \left (y-\frac {2 x^{3}}{5}-2 \sqrt {x}\right )}{5 x} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
✓ |
✗ |
11.600 |
|
| \(713\) |
\begin{align*}
y^{\prime }&=\frac {F \left (y^{{3}/{2}}-\frac {3 \,{\mathrm e}^{x}}{2}\right ) {\mathrm e}^{x}}{\sqrt {y}} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
✗ |
11.355 |
|
| \(714\) |
\begin{align*}
y^{\prime }&=\frac {F \left (-\left (x -y\right ) \left (x +y\right )\right ) x}{y} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
✗ |
49.799 |
|
| \(715\) |
\begin{align*}
y^{\prime }&=\frac {y^{2} \left (2+F \left (\frac {x^{2}-y}{y x^{2}}\right ) x^{2}\right )}{x^{3}} \\
\end{align*} |
[NONE] |
✓ |
✓ |
✗ |
10.293 |
|
| \(716\) |
\begin{align*}
y^{\prime }&=\frac {2 F \left (y+\ln \left (2 x +1\right )\right ) x +F \left (y+\ln \left (2 x +1\right )\right )-2}{2 x +1} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
✗ |
10.565 |
|
| \(717\) |
\begin{align*}
y^{\prime }&=\frac {2 y^{3}}{1+2 F \left (\frac {1+4 x y^{2}}{y^{2}}\right ) y} \\
\end{align*} |
[‘x=_G(y,y’)‘] |
✓ |
✓ |
✗ |
8.970 |
|
| \(718\) |
\begin{align*}
y^{\prime }&=-\left (-{\mathrm e}^{-x^{2}}+x^{2} {\mathrm e}^{-x^{2}}-F \left (y-\frac {x^{2} {\mathrm e}^{-x^{2}}}{2}\right )\right ) x \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
✓ |
✗ |
20.252 |
|
| \(719\) |
\begin{align*}
y^{\prime }&=\frac {F \left (\frac {\left (3+y\right ) {\mathrm e}^{\frac {3 x^{2}}{2}}}{3 y}\right ) x y^{2} {\mathrm e}^{3 x^{2}} {\mathrm e}^{-\frac {9 x^{2}}{2}}}{9} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
✗ |
33.689 |
|
| \(720\) |
\begin{align*}
y^{\prime }&=\frac {\left (1+y\right ) \left (\left (y-\ln \left (1+y\right )-\ln \left (x \right )\right ) x +1\right )}{y x} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✓ |
76.688 |
|
| \(721\) |
\begin{align*}
y^{\prime }&=\frac {6 y}{8 y^{4}+9 y^{3}+12 y^{2}+6 y-F \left (-\frac {y^{4}}{3}-\frac {y^{3}}{2}-y^{2}-y+x \right )} \\
\end{align*} |
[‘x=_G(y,y’)‘] |
✓ |
✓ |
✗ |
10.457 |
|
| \(722\) |
\begin{align*}
y^{\prime }&=\frac {i x^{2} \left (i-2 \sqrt {-x^{3}+6 y}\right )}{2} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
✗ |
2.149 |
|
| \(723\) |
\begin{align*}
y^{\prime }&=\frac {1+2 x^{5} \sqrt {4 x^{2} y+1}}{2 x^{3}} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✗ |
39.707 |
|
| \(724\) |
\begin{align*}
y^{\prime }&=-\left (-\ln \left (\ln \left (y\right )\right )+\ln \left (x \right )\right ) y \\
\end{align*} |
[‘x=_G(y,y’)‘] |
✓ |
✓ |
✗ |
38.269 |
|
| \(725\) |
\begin{align*}
y^{\prime }&=\left (-\ln \left (\ln \left (y\right )\right )+\ln \left (x \right )\right )^{2} y \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✗ |
45.416 |
|
| \(726\) |
\begin{align*}
y^{\prime }&=\frac {y}{\ln \left (\ln \left (y\right )\right )-\ln \left (x \right )+1} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✗ |
64.157 |
|
| \(727\) |
\begin{align*}
y^{\prime }&=\frac {1+2 \sqrt {4 x^{2} y+1}\, x^{4}}{2 x^{3}} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✗ |
40.429 |
|
| \(728\) |
\begin{align*}
y^{\prime }&=-\frac {x^{3} \left (\sqrt {a}\, x +\sqrt {a}-2 \sqrt {a \,x^{4}+8 y}\right ) \sqrt {a}}{2 \left (x +1\right )} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
✓ |
✗ |
62.850 |
|
| \(729\) |
\begin{align*}
y^{\prime }&=-\frac {\left (\sqrt {a}\, x^{4}+\sqrt {a}\, x^{3}-2 \sqrt {a \,x^{4}+8 y}\right ) \sqrt {a}}{2 \left (x +1\right )} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
✓ |
✓ |
2.456 |
|
| \(730\) |
\begin{align*}
y^{\prime }&=\frac {\left (-2 y^{{3}/{2}}+3 \,{\mathrm e}^{x}\right )^{2} {\mathrm e}^{x}}{4 \sqrt {y}} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
✗ |
14.894 |
|
| \(731\) |
\begin{align*}
y^{\prime }&=\frac {x^{2} \left (3 x +\sqrt {-9 x^{4}+4 y^{3}}\right )}{y^{2}} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✗ |
331.108 |
|
| \(732\) |
\begin{align*}
y^{\prime }&=\frac {x +1+2 x^{6} \sqrt {4 x^{2} y+1}}{2 x^{3} \left (x +1\right )} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✗ |
18.613 |
|
| \(733\) |
\begin{align*}
y^{\prime }&=\frac {x^{2} \left (x +1+2 x \sqrt {x^{3}-6 y}\right )}{2 x +2} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
✓ |
✗ |
59.947 |
|
| \(734\) |
\begin{align*}
y^{\prime }&=\frac {y+x^{2} \sqrt {x^{2}+y^{2}}}{x} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✗ |
36.192 |
|
| \(735\) |
\begin{align*}
y^{\prime }&=\frac {-x^{2}+1+4 x^{3} \sqrt {x^{2}-2 x +1+8 y}}{4 x +4} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
✓ |
✗ |
32.733 |
|
| \(736\) |
\begin{align*}
y^{\prime }&=\frac {y+x^{3} \sqrt {x^{2}+y^{2}}}{x} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✗ |
16.221 |
|
| \(737\) |
\begin{align*}
y^{\prime }&=\frac {x +1+2 \sqrt {4 x^{2} y+1}\, x^{3}}{2 x^{3} \left (x +1\right )} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✗ |
24.486 |
|
| \(738\) |
\begin{align*}
y^{\prime }&=\frac {x \left (-2 x -2+3 x^{2} \sqrt {x^{2}+3 y}\right )}{3 x +3} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
✓ |
✗ |
49.652 |
|
| \(739\) |
\begin{align*}
y^{\prime }&=-\frac {\left (-\ln \left (-1+y\right )+\ln \left (1+y\right )+2 \ln \left (x \right )\right ) x \left (1+y\right )^{2}}{8} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✗ |
150.817 |
|
| \(740\) |
\begin{align*}
y^{\prime }&=\frac {\left (-\ln \left (-1+y\right )+\ln \left (1+y\right )+2 \ln \left (x \right )\right )^{2} x \left (1+y\right )^{2}}{16} \\
\end{align*} |
[‘x=_G(y,y’)‘] |
✓ |
✓ |
✗ |
154.674 |
|
| \(741\) |
\begin{align*}
y^{\prime }&=\frac {2 a x +2 a +x^{3} \sqrt {-y^{2}+4 a x}}{\left (x +1\right ) y} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✗ |
80.530 |
|
| \(742\) |
\begin{align*}
y^{\prime }&=-\frac {\left (\ln \left (y\right ) x +\ln \left (y\right )-1\right ) y}{x +1} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
52.832 |
|
| \(743\) |
\begin{align*}
y^{\prime }&=\frac {x^{2}+2 x +1+2 x^{3} \sqrt {x^{2}+2 x +1-4 y}}{2 x +2} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
✓ |
✗ |
31.900 |
|
| \(744\) |
\begin{align*}
y^{\prime }&=\frac {-x^{2}+x +2+2 x^{3} \sqrt {x^{2}-4 x +4 y}}{2 x +2} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
✓ |
✗ |
30.839 |
|
| \(745\) |
\begin{align*}
y^{\prime }&=\frac {3 x^{4}+3 x^{3}+\sqrt {9 x^{4}-4 y^{3}}}{\left (x +1\right ) y^{2}} \\
\end{align*} |
[_rational] |
✓ |
✓ |
✗ |
139.089 |
|
| \(746\) |
\begin{align*}
y^{\prime }&=\frac {x^{3} \left (3 x +3+\sqrt {9 x^{4}-4 y^{3}}\right )}{\left (x +1\right ) y^{2}} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✗ |
292.107 |
|
| \(747\) |
\begin{align*}
y^{\prime }&=\frac {\left (2 y^{{3}/{2}}-3 \,{\mathrm e}^{x}\right )^{3} {\mathrm e}^{x}}{4 \left (2 y^{{3}/{2}}-3 \,{\mathrm e}^{x}+2\right ) \sqrt {y}} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
✗ |
32.648 |
|
| \(748\) |
\begin{align*}
y^{\prime }&=\frac {-x^{2}-x -a x -a +2 x^{3} \sqrt {x^{2}+2 a x +a^{2}+4 y}}{2 x +2} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
✓ |
✗ |
32.773 |
|
| \(749\) |
\begin{align*}
y^{\prime }&=\frac {\left (-\ln \left (y\right ) x -\ln \left (y\right )+x^{3}\right ) y}{x +1} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
18.919 |
|
| \(750\) |
\begin{align*}
y^{\prime }&=-\frac {\cos \left (y\right ) \left (x -\cos \left (y\right )+1\right )}{\left (x \sin \left (y\right )-1\right ) \left (x +1\right )} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✗ |
116.404 |
|
| \(751\) |
\begin{align*}
y^{\prime }&=\frac {\cos \left (y\right ) \left (\cos \left (y\right ) x^{3}-x -1\right )}{\left (x \sin \left (y\right )-1\right ) \left (x +1\right )} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✗ |
57.931 |
|
| \(752\) |
\begin{align*}
y^{\prime }&=\frac {\left (x +1+x^{4} \ln \left (y\right )\right ) y \ln \left (y\right )}{x \left (x +1\right )} \\
\end{align*} |
[‘x=_G(y,y’)‘] |
✓ |
✓ |
✓ |
19.987 |
|
| \(753\) |
\begin{align*}
y^{\prime }&=\frac {\left (2 x +2+x^{3} y\right ) y}{\left (\ln \left (y\right )+2 x -1\right ) \left (x +1\right )} \\
\end{align*} |
[‘x=_G(y,y’)‘] |
✓ |
✓ |
✗ |
16.158 |
|
| \(754\) |
\begin{align*}
y^{\prime }&=-\frac {\left (\ln \left (y\right ) x +\ln \left (y\right )-x \right ) y}{x \left (x +1\right )} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
66.183 |
|
| \(755\) |
\begin{align*}
y^{\prime }&=\frac {\left (-\ln \left (y\right ) x -\ln \left (y\right )+x^{4}\right ) y}{x \left (x +1\right )} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
21.480 |
|
| \(756\) |
\begin{align*}
y^{\prime }&=\frac {\left (x +1+\ln \left (y\right ) x \right ) \ln \left (y\right ) y}{x \left (x +1\right )} \\
\end{align*} |
[‘x=_G(y,y’)‘] |
✓ |
✓ |
✓ |
57.424 |
|
| \(757\) |
\begin{align*}
y^{\prime }&=\frac {y x +y+x \sqrt {x^{2}+y^{2}}}{x \left (x +1\right )} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✗ |
40.961 |
|
| \(758\) |
\begin{align*}
y^{\prime }&=-\frac {-\frac {1}{x}-\textit {\_F1} \left (y+\frac {1}{x}\right )}{x} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
✓ |
✗ |
11.087 |
|
| \(759\) |
\begin{align*}
y^{\prime }&=\frac {\textit {\_F1} \left (y^{2}-2 \ln \left (x \right )\right )}{\sqrt {y^{2}}\, x} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
✗ |
15.961 |
|
| \(760\) |
\begin{align*}
y^{\prime }&=\frac {-x \sin \left (2 y\right )-\sin \left (2 y\right )+\cos \left (2 y\right ) x^{4}+x^{4}}{2 x \left (x +1\right )} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✗ |
29.302 |
|
| \(761\) |
\begin{align*}
y^{\prime }&=\frac {y x +y+x^{4} \sqrt {x^{2}+y^{2}}}{x \left (x +1\right )} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✗ |
26.965 |
|
| \(762\) |
\begin{align*}
y^{\prime }&=\frac {-x \sin \left (2 y\right )-\sin \left (2 y\right )+x \cos \left (2 y\right )+x}{2 x \left (x +1\right )} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✗ |
108.076 |
|
| \(763\) |
\begin{align*}
y^{\prime }&=-\frac {1}{-x -\textit {\_F1} \left (y-\ln \left (x \right )\right ) y \,{\mathrm e}^{y}} \\
\end{align*} |
[NONE] |
✓ |
✓ |
✗ |
12.395 |
|
| \(764\) |
\begin{align*}
y^{\prime }&=\frac {x^{3} {\mathrm e}^{y}+x^{4}+{\mathrm e}^{y} y-{\mathrm e}^{y} \ln \left ({\mathrm e}^{y}+x \right )+y x -\ln \left ({\mathrm e}^{y}+x \right ) x +x}{x^{2}} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✗ |
46.445 |
|
| \(765\) |
\begin{align*}
y^{\prime }&=\frac {x^{2}}{2}+\sqrt {x^{3}-6 y}+x^{2} \sqrt {x^{3}-6 y}+x^{3} \sqrt {x^{3}-6 y} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
✓ |
✗ |
61.729 |
|
| \(766\) |
\begin{align*}
y^{\prime }&=\frac {\left (-\sqrt {a}\, x^{3}+2 \sqrt {a \,x^{4}+8 y}+2 x^{2} \sqrt {a \,x^{4}+8 y}+2 x^{3} \sqrt {a \,x^{4}+8 y}\right ) \sqrt {a}}{2} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
✓ |
✗ |
51.020 |
|
| \(767\) |
\begin{align*}
y^{\prime }&=\frac {-2 \cos \left (y\right )+x^{3} \cos \left (2 y\right ) \ln \left (x \right )+x^{3} \ln \left (x \right )}{2 \sin \left (y\right ) \ln \left (x \right ) x} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✓ |
25.875 |
|
| \(768\) |
\begin{align*}
y^{\prime }&=-\frac {2 x}{3}+\sqrt {x^{2}+3 y}+x^{2} \sqrt {x^{2}+3 y}+x^{3} \sqrt {x^{2}+3 y} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
✓ |
✗ |
43.204 |
|
| \(769\) |
\begin{align*}
y^{\prime }&=\frac {-2 \cos \left (y\right )+x^{2} \cos \left (2 y\right ) \ln \left (x \right )+\ln \left (x \right ) x^{2}}{2 \sin \left (y\right ) \ln \left (x \right ) x} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✓ |
25.005 |
|
| \(770\) |
\begin{align*}
y^{\prime }&=\frac {\left (3 x y^{2}+x +3 y^{2}\right ) y}{\left (x +6 y^{2}\right ) x \left (x +1\right )} \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✗ |
35.185 |
|
| \(771\) |
\begin{align*}
y^{\prime }&=-\frac {-y+x^{3} \sqrt {x^{2}+y^{2}}-x^{2} \sqrt {x^{2}+y^{2}}\, y}{x} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✗ |
20.040 |
|
| \(772\) |
\begin{align*}
y^{\prime }&=\frac {1+2 \sqrt {4 x^{2} y+1}\, x^{3}+2 x^{5} \sqrt {4 x^{2} y+1}+2 x^{6} \sqrt {4 x^{2} y+1}}{2 x^{3}} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✗ |
24.187 |
|
| \(773\) |
\begin{align*}
y^{\prime }&=\frac {2 a +\sqrt {-y^{2}+4 a x}+x^{2} \sqrt {-y^{2}+4 a x}+x^{3} \sqrt {-y^{2}+4 a x}}{y} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✗ |
62.578 |
|
| \(774\) |
\begin{align*}
y^{\prime }&=-\frac {-y+x^{4} \sqrt {x^{2}+y^{2}}-x^{3} \sqrt {x^{2}+y^{2}}\, y}{x} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✗ |
19.696 |
|
| \(775\) |
\begin{align*}
y^{\prime }&=\frac {\left (x^{4}+3 x y^{2}+3 y^{2}\right ) y}{\left (x +6 y^{2}\right ) x \left (x +1\right )} \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✗ |
14.400 |
|
| \(776\) |
\begin{align*}
y^{\prime }&=-\frac {1}{-\left (y^{3}\right )^{{2}/{3}} x -\textit {\_F1} \left (y^{3}-3 \ln \left (x \right )\right ) \left (y^{3}\right )^{{1}/{3}} x} \\
\end{align*} |
[NONE] |
✗ |
✗ |
✗ |
17.750 |
|
| \(777\) |
\begin{align*}
y^{\prime }&=\frac {3 x^{3}+\sqrt {-9 x^{4}+4 y^{3}}+x^{2} \sqrt {-9 x^{4}+4 y^{3}}+x^{3} \sqrt {-9 x^{4}+4 y^{3}}}{y^{2}} \\
\end{align*} |
[NONE] |
✓ |
✓ |
✗ |
110.018 |
|
| \(778\) |
\begin{align*}
y^{\prime }&=\frac {1}{-x +\left (\frac {1}{y}+1\right ) x +\textit {\_F1} \left (\left (\frac {1}{y}+1\right ) x \right ) x^{2}-\textit {\_F1} \left (\left (\frac {1}{y}+1\right ) x \right ) x^{2} \left (\frac {1}{y}+1\right )} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✗ |
14.095 |
|
| \(779\) |
\begin{align*}
y^{\prime }&=\frac {x}{2}+\frac {1}{2}+\sqrt {x^{2}+2 x +1-4 y}+x^{2} \sqrt {x^{2}+2 x +1-4 y}+x^{3} \sqrt {x^{2}+2 x +1-4 y} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
✓ |
✗ |
42.930 |
|
| \(780\) |
\begin{align*}
y^{\prime }&=\frac {\cosh \left (x \right )}{\sinh \left (x \right )}+\textit {\_F1} \left (y-\ln \left (\sinh \left (x \right )\right )\right ) \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
✗ |
23.191 |
|
| \(781\) |
\begin{align*}
y^{\prime }&=-\frac {x}{2}+1+\sqrt {x^{2}-4 x +4 y}+x^{2} \sqrt {x^{2}-4 x +4 y}+x^{3} \sqrt {x^{2}-4 x +4 y} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
✓ |
✗ |
44.717 |
|
| \(782\) |
\begin{align*}
y^{\prime }&=\frac {1}{\sin \left (x \right )}+\textit {\_F1} \left (y-\ln \left (\sin \left (x \right )\right )+\ln \left (\cos \left (x \right )+1\right )\right ) \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
✗ |
28.737 |
|
| \(783\) |
\begin{align*}
y^{\prime }&=\frac {y \left (\ln \left (x \right )+\ln \left (y\right )-1+\ln \left (x \right )^{2} x^{2}+2 x^{2} \ln \left (y\right ) \ln \left (x \right )+x^{2} \ln \left (y\right )^{2}\right )}{x} \\
\end{align*} |
[NONE] |
✓ |
✓ |
✗ |
48.271 |
|
| \(784\) |
\begin{align*}
y^{\prime }&=\frac {y \left (\ln \left (y\right )-1+\ln \left (x \right )+x^{3} \ln \left (x \right )^{2}+2 x^{3} \ln \left (y\right ) \ln \left (x \right )+x^{3} \ln \left (y\right )^{2}\right )}{x} \\
\end{align*} |
[NONE] |
✓ |
✓ |
✗ |
46.216 |
|
| \(785\) |
\begin{align*}
y^{\prime }&=-\frac {\left (-\frac {1}{x}-\textit {\_F1} \left (y^{2}-2 x \right )\right ) x}{\sqrt {y^{2}}} \\
\end{align*} |
[NONE] |
✓ |
✓ |
✗ |
14.698 |
|
| \(786\) |
\begin{align*}
y^{\prime }&=-\frac {x}{4}+\frac {1}{4}+\sqrt {x^{2}-2 x +1+8 y}+x^{2} \sqrt {x^{2}-2 x +1+8 y}+x^{3} \sqrt {x^{2}-2 x +1+8 y} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
✓ |
✗ |
43.891 |
|
| \(787\) |
\begin{align*}
y^{\prime }&=-\frac {-x -\textit {\_F1} \left (y^{2}-2 x \right )}{\sqrt {y^{2}}\, x} \\
\end{align*} |
[NONE] |
✓ |
✓ |
✗ |
15.226 |
|
| \(788\) |
\begin{align*}
y^{\prime }&=-\frac {\left (-\frac {y \,{\mathrm e}^{\frac {1}{x}}}{x}-\textit {\_F1} \left (y \,{\mathrm e}^{\frac {1}{x}}\right )\right ) {\mathrm e}^{-\frac {1}{x}}}{x} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✗ |
13.907 |
|
| \(789\) |
\begin{align*}
y^{\prime }&=\frac {y+x \sqrt {x^{2}+y^{2}}+x^{3} \sqrt {x^{2}+y^{2}}+x^{4} \sqrt {x^{2}+y^{2}}}{x} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✗ |
21.945 |
|
| \(790\) |
\begin{align*}
y^{\prime }&=\left (\frac {\ln \left (-1+y\right ) y}{\left (1-y\right ) \ln \left (x \right ) x}-\frac {\ln \left (-1+y\right )}{\left (1-y\right ) \ln \left (x \right ) x}-f \left (x \right )\right ) \left (1-y\right ) \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✗ |
34.624 |
|
| \(791\) |
\begin{align*}
y^{\prime }&=-\frac {x}{2}-\frac {a}{2}+\sqrt {x^{2}+2 a x +a^{2}+4 y}+x^{2} \sqrt {x^{2}+2 a x +a^{2}+4 y}+x^{3} \sqrt {x^{2}+2 a x +a^{2}+4 y} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
✓ |
✗ |
45.966 |
|
| \(792\) |
\begin{align*}
y^{\prime }&=\frac {\left ({\mathrm e}^{-\frac {y}{x}} y+{\mathrm e}^{-\frac {y}{x}} x +x +x^{3}+x^{4}\right ) {\mathrm e}^{\frac {y}{x}}}{x} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✗ |
16.206 |
|
| \(793\) |
\begin{align*}
y^{\prime }&=-\frac {-y x -y+x^{5} \sqrt {x^{2}+y^{2}}-x^{4} \sqrt {x^{2}+y^{2}}\, y}{x \left (x +1\right )} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✗ |
27.311 |
|
| \(794\) |
\begin{align*}
y^{\prime }&=-\frac {-y x -y+x^{2} \sqrt {x^{2}+y^{2}}-x \sqrt {x^{2}+y^{2}}\, y}{x \left (x +1\right )} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✗ |
30.427 |
|
| \(795\) |
\begin{align*}
y^{\prime }&=-\frac {i \left (32 i x +64+64 y^{4}+32 y^{2} x^{2}+4 x^{4}+64 y^{6}+48 x^{2} y^{4}+12 y^{2} x^{4}+x^{6}\right )}{128 y} \\
\end{align*} |
[_rational] |
✗ |
✗ |
✗ |
21.545 |
|
| \(796\) |
\begin{align*}
y^{\prime }&=-\frac {\left (-8-8 y^{3}+24 y^{{3}/{2}} {\mathrm e}^{x}-18 \,{\mathrm e}^{2 x}-8 y^{{9}/{2}}+36 \,{\mathrm e}^{x} y^{3}-54 \,{\mathrm e}^{2 x} y^{{3}/{2}}+27 \,{\mathrm e}^{3 x}\right ) {\mathrm e}^{x}}{8 \sqrt {y}} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
✗ |
48.817 |
|
| \(797\) |
\begin{align*}
y^{\prime }&=-\frac {i \left (i x +1+x^{4}+2 y^{2} x^{2}+y^{4}+x^{6}+3 y^{2} x^{4}+3 x^{2} y^{4}+y^{6}\right )}{y} \\
\end{align*} |
[_rational] |
✗ |
✗ |
✗ |
19.285 |
|
| \(798\) |
\begin{align*}
y^{\prime }&=\frac {y \left (\ln \left (y\right ) x +\ln \left (y\right )-x -1+x \ln \left (x \right )+\ln \left (x \right )+x^{4} \ln \left (x \right )^{2}+2 x^{4} \ln \left (y\right ) \ln \left (x \right )+x^{4} \ln \left (y\right )^{2}\right )}{x \left (x +1\right )} \\
\end{align*} |
[NONE] |
✓ |
✓ |
✗ |
47.550 |
|
| \(799\) |
\begin{align*}
y^{\prime }&=\frac {y \left (x \ln \left (x \right )+\ln \left (x \right )+\ln \left (y\right ) x +\ln \left (y\right )-x -1+\ln \left (x \right )^{2} x +2 x \ln \left (y\right ) \ln \left (x \right )+x \ln \left (y\right )^{2}\right )}{x \left (x +1\right )} \\
\end{align*} |
[NONE] |
✓ |
✓ |
✗ |
53.818 |
|
| \(800\) |
\begin{align*}
y^{\prime }&=\frac {\left ({\mathrm e}^{-\frac {y}{x}} y x +{\mathrm e}^{-\frac {y}{x}} y+{\mathrm e}^{-\frac {y}{x}} x^{2}+{\mathrm e}^{-\frac {y}{x}} x +x \right ) {\mathrm e}^{\frac {y}{x}}}{x \left (x +1\right )} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✗ |
21.362 |
|
| \(801\) |
\begin{align*}
y^{\prime }&=\frac {\left ({\mathrm e}^{-\frac {y}{x}} y x +{\mathrm e}^{-\frac {y}{x}} y+{\mathrm e}^{-\frac {y}{x}} x^{2}+{\mathrm e}^{-\frac {y}{x}} x +x^{4}\right ) {\mathrm e}^{\frac {y}{x}}}{x \left (x +1\right )} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✗ |
16.393 |
|
| \(802\) |
\begin{align*}
y^{\prime }&=-\frac {-y+x^{2} \sqrt {x^{2}+y^{2}}-x \sqrt {x^{2}+y^{2}}\, y+x^{4} \sqrt {x^{2}+y^{2}}-x^{3} \sqrt {x^{2}+y^{2}}\, y+x^{5} \sqrt {x^{2}+y^{2}}-x^{4} \sqrt {x^{2}+y^{2}}\, y}{x} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✗ |
29.533 |
|
| \(803\) |
\begin{align*}
y^{\prime }&=\frac {y \left (\ln \left (x \right )+\ln \left (y\right )-1+\ln \left (x \right )^{2} x +2 x \ln \left (y\right ) \ln \left (x \right )+x \ln \left (y\right )^{2}+x^{3} \ln \left (x \right )^{2}+2 x^{3} \ln \left (y\right ) \ln \left (x \right )+x^{3} \ln \left (y\right )^{2}+x^{4} \ln \left (x \right )^{2}+2 x^{4} \ln \left (y\right ) \ln \left (x \right )+x^{4} \ln \left (y\right )^{2}\right )}{x} \\
\end{align*} |
[NONE] |
✓ |
✓ |
✗ |
47.025 |
|
| \(804\) |
\begin{align*}
y^{\prime }&=\frac {y \left (-1-x^{\frac {2}{1+\ln \left (x \right )}} {\mathrm e}^{\frac {2 \ln \left (x \right )^{2}}{1+\ln \left (x \right )}} x^{2}-x^{\frac {2}{1+\ln \left (x \right )}} {\mathrm e}^{\frac {2 \ln \left (x \right )^{2}}{1+\ln \left (x \right )}} x^{2} \ln \left (x \right )+x^{\frac {2}{1+\ln \left (x \right )}} {\mathrm e}^{\frac {2 \ln \left (x \right )^{2}}{1+\ln \left (x \right )}} x^{2} y+2 x^{\frac {2}{1+\ln \left (x \right )}} {\mathrm e}^{\frac {2 \ln \left (x \right )^{2}}{1+\ln \left (x \right )}} x^{2} y \ln \left (x \right )+x^{\frac {2}{1+\ln \left (x \right )}} {\mathrm e}^{\frac {2 \ln \left (x \right )^{2}}{1+\ln \left (x \right )}} x^{2} y \ln \left (x \right )^{2}\right )}{\left (1+\ln \left (x \right )\right ) x} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
101.083 |
|
| \(805\) |
\begin{align*}
y^{\prime }&=\frac {y \left (-1-x^{3} x^{\frac {2}{1+\ln \left (x \right )}} {\mathrm e}^{\frac {2 \ln \left (x \right )^{2}}{1+\ln \left (x \right )}}-x^{3} x^{\frac {2}{1+\ln \left (x \right )}} {\mathrm e}^{\frac {2 \ln \left (x \right )^{2}}{1+\ln \left (x \right )}} \ln \left (x \right )+x^{3} x^{\frac {2}{1+\ln \left (x \right )}} {\mathrm e}^{\frac {2 \ln \left (x \right )^{2}}{1+\ln \left (x \right )}} y+2 x^{3} x^{\frac {2}{1+\ln \left (x \right )}} {\mathrm e}^{\frac {2 \ln \left (x \right )^{2}}{1+\ln \left (x \right )}} y \ln \left (x \right )+x^{3} x^{\frac {2}{1+\ln \left (x \right )}} {\mathrm e}^{\frac {2 \ln \left (x \right )^{2}}{1+\ln \left (x \right )}} y \ln \left (x \right )^{2}\right )}{\left (1+\ln \left (x \right )\right ) x} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
100.014 |
|
| \(806\) |
\begin{align*}
y^{\prime }&=\frac {y \left (y^{2} x^{2}+y x \,{\mathrm e}^{x}+{\mathrm e}^{2 x}\right ) {\mathrm e}^{-2 x} \left (x -1\right )}{x} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘], _Abel] |
✓ |
✓ |
✗ |
38.797 |
|
| \(807\) |
\begin{align*}
y^{\prime \prime }-\left (x^{2}+a \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
13.593 |
|
| \(808\) |
\begin{align*}
y^{\prime \prime }-\left (a^{2} x^{2 n}-1\right ) y&=0 \\
\end{align*} |
[_Titchmarsh] |
✗ |
✗ |
✗ |
4.743 |
|
| \(809\) |
\begin{align*}
y^{\prime \prime }+\left (a \,x^{2 c}+b \,x^{c -1}\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
5.431 |
|
| \(810\) |
\begin{align*}
y^{\prime \prime }-\left (4 a^{2} b^{2} x^{2} {\mathrm e}^{2 b \,x^{2}}-1\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
5.061 |
|
| \(811\) |
\begin{align*}
y^{\prime \prime }+\left (a \,{\mathrm e}^{2 x}+b \,{\mathrm e}^{x}+c \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
4.966 |
|
| \(812\) |
\begin{align*}
y^{\prime \prime }+\left (a \cosh \left (x \right )^{2}+b \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
10.571 |
|
| \(813\) |
\begin{align*}
y^{\prime \prime }+\left (a \cos \left (2 x \right )+b \right ) y&=0 \\
\end{align*} |
[_ellipsoidal] |
✓ |
✓ |
✗ |
20.413 |
|
| \(814\) |
\begin{align*}
y^{\prime \prime }+\left (a \cos \left (x \right )^{2}+b \right ) y&=0 \\
\end{align*} |
[_ellipsoidal] |
✓ |
✓ |
✗ |
20.946 |
|
| \(815\) |
\begin{align*}
y^{\prime \prime }-\left (\frac {m \left (m -1\right )}{\cos \left (x \right )^{2}}+\frac {n \left (n -1\right )}{\sin \left (x \right )^{2}}+a \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
34.534 |
|
| \(816\) |
\begin{align*}
y^{\prime \prime }-\left (n \left (n +1\right ) k^{2} \operatorname {JacobiSN}\left (x , k\right )^{2}+b \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
4.487 |
|
| \(817\) |
\begin{align*}
y^{\prime \prime }-\left (f \left (x \right )^{2}+f^{\prime }\left (x \right )\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
11.494 |
|
| \(818\) |
\begin{align*}
y^{\prime \prime }+a y^{\prime }-\left (b^{2} x^{2}+c \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
29.707 |
|
| \(819\) |
\begin{align*}
y^{\prime \prime }+2 a y^{\prime }+f \left (x \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
28.279 |
|
| \(820\) |
\begin{align*}
y^{\prime \prime }+y^{\prime } x +\left (n +1\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
31.793 |
|
| \(821\) |
\begin{align*}
y^{\prime \prime }+y^{\prime } x -n y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
23.453 |
|
| \(822\) |
\begin{align*}
-a y-y^{\prime } x +y^{\prime \prime }&=0 \\
\end{align*} |
[_Hermite] |
✓ |
✓ |
✗ |
31.607 |
|
| \(823\) |
\begin{align*}
y^{\prime \prime }-2 y^{\prime } x +a y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
23.635 |
|
| \(824\) |
\begin{align*}
y^{\prime \prime }-4 y^{\prime } x +\left (3 x^{2}+2 n -1\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
32.147 |
|
| \(825\) |
\begin{align*}
b y+a x y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
32.754 |
|
| \(826\) |
\begin{align*}
y^{\prime \prime }+\left (a x +b \right ) y^{\prime }+\left (c x +d \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
32.010 |
|
| \(827\) |
\begin{align*}
y^{\prime \prime }+\left (a x +b \right ) y^{\prime }+\left (\operatorname {a1} \,x^{2}+\operatorname {b1} x +\operatorname {c1} \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
26.684 |
|
| \(828\) |
\begin{align*}
y^{\prime \prime }+a \,x^{-1+q} y^{\prime }+b \,x^{q -2} y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
18.830 |
|
| \(829\) |
\begin{align*}
y^{\prime \prime }+2 n y^{\prime } \cot \left (x \right )+\left (-a^{2}+n^{2}\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
32.326 |
|
| \(830\) |
\begin{align*}
y^{\prime \prime }+\cot \left (x \right ) y^{\prime }+v \left (v +1\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
26.433 |
|
| \(831\) |
\begin{align*}
b y+a \tan \left (x \right ) y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
31.888 |
|
| \(832\) |
\begin{align*}
y^{\prime \prime }-\left (\frac {f^{\prime }\left (x \right )}{f \left (x \right )}+2 a \right ) y^{\prime }+\left (\frac {a f^{\prime }\left (x \right )}{f \left (x \right )}+a^{2}-b^{2} f \left (x \right )^{2}\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
39.857 |
|
| \(833\) |
\begin{align*}
y^{\prime \prime }-\left (\frac {2 f^{\prime }\left (x \right )}{f \left (x \right )}+\frac {g^{\prime \prime }\left (x \right )}{g^{\prime }\left (x \right )}-\frac {g^{\prime }\left (x \right )}{g \left (x \right )}\right ) y^{\prime }+\left (\frac {f^{\prime }\left (x \right ) \left (\frac {2 f^{\prime }\left (x \right )}{f \left (x \right )}+\frac {g^{\prime \prime }\left (x \right )}{g^{\prime }\left (x \right )}-\frac {g^{\prime }\left (x \right )}{g \left (x \right )}\right )}{f \left (x \right )}-\frac {f^{\prime \prime }\left (x \right )}{f \left (x \right )}-\frac {v^{2} {g^{\prime }\left (x \right )}^{2}}{g \left (x \right )^{2}}+{g^{\prime }\left (x \right )}^{2}\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
13.449 |
|
| \(834\) |
\begin{align*}
y^{\prime \prime }-\left (\frac {g^{\prime \prime }\left (x \right )}{g^{\prime }\left (x \right )}+\frac {\left (2 v -1\right ) g^{\prime }\left (x \right )}{g \left (x \right )}+\frac {2 h^{\prime }\left (x \right )}{h \left (x \right )}\right ) y^{\prime }+\left (\frac {h^{\prime }\left (x \right ) \left (\frac {g^{\prime \prime }\left (x \right )}{g^{\prime }\left (x \right )}+\frac {\left (2 v -1\right ) g^{\prime }\left (x \right )}{g \left (x \right )}+\frac {2 h^{\prime }\left (x \right )}{h \left (x \right )}\right )}{h \left (x \right )}-\frac {h^{\prime \prime }\left (x \right )}{h \left (x \right )}+{g^{\prime }\left (x \right )}^{2}\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
13.971 |
|
| \(835\) |
\begin{align*}
4 y^{\prime \prime }-\left (x^{2}+a \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
17.780 |
|
| \(836\) |
\begin{align*}
a y^{\prime \prime }-\left (a b +c +x \right ) y^{\prime }+\left (b \left (x +c \right )+d \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
37.395 |
|
| \(837\) |
\begin{align*}
\left (a +x \right ) y+y^{\prime \prime } x&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
11.605 |
|
| \(838\) |
\begin{align*}
y^{\prime \prime } x +y^{\prime }+\left (a +x \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
18.844 |
|
| \(839\) |
\begin{align*}
y^{\prime \prime } x -y^{\prime }+x^{3} \left ({\mathrm e}^{x^{2}}-v^{2}\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
14.057 |
|
| \(840\) |
\begin{align*}
y^{\prime \prime } x +\left (x +b \right ) y^{\prime }+a y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
28.689 |
|
| \(841\) |
\begin{align*}
y^{\prime \prime } x +\left (x +a +b \right ) y^{\prime }+a y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
30.183 |
|
| \(842\) |
\begin{align*}
y^{\prime \prime } x -y^{\prime } x -a y&=0 \\
\end{align*} |
[_Laguerre] |
✓ |
✓ |
✗ |
23.803 |
|
| \(843\) |
\begin{align*}
y^{\prime \prime } x +\left (b -x \right ) y^{\prime }-a y&=0 \\
\end{align*} |
[_Laguerre] |
✓ |
✓ |
✗ |
28.610 |
|
| \(844\) |
\begin{align*}
y^{\prime \prime } x -2 \left (x -1\right ) y^{\prime }-y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
26.232 |
|
| \(845\) |
\begin{align*}
y^{\prime \prime } x -\left (3 x -2\right ) y^{\prime }-\left (2 x -3\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
26.640 |
|
| \(846\) |
\begin{align*}
y^{\prime \prime } x +\left (a x +b +n \right ) y^{\prime }+n a y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
30.866 |
|
| \(847\) |
\begin{align*}
y^{\prime \prime } x -\left (a +b \right ) \left (x +1\right ) y^{\prime }+a b x y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
31.915 |
|
| \(848\) |
\begin{align*}
\left (a b x +a n +b m \right ) y+\left (m +n +\left (a +b \right ) x \right ) y^{\prime }+y^{\prime \prime } x&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
34.122 |
|
| \(849\) |
\begin{align*}
y^{\prime \prime } x +\left (a x +b \right ) y^{\prime }+\left (c x +d \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
49.343 |
|
| \(850\) |
\begin{align*}
y^{\prime \prime } x -2 \left (x^{2}-a \right ) y^{\prime }+2 n x y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
85.494 |
|
| \(851\) |
\begin{align*}
2 y^{\prime \prime } x -\left (x -1\right ) y^{\prime }+a y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
19.286 |
|
| \(852\) |
\begin{align*}
2 y^{\prime \prime } x -\left (2 x -1\right ) y^{\prime }+a y&=0 \\
\end{align*} |
[_Laguerre] |
✓ |
✓ |
✗ |
19.262 |
|
| \(853\) |
\begin{align*}
4 y^{\prime \prime } x -\left (a +x \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
7.218 |
|
| \(854\) |
\begin{align*}
4 y^{\prime \prime } x +4 y-\left (2+x \right ) y+l y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
30.104 |
|
| \(855\) |
\begin{align*}
4 y^{\prime \prime } x +4 m y^{\prime }-\left (x -2 m -4 n \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
21.899 |
|
| \(856\) |
\begin{align*}
16 y^{\prime \prime } x +8 y^{\prime }-\left (a +x \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
17.291 |
|
| \(857\) |
\begin{align*}
5 \left (a x +b \right ) y^{\prime \prime }+8 a y^{\prime }+c \left (a x +b \right )^{{1}/{5}} y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
53.444 |
|
| \(858\) |
\begin{align*}
2 a x y^{\prime \prime }+\left (b x +a \right ) y^{\prime }+c y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
41.835 |
|
| \(859\) |
\begin{align*}
2 a x y^{\prime \prime }+\left (b x +3 a \right ) y^{\prime }+c y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
42.045 |
|
| \(860\) |
\begin{align*}
\left (\operatorname {a2} x +\operatorname {b2} \right ) y^{\prime \prime }+\left (\operatorname {a1} x +\operatorname {b1} \right ) y^{\prime }+\left (\operatorname {a0} x +\operatorname {b0} \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
70.527 |
|
| \(861\) |
\begin{align*}
x^{2} y^{\prime \prime }+\left (a \,x^{2}+b x +c \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
9.475 |
|
| \(862\) |
\begin{align*}
x^{2} y^{\prime \prime }+\frac {y}{\ln \left (x \right )}-x \,{\mathrm e}^{x} \left (2+x \ln \left (x \right )\right )&=0 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✗ |
4.701 |
|
| \(863\) |
\begin{align*}
x^{2} y^{\prime \prime }+a y^{\prime }-y x&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
40.619 |
|
| \(864\) |
\begin{align*}
x^{2} y^{\prime \prime }+2 y^{\prime } x +\left (l \,x^{2}+a x -n \left (n +1\right )\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
46.532 |
|
| \(865\) |
\begin{align*}
x^{2} y^{\prime \prime }+2 \left (x -1\right ) y^{\prime }+a y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
44.264 |
|
| \(866\) |
\begin{align*}
x^{2} y^{\prime \prime }+2 \left (a +x \right ) y^{\prime }-b \left (b -1\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
39.163 |
|
| \(867\) |
\begin{align*}
x^{2} y^{\prime \prime }+\left (a x +b \right ) y^{\prime }+c y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
40.425 |
|
| \(868\) |
\begin{align*}
x^{2} y^{\prime \prime }+x^{2} y^{\prime }+\left (a x +b \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
18.973 |
|
| \(869\) |
\begin{align*}
-y+x \left (x +3\right ) y^{\prime }+x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
54.825 |
|
| \(870\) |
\begin{align*}
x^{2} y^{\prime \prime }-\left (x^{2}-2 x \right ) y^{\prime }-\left (a +x \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
64.221 |
|
| \(871\) |
\begin{align*}
x^{2} y^{\prime \prime }+2 x^{2} y^{\prime }-v \left (v -1\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
21.451 |
|
| \(872\) |
\begin{align*}
x^{2} y^{\prime \prime }+a \,x^{2} y^{\prime }+f \left (x \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
24.577 |
|
| \(873\) |
\begin{align*}
x^{2} y^{\prime \prime }+\left (2 a x +b \right ) x y^{\prime }+\left (a b x +c \,x^{2}+d \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
65.575 |
|
| \(874\) |
\begin{align*}
x^{2} y^{\prime \prime }+\left (a x +b \right ) y^{\prime } x +\left (\operatorname {a1} \,x^{2}+\operatorname {b1} x +\operatorname {c1} \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
15.791 |
|
| \(875\) |
\begin{align*}
x^{2} y^{\prime \prime }-2 x \left (x^{2}-a \right ) y^{\prime }+\left (2 n \,x^{2}+\left (\left (-1\right )^{n}-1\right ) a \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
11.955 |
|
| \(876\) |
\begin{align*}
x^{2} y^{\prime \prime }+\left (a \,x^{2}+b \right ) x y^{\prime }+f \left (x \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
11.692 |
|
| \(877\) |
\begin{align*}
x^{2} y^{\prime \prime }+\left (x^{3}+1\right ) x y^{\prime }-y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
11.113 |
|
| \(878\) |
\begin{align*}
x^{2} y^{\prime \prime }+\left (-x^{4}+\left (2 n +2 a +1\right ) x^{2}+\left (-1\right )^{n} a -a^{2}\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
3.756 |
|
| \(879\) |
\begin{align*}
x^{2} y^{\prime \prime }+\left (a \,x^{n}+b \right ) y^{\prime } x +\left (\operatorname {a1} \,x^{2 n}+\operatorname {b1} \,x^{n}+\operatorname {c1} \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
10.877 |
|
| \(880\) |
\begin{align*}
x^{2} y^{\prime \prime }-\left (2 x^{2} \tan \left (x \right )-x \right ) y^{\prime }-\left (a +x \tan \left (x \right )\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
32.892 |
|
| \(881\) |
\begin{align*}
x^{2} y^{\prime \prime }+\left (2 x^{2} \cot \left (x \right )+x \right ) y^{\prime }+\left (x \cot \left (x \right )+a \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
31.777 |
|
| \(882\) |
\begin{align*}
x^{2} y^{\prime \prime }+2 x f \left (x \right ) y^{\prime }+\left (f^{\prime }\left (x \right ) x +f \left (x \right )^{2}-f \left (x \right )+a \,x^{2}+b x +c \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
8.687 |
|
| \(883\) |
\begin{align*}
x^{2} y^{\prime \prime }+2 x^{2} f \left (x \right ) y^{\prime }+\left (x^{2} \left (f^{\prime }\left (x \right )+f \left (x \right )^{2}+a \right )-v \left (v -1\right )\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
6.931 |
|
| \(884\) |
\begin{align*}
x^{2} y^{\prime \prime }+\left (x -2 x^{2} f \left (x \right )\right ) y^{\prime }+\left (x^{2} \left (1+f \left (x \right )^{2}-f^{\prime }\left (x \right )\right )-f \left (x \right ) x -v^{2}\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
12.064 |
|
| \(885\) |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime \prime }+2 y^{\prime } x -v \left (v -1\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
19.614 |
|
| \(886\) |
\begin{align*}
\left (x^{2}-1\right ) y^{\prime \prime }-v \left (v +1\right ) y&=0 \\
\end{align*} |
[_Gegenbauer] |
✓ |
✓ |
✓ |
2.639 |
|
| \(887\) |
\begin{align*}
\left (x^{2}-1\right ) y^{\prime \prime }-n \left (n +1\right ) y+\frac {\left (n +1\right ) \operatorname {LegendreP}\left (n +1, x\right )-\left (n +1\right ) x \operatorname {LegendreP}\left (n , x\right )}{x^{2}-1}&=0 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✗ |
3.374 |
|
| \(888\) |
\begin{align*}
\left (x^{2}-1\right ) y^{\prime \prime }+y^{\prime } x +f \left (x \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
70.575 |
|
| \(889\) |
\begin{align*}
\left (x^{2}-1\right ) y^{\prime \prime }+2 y^{\prime } x -l y&=0 \\
\end{align*} |
[_Gegenbauer] |
✓ |
✓ |
✗ |
59.760 |
|
| \(890\) |
\begin{align*}
\left (x^{2}-1\right ) y^{\prime \prime }+2 y^{\prime } x -v \left (v +1\right ) y&=0 \\
\end{align*} |
[_Gegenbauer] |
✓ |
✓ |
✗ |
80.994 |
|
| \(891\) |
\begin{align*}
\left (x^{2}-1\right ) y^{\prime \prime }-2 y^{\prime } x -\left (v +2\right ) \left (v -1\right ) y&=0 \\
\end{align*} |
[_Gegenbauer] |
✓ |
✓ |
✗ |
653.674 |
|
| \(892\) |
\begin{align*}
\left (x^{2}-1\right ) y^{\prime \prime }+2 \left (n +1\right ) x y^{\prime }-\left (v +n +1\right ) \left (v -n \right ) y&=0 \\
\end{align*} |
[_Gegenbauer] |
✓ |
✓ |
✗ |
44.149 |
|
| \(893\) |
\begin{align*}
\left (x^{2}-1\right ) y^{\prime \prime }-2 \left (n -1\right ) x y^{\prime }-\left (v -n +1\right ) \left (v +n \right ) y&=0 \\
\end{align*} |
[_Gegenbauer] |
✓ |
✓ |
✗ |
47.805 |
|
| \(894\) |
\begin{align*}
\left (x^{2}-1\right ) y^{\prime \prime }-2 \left (v -1\right ) x y^{\prime }-2 v y&=0 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✗ |
0.026 |
|
| \(895\) |
\begin{align*}
\left (x^{2}-1\right ) y^{\prime \prime }+a x y^{\prime }+\left (b \,x^{2}+c x +d \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
36.414 |
|
| \(896\) |
\begin{align*}
\left (x^{2}-1\right ) y^{\prime \prime }+\left (a x +b \right ) y^{\prime }+c y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
105.208 |
|
| \(897\) |
\begin{align*}
x \left (x +1\right ) y^{\prime \prime }+\left (a x +b \right ) y^{\prime }+c y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
65.870 |
|
| \(898\) |
\begin{align*}
x \left (x -1\right ) y^{\prime \prime }+\left (2 x -1\right ) y^{\prime }-v \left (v +1\right ) y&=0 \\
\end{align*} |
[_Jacobi] |
✓ |
✓ |
✗ |
56.886 |
|
| \(899\) |
\begin{align*}
x \left (x -1\right ) y^{\prime \prime }+\left (a x +b \right ) y^{\prime }+c y&=0 \\
\end{align*} |
[_Jacobi] |
✓ |
✓ |
✗ |
66.313 |
|
| \(900\) |
\begin{align*}
x \left (x -1\right ) y^{\prime \prime }+\left (\left (1+a \right ) x +b \right ) y^{\prime }-l y&=0 \\
\end{align*} |
[_Jacobi] |
✓ |
✓ |
✗ |
77.956 |
|
| \(901\) |
\begin{align*}
x \left (2+x \right ) y^{\prime \prime }+2 \left (n +1+\left (n +1-2 l \right ) x -l \,x^{2}\right ) y^{\prime }+\left (2 l \left (p -n -1\right ) x +2 p l +m \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
124.468 |
|
| \(902\) |
\begin{align*}
\left (x -1\right ) \left (x -2\right ) y^{\prime \prime }-\left (2 x -3\right ) y^{\prime }+y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
416.378 |
|
| \(903\) |
\begin{align*}
2 x \left (x -1\right ) y^{\prime \prime }+\left (2 x -1\right ) y^{\prime }+\left (a x +b \right ) y&=0 \\
\end{align*} |
[_Jacobi] |
✓ |
✓ |
✗ |
32.771 |
|
| \(904\) |
\begin{align*}
2 x \left (x -1\right ) y^{\prime \prime }+\left (\left (2 v +5\right ) x -2 v -3\right ) y^{\prime }+\left (v +1\right ) y&=0 \\
\end{align*} |
[_Jacobi] |
✓ |
✓ |
✗ |
61.493 |
|
| \(905\) |
\begin{align*}
4 x^{2} y^{\prime \prime }-\left (-4 k x +4 m^{2}+x^{2}-1\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
2.279 |
|
| \(906\) |
\begin{align*}
4 x^{2} y^{\prime \prime }+4 y^{\prime } x +\left (-x^{2}+2 \left (1-m +2 l \right ) x -m^{2}+1\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
29.909 |
|
| \(907\) |
\begin{align*}
4 x^{2} y^{\prime \prime }+4 y^{\prime } x +f \left (x \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
4.931 |
|
| \(908\) |
\begin{align*}
x \left (4 x -1\right ) y^{\prime \prime }+\left (\left (4 a +2\right ) x -a \right ) y^{\prime }+a \left (-1+a \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
57.586 |
|
| \(909\) |
\begin{align*}
48 x \left (x -1\right ) y^{\prime \prime }+\left (152 x -40\right ) y^{\prime }+53 y&=0 \\
\end{align*} |
[_Jacobi] |
✓ |
✓ |
✗ |
26.875 |
|
| \(910\) |
\begin{align*}
144 x \left (x -1\right ) y^{\prime \prime }+\left (120 x -48\right ) y^{\prime }+y&=0 \\
\end{align*} |
[_Jacobi] |
✓ |
✓ |
✗ |
46.718 |
|
| \(911\) |
\begin{align*}
144 x \left (x -1\right ) y^{\prime \prime }+\left (168 x -96\right ) y^{\prime }+y&=0 \\
\end{align*} |
[_Jacobi] |
✓ |
✓ |
✗ |
46.113 |
|
| \(912\) |
\begin{align*}
a \,x^{2} y^{\prime \prime }+b x y^{\prime }+\left (c \,x^{2}+d x +f \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
10.853 |
|
| \(913\) |
\begin{align*}
\operatorname {a2} \,x^{2} y^{\prime \prime }+\left (\operatorname {a1} \,x^{2}+\operatorname {b1} x \right ) y^{\prime }+\left (\operatorname {a0} \,x^{2}+\operatorname {b0} x +\operatorname {c0} \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
10.870 |
|
| \(914\) |
\begin{align*}
\operatorname {A2} \left (a x +b \right )^{2} y^{\prime \prime }+\operatorname {A1} \left (a x +b \right ) y^{\prime }+\operatorname {A0} \left (a x +b \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
78.342 |
|
| \(915\) |
\begin{align*}
\left (a \,x^{2}+b x +c \right ) y^{\prime \prime }+\left (d x +f \right ) y^{\prime }+g y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
130.063 |
|
| \(916\) |
\begin{align*}
-y+2 y^{\prime } x +x^{3} y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
21.030 |
|
| \(917\) |
\begin{align*}
x^{3} y^{\prime \prime }+x^{2} y^{\prime }+\left (a \,x^{2}+b x +a \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✗ |
✗ |
29.631 |
|
| \(918\) |
\begin{align*}
x^{3} y^{\prime \prime }-\left (x^{2}-1\right ) y^{\prime }+y x&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
32.918 |
|
| \(919\) |
\begin{align*}
x \left (x^{2}+1\right ) y^{\prime \prime }+\left (2 x^{2}+1\right ) y^{\prime }-v \left (v +1\right ) x y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
103.791 |
|
| \(920\) |
\begin{align*}
x \left (x^{2}+1\right ) y^{\prime \prime }+\left (2 \left (n +1\right ) x^{2}+2 n +1\right ) y^{\prime }-\left (v -n \right ) \left (v +n +1\right ) x y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
123.387 |
|
| \(921\) |
\begin{align*}
x \left (x^{2}+1\right ) y^{\prime \prime }-\left (2 \left (n -1\right ) x^{2}+2 n -1\right ) y^{\prime }+\left (v +n \right ) \left (-v +n -1\right ) x y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
126.481 |
|
| \(922\) |
\begin{align*}
x \left (x^{2}-1\right ) y^{\prime \prime }+\left (x^{2}-1\right ) y^{\prime }-y x&=0 \\
\end{align*} |
[[_elliptic, _class_II]] |
✓ |
✓ |
✗ |
186.239 |
|
| \(923\) |
\begin{align*}
x \left (x^{2}-1\right ) y^{\prime \prime }+\left (3 x^{2}-1\right ) y^{\prime }+y x&=0 \\
\end{align*} |
[[_elliptic, _class_I]] |
✓ |
✓ |
✗ |
65.150 |
|
| \(924\) |
\begin{align*}
x \left (x^{2}-1\right ) y^{\prime \prime }+\left (a \,x^{2}+b \right ) y^{\prime }+c x y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
112.510 |
|
| \(925\) |
\begin{align*}
y^{\prime \prime }&=-\frac {\left (\left (a +b +1\right ) x +\alpha +\beta -1\right ) y^{\prime }}{x \left (x -1\right )}-\frac {\left (a b x -\alpha \beta \right ) y}{x^{2} \left (x -1\right )} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
118.779 |
|
| \(926\) |
\begin{align*}
y^{\prime \prime }&=\frac {2 y^{\prime }}{x \left (x -2\right )}-\frac {y}{x^{2} \left (x -2\right )} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
93.665 |
|
| \(927\) |
\begin{align*}
y^{\prime \prime }&=-\frac {\left (\left (\alpha +\beta +1\right ) x^{2}-\left (\alpha +\beta +1+a \left (\gamma +\delta \right )-\delta \right ) x +a \gamma \right ) y^{\prime }}{x \left (x -1\right ) \left (x -a \right )}-\frac {\left (\alpha \beta x -q \right ) y}{x \left (x -1\right ) \left (x -a \right )} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
340.567 |
|
| \(928\) |
\begin{align*}
y^{\prime \prime }&=-\frac {\left (A \,x^{2}+B x +C \right ) y^{\prime }}{\left (x -a \right ) \left (-b +x \right ) \left (x -c \right )}-\frac {\left (\operatorname {DD} x +E \right ) y}{\left (x -a \right ) \left (-b +x \right ) \left (x -c \right )} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
370.119 |
|
| \(929\) |
\begin{align*}
y^{\prime \prime }&=-\frac {\left (3 x -1\right ) y^{\prime }}{2 x \left (x -1\right )}+\frac {v \left (v +1\right ) y}{4 x^{2}} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
20.123 |
|
| \(930\) |
\begin{align*}
y^{\prime \prime }&=-\frac {\left (\left (1+a \right ) x -1\right ) y^{\prime }}{x \left (x -1\right )}-\frac {\left (\left (a^{2}-b^{2}\right ) x +c^{2}\right ) y}{4 x^{2} \left (x -1\right )} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
63.130 |
|
| \(931\) |
\begin{align*}
y^{\prime \prime }&=-\frac {\left (3 x -1\right ) y^{\prime }}{2 x \left (x -1\right )}-\frac {\left (a x +b \right ) y}{4 x \left (x -1\right )^{2}} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
12.336 |
|
| \(932\) |
\begin{align*}
y^{\prime \prime }&=-\frac {\left (a \left (b +2\right ) x^{2}+\left (c -d +1\right ) x \right ) y^{\prime }}{\left (a x +1\right ) x^{2}}-\frac {\left (a b x -c d \right ) y}{\left (a x +1\right ) x^{2}} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
168.604 |
|
| \(933\) |
\begin{align*}
y^{\prime \prime }&=-\frac {\left (2 a x +b \right ) y^{\prime }}{x \left (a x +b \right )}-\frac {\left (a v x -b \right ) y}{\left (a x +b \right ) x^{2}}+A x \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✗ |
134.572 |
|
| \(934\) |
\begin{align*}
y^{\prime \prime }&=-\frac {\left (x^{2} a \left (1-a \right )-b \left (x +b \right )\right ) y}{x^{4}} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
3.098 |
|
| \(935\) |
\begin{align*}
y^{\prime \prime }&=-\frac {\left ({\mathrm e}^{\frac {2}{x}}-v^{2}\right ) y}{x^{4}} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
2.242 |
|
| \(936\) |
\begin{align*}
y^{\prime \prime }&=-\frac {y^{\prime }}{x}-\frac {\left (b \,x^{2}+a \left (x^{4}+1\right )\right ) y}{x^{4}} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
7.069 |
|
| \(937\) |
\begin{align*}
y^{\prime \prime }&=-\frac {\left (x^{2}+1\right ) y^{\prime }}{x^{3}}-\frac {y}{x^{4}} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
16.645 |
|
| \(938\) |
\begin{align*}
y^{\prime \prime }&=-\frac {\left (2 x^{2}+1\right ) y^{\prime }}{x \left (x^{2}+1\right )}-\frac {\left (-v \left (v +1\right ) x^{2}-n^{2}\right ) y}{x^{2} \left (x^{2}+1\right )} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
80.903 |
|
| \(939\) |
\begin{align*}
y^{\prime \prime }&=-\frac {\left (a \,x^{2}+a -1\right ) y^{\prime }}{x \left (x^{2}+1\right )}-\frac {\left (b \,x^{2}+c \right ) y}{x^{2} \left (x^{2}+1\right )} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
114.830 |
|
| \(940\) |
\begin{align*}
y^{\prime \prime }&=-\frac {2 x y^{\prime }}{x^{2}-1}-\frac {v \left (v +1\right ) y}{x^{2} \left (x^{2}-1\right )} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
27.822 |
|
| \(941\) |
\begin{align*}
y^{\prime \prime }&=-\frac {2 x y^{\prime }}{x^{2}-1}+\frac {v \left (v +1\right ) y}{x^{2}} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
37.349 |
|
| \(942\) |
\begin{align*}
x^{2} \left (x^{2}-1\right ) y^{\prime \prime }-2 x^{3} y^{\prime }-\left (\left (a -n \right ) \left (a +n +1\right ) x^{2} \left (x^{2}-1\right )+2 a \,x^{2}+n \left (n +1\right ) \left (x^{2}-1\right )\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✗ |
✗ |
157.890 |
|
| \(943\) |
\begin{align*}
y^{\prime \prime }&=-\frac {\left (a \,x^{2}+a -2\right ) y^{\prime }}{x \left (x^{2}-1\right )}-\frac {b y}{x^{2}} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
119.489 |
|
| \(944\) |
\begin{align*}
y^{\prime \prime }&=\frac {\left (2 b c \,x^{c} \left (x^{2}-1\right )+2 \left (-1+a \right ) x^{2}-2 a \right ) y^{\prime }}{x \left (x^{2}-1\right )}-\frac {\left (b^{2} c^{2} x^{2 c} \left (x^{2}-1\right )+b c \,x^{c +2} \left (2 a -c -1\right )-b c \,x^{c} \left (2 a -c +1\right )+x^{2} \left (a \left (-1+a \right )-v \left (v +1\right )\right )-a \left (1+a \right )\right ) y}{x^{2} \left (x^{2}-1\right )} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
413.648 |
|
| \(945\) |
\begin{align*}
y^{\prime \prime }&=-\frac {2 x y^{\prime }}{x^{2}+1}-\frac {\left (a^{2} \left (x^{2}+1\right )^{2}-n \left (n +1\right ) \left (x^{2}+1\right )+m^{2}\right ) y}{\left (x^{2}+1\right )^{2}} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
105.165 |
|
| \(946\) |
\begin{align*}
y^{\prime \prime }&=-\frac {a x y^{\prime }}{x^{2}+1}-\frac {b y}{\left (x^{2}+1\right )^{2}} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
74.318 |
|
| \(947\) |
\begin{align*}
y^{\prime \prime }&=-\frac {2 x y^{\prime }}{x^{2}-1}-\frac {\left (-a^{2}-\lambda \left (x^{2}-1\right )\right ) y}{\left (x^{2}-1\right )^{2}} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
66.071 |
|
| \(948\) |
\begin{align*}
y^{\prime \prime }&=-\frac {2 x y^{\prime }}{x^{2}-1}-\frac {\left (\left (x^{2}-1\right ) \left (a \,x^{2}+b x +c \right )-k^{2}\right ) y}{\left (x^{2}-1\right )^{2}} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
91.480 |
|
| \(949\) |
\begin{align*}
y^{\prime \prime }&=-\frac {2 x y^{\prime }}{x^{2}-1}-\frac {\left (-a^{2} \left (x^{2}-1\right )^{2}-n \left (n +1\right ) \left (x^{2}-1\right )-m^{2}\right ) y}{\left (x^{2}-1\right )^{2}} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
88.433 |
|
| \(950\) |
\begin{align*}
y^{\prime \prime }&=\frac {2 x \left (2 a -1\right ) y^{\prime }}{x^{2}-1}-\frac {\left (x^{2} \left (2 a \left (2 a -1\right )-v \left (v +1\right )\right )+2 a +v \left (v +1\right )\right ) y}{\left (x^{2}-1\right )^{2}} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
131.747 |
|
| \(951\) |
\begin{align*}
y^{\prime \prime }&=-\frac {2 x \left (n +1-2 a \right ) y^{\prime }}{x^{2}-1}-\frac {\left (4 a \,x^{2} \left (a -n \right )-\left (x^{2}-1\right ) \left (2 a +\left (v -n \right ) \left (v +n +1\right )\right )\right ) y}{\left (x^{2}-1\right )^{2}} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
169.271 |
|
| \(952\) |
\begin{align*}
y^{\prime \prime }&=-\frac {\left (-x^{2} \left (a^{2}-1\right )+2 \left (a +3\right ) b x -b^{2}\right ) y}{4 x^{2}} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
3.299 |
|
| \(953\) |
\begin{align*}
y^{\prime \prime }&=-\frac {\left (3 x -1\right ) y^{\prime }}{2 x \left (x -1\right )}-\frac {\left (v \left (v +1\right ) \left (x -1\right )-a^{2} x \right ) y}{4 x^{2} \left (x -1\right )^{2}} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
36.827 |
|
| \(954\) |
\begin{align*}
y^{\prime \prime }&=-\frac {\left (3 x -1\right ) y^{\prime }}{2 x \left (x -1\right )}-\frac {\left (-v \left (v +1\right ) \left (x -1\right )^{2}-4 n^{2} x \right ) y}{4 x^{2} \left (x -1\right )^{2}} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
40.006 |
|
| \(955\) |
\begin{align*}
y^{\prime \prime }&=-\frac {b x y^{\prime }}{\left (x^{2}-1\right ) a}-\frac {\left (c \,x^{2}+d x +e \right ) y}{a \left (x^{2}-1\right )^{2}} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
106.168 |
|
| \(956\) |
\begin{align*}
y^{\prime \prime }&=-\frac {\left (b \,x^{2}+c x +d \right ) y}{a \,x^{2} \left (x -1\right )^{2}} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
5.953 |
|
| \(957\) |
\begin{align*}
y^{\prime \prime }&=-\frac {\left (3 x^{2}-1\right ) y^{\prime }}{\left (x^{2}-1\right ) x}-\frac {\left (x^{2}-1-\left (2 v +1\right )^{2}\right ) y}{\left (x^{2}-1\right )^{2}} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
127.919 |
|
| \(958\) |
\begin{align*}
y^{\prime \prime }&=-\frac {\left (\left (1-4 a \right ) x^{2}-1\right ) y^{\prime }}{x \left (x^{2}-1\right )}-\frac {\left (\left (-v^{2}+x^{2}\right ) \left (x^{2}-1\right )^{2}+4 a \left (1+a \right ) x^{4}-2 a \,x^{2} \left (x^{2}-1\right )\right ) y}{x^{2} \left (x^{2}-1\right )^{2}} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✗ |
✗ |
209.754 |
|
| \(959\) |
\begin{align*}
y^{\prime \prime }&=-\left (\frac {1-\operatorname {a1} -\operatorname {b1}}{x -\operatorname {c1}}+\frac {1-\operatorname {a2} -\operatorname {b2}}{x -\operatorname {c2}}+\frac {1-\operatorname {a3} -\operatorname {b3}}{x -\operatorname {c3}}\right ) y^{\prime }-\frac {\left (\frac {\operatorname {a1} \operatorname {b1} \left (\operatorname {c1} -\operatorname {c3} \right ) \left (\operatorname {c1} -\operatorname {c2} \right )}{x -\operatorname {c1}}+\frac {\operatorname {a2} \operatorname {b2} \left (\operatorname {c2} -\operatorname {c1} \right ) \left (\operatorname {c2} -\operatorname {c3} \right )}{x -\operatorname {c2}}+\frac {\operatorname {a3} \operatorname {b3} \left (\operatorname {c3} -\operatorname {c2} \right ) \left (\operatorname {c3} -\operatorname {c1} \right )}{x -\operatorname {c3}}\right ) y}{\left (x -\operatorname {c1} \right ) \left (x -\operatorname {c2} \right ) \left (x -\operatorname {c3} \right )} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
1052.560 |
|
| \(960\) |
\begin{align*}
y^{\prime \prime }&=-\left (\frac {\left (1-\operatorname {al1} -\operatorname {bl1} \right ) \operatorname {b1}}{\operatorname {b1} x -\operatorname {a1}}+\frac {\left (1-\operatorname {al2} -\operatorname {bl2} \right ) \operatorname {b2}}{\operatorname {b2} x -\operatorname {a2}}+\frac {\left (1-\operatorname {al3} -\operatorname {bl3} \right ) \operatorname {b3}}{\operatorname {b3} x -\operatorname {a3}}\right ) y^{\prime }-\frac {\left (\frac {\operatorname {al1} \operatorname {bl1} \left (\operatorname {a1} \operatorname {b2} -\operatorname {a2} \operatorname {b1} \right ) \left (-\operatorname {a1} \operatorname {b3} +\operatorname {a3} \operatorname {b1} \right )}{\operatorname {b1} x -\operatorname {a1}}+\frac {\operatorname {al2} \operatorname {bl2} \left (\operatorname {a2} \operatorname {b3} -\operatorname {a3} \operatorname {b2} \right ) \left (\operatorname {a1} \operatorname {b2} -\operatorname {a2} \operatorname {b1} \right )}{\operatorname {b2} x -\operatorname {a2}}+\frac {\operatorname {al3} \operatorname {bl3} \left (-\operatorname {a1} \operatorname {b3} +\operatorname {a3} \operatorname {b1} \right ) \left (\operatorname {a2} \operatorname {b3} -\operatorname {a3} \operatorname {b2} \right )}{\operatorname {b3} x -\operatorname {a3}}\right ) y}{\left (\operatorname {b1} x -\operatorname {a1} \right ) \left (\operatorname {b2} x -\operatorname {a2} \right ) \left (\operatorname {b3} x -\operatorname {a3} \right )} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
1271.608 |
|
| \(961\) |
\begin{align*}
y^{\prime \prime }&=-\frac {\left (x^{2} \left (\left (x^{2}-\operatorname {a1} \right ) \left (x^{2}-\operatorname {a2} \right )+\left (x^{2}-\operatorname {a2} \right ) \left (x^{2}-\operatorname {a3} \right )+\left (x^{2}-\operatorname {a3} \right ) \left (x^{2}-\operatorname {a1} \right )\right )-\left (x^{2}-\operatorname {a1} \right ) \left (x^{2}-\operatorname {a2} \right ) \left (x^{2}-\operatorname {a3} \right )\right ) y^{\prime }}{x \left (x^{2}-\operatorname {a1} \right ) \left (x^{2}-\operatorname {a2} \right ) \left (x^{2}-\operatorname {a3} \right )}-\frac {\left (A \,x^{2}+B \right ) y}{x \left (x^{2}-\operatorname {a1} \right ) \left (x^{2}-\operatorname {a2} \right ) \left (x^{2}-\operatorname {a3} \right )} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
1297.271 |
|
| \(962\) |
\begin{align*}
y^{\prime \prime }&=-\frac {\left (a p \,x^{b}+q \right ) y^{\prime }}{x \left (a \,x^{b}-1\right )}-\frac {\left (a r \,x^{b}+s \right ) y}{x^{2} \left (a \,x^{b}-1\right )} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
26.686 |
|
| \(963\) |
\begin{align*}
y^{\prime \prime }&=\frac {y}{{\mathrm e}^{x}+1} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✗ |
1.626 |
|
| \(964\) |
\begin{align*}
y^{\prime \prime }&=-\frac {\left (-a^{2} \sinh \left (x \right )^{2}-n \left (n -1\right )\right ) y}{\sinh \left (x \right )^{2}} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
6.206 |
|
| \(965\) |
\begin{align*}
y^{\prime \prime }&=-\frac {2 n \cosh \left (x \right ) y^{\prime }}{\sinh \left (x \right )}-\left (-a^{2}+n^{2}\right ) y \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
16.947 |
|
| \(966\) |
\begin{align*}
y^{\prime \prime }&=-\frac {\left (2 n +1\right ) \cos \left (x \right ) y^{\prime }}{\sin \left (x \right )}-\left (v +n +1\right ) \left (v -n \right ) y \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
4.502 |
|
| \(967\) |
\begin{align*}
\cos \left (x \right )^{2} y^{\prime \prime }-\left (a \cos \left (x \right )^{2}+n \left (n -1\right )\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
3.031 |
|
| \(968\) |
\begin{align*}
y^{\prime \prime }&=-\frac {a y}{\sin \left (x \right )^{2}} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
2.353 |
|
| \(969\) |
\begin{align*}
\sin \left (x \right )^{2} y^{\prime \prime }-\left (a \sin \left (x \right )^{2}+n \left (n -1\right )\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
2.933 |
|
| \(970\) |
\begin{align*}
y^{\prime \prime }&=-\frac {\left (-a^{2} \cos \left (x \right )^{2}-\left (3-2 a \right ) \cos \left (x \right )-3+3 a \right ) y}{\sin \left (x \right )^{2}} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
4.935 |
|
| \(971\) |
\begin{align*}
\sin \left (x \right )^{2} y^{\prime \prime }-\left (a^{2} \cos \left (x \right )^{2}+b \cos \left (x \right )+\frac {b^{2}}{\left (2 a -3\right )^{2}}+3 a +2\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
10.682 |
|
| \(972\) |
\begin{align*}
y^{\prime \prime }&=-\frac {\left (-\left (a^{2} b^{2}-\left (1+a \right )^{2}\right ) \sin \left (x \right )^{2}-a \left (1+a \right ) b \sin \left (2 x \right )-a \left (-1+a \right )\right ) y}{\sin \left (x \right )^{2}} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
8.803 |
|
| \(973\) |
\begin{align*}
y^{\prime \prime }&=-\frac {\left (a \cos \left (x \right )^{2}+b \sin \left (x \right )^{2}+c \right ) y}{\sin \left (x \right )^{2}} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
3.703 |
|
| \(974\) |
\begin{align*}
y^{\prime \prime }&=-\frac {\cos \left (x \right ) y^{\prime }}{\sin \left (x \right )}-\frac {\left (v \left (v +1\right ) \sin \left (x \right )^{2}-n^{2}\right ) y}{\sin \left (x \right )^{2}} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
4.463 |
|
| \(975\) |
\begin{align*}
y^{\prime \prime }&=-\frac {\sin \left (x \right ) y^{\prime }}{\cos \left (x \right )}-\frac {\left (2 x^{2}+x^{2} \sin \left (x \right )^{2}-24 \cos \left (x \right )^{2}\right ) y}{4 x^{2} \cos \left (x \right )^{2}}+\sqrt {\cos \left (x \right )} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✗ |
8.266 |
|
| \(976\) |
\begin{align*}
y^{\prime \prime }&=-\frac {b \cos \left (x \right ) y^{\prime }}{\sin \left (x \right ) a}-\frac {\left (c \cos \left (x \right )^{2}+d \cos \left (x \right )+e \right ) y}{a \sin \left (x \right )^{2}} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
6.625 |
|
| \(977\) |
\begin{align*}
y^{\prime \prime }&=-\frac {4 \sin \left (3 x \right ) y}{\sin \left (x \right )^{3}} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
3.437 |
|
| \(978\) |
\begin{align*}
y^{\prime \prime }&=-\frac {\left (4 v \left (v +1\right ) \sin \left (x \right )^{2}-\cos \left (x \right )^{2}+2-4 n^{2}\right ) y}{4 \sin \left (x \right )^{2}} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
4.417 |
|
| \(979\) |
\begin{align*}
y^{\prime \prime }&=-\frac {\left (-a \cos \left (x \right )^{2} \sin \left (x \right )^{2}-m \left (m -1\right ) \sin \left (x \right )^{2}-n \left (n -1\right ) \cos \left (x \right )^{2}\right ) y}{\cos \left (x \right )^{2} \sin \left (x \right )^{2}} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
5.808 |
|
| \(980\) |
\begin{align*}
y^{\prime \prime }&=-\frac {f^{\prime }\left (x \right ) y^{\prime }}{2 f \left (x \right )}-\frac {g \left (x \right ) y}{f \left (x \right )} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
2.979 |
|
| \(981\) |
\begin{align*}
y^{\prime \prime }&=-\frac {\left (2 f \left (x \right ) {g^{\prime }\left (x \right )}^{2} g \left (x \right )-\left (g \left (x \right )^{2}-1\right ) \left (f \left (x \right ) g^{\prime \prime }\left (x \right )+2 f^{\prime }\left (x \right ) g^{\prime }\left (x \right )\right )\right ) y^{\prime }}{f \left (x \right ) g^{\prime }\left (x \right ) \left (g \left (x \right )^{2}-1\right )}-\frac {\left (\left (g \left (x \right )^{2}-1\right ) \left (f^{\prime }\left (x \right ) \left (f \left (x \right ) g^{\prime \prime }\left (x \right )+2 f^{\prime }\left (x \right ) g^{\prime }\left (x \right )\right )-f \left (x \right ) f^{\prime \prime }\left (x \right ) g^{\prime }\left (x \right )\right )-\left (2 f^{\prime }\left (x \right ) g \left (x \right )+v \left (v +1\right ) f \left (x \right ) g^{\prime }\left (x \right )\right ) f \left (x \right ) {g^{\prime }\left (x \right )}^{2}\right ) y}{f \left (x \right )^{2} g^{\prime }\left (x \right ) \left (g \left (x \right )^{2}-1\right )} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
5.021 |
|
| \(982\) |
\begin{align*}
y^{\prime \prime \prime }+y a \,x^{3}-b x&=0 \\
\end{align*} |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✗ |
0.037 |
|
| \(983\) |
\begin{align*}
y^{\prime \prime \prime }-a \,x^{b} y&=0 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.033 |
|
| \(984\) |
\begin{align*}
a y+2 a x y^{\prime }+y^{\prime \prime \prime }&=0 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.036 |
|
| \(985\) |
\begin{align*}
y^{\prime \prime \prime }-x^{2} y^{\prime \prime }+\left (a +b -1\right ) x y^{\prime }-a b y&=0 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.042 |
|
| \(986\) |
\begin{align*}
y^{\prime \prime \prime }+x^{2 c -2} y^{\prime }+\left (c -1\right ) x^{2 c -3} y&=0 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.057 |
|
| \(987\) |
\begin{align*}
y^{\prime \prime \prime }-\left (6 k^{2} \sin \left (x \right )^{2}+a \right ) y^{\prime }+b y&=0 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
0.048 |
|
| \(988\) |
\begin{align*}
y f^{\prime }\left (x \right )+2 f \left (x \right ) y^{\prime }+y^{\prime \prime \prime }&=0 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
0.041 |
|
| \(989\) |
\begin{align*}
y^{\prime \prime \prime }-6 y^{\prime \prime } x +2 \left (4 x^{2}+2 a -1\right ) y^{\prime }-8 a x y&=0 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.042 |
|
| \(990\) |
\begin{align*}
a^{3} x^{3} y+3 a^{2} x^{2} y^{\prime }+3 a x y^{\prime \prime }+y^{\prime \prime \prime }&=0 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.041 |
|
| \(991\) |
\begin{align*}
f \left (x \right ) y+y^{\prime }+f \left (x \right ) y^{\prime \prime }+y^{\prime \prime \prime }&=0 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.038 |
|
| \(992\) |
\begin{align*}
y^{\prime \prime \prime }+f \left (x \right ) \left (x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y\right )&=0 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.043 |
|
| \(993\) |
\begin{align*}
x y^{\prime \prime \prime }+3 y^{\prime \prime }+y x&=0 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.033 |
|
| \(994\) |
\begin{align*}
x y^{\prime \prime \prime }+3 y^{\prime \prime }-a \,x^{2} y&=0 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.037 |
|
| \(995\) |
\begin{align*}
x y^{\prime \prime \prime }+\left (a +b \right ) y^{\prime \prime }-y^{\prime } x -a y&=0 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.038 |
|
| \(996\) |
\begin{align*}
x y^{\prime \prime \prime }-\left (x +2 v \right ) y^{\prime \prime }-\left (x -2 v -1\right ) y^{\prime }+\left (x -1\right ) y&=0 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.041 |
|
| \(997\) |
\begin{align*}
2 x y^{\prime \prime \prime }+3 y^{\prime \prime }+a x y-b&=0 \\
\end{align*} |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✗ |
0.036 |
|
| \(998\) |
\begin{align*}
2 x y^{\prime \prime \prime }-4 \left (x +\nu -1\right ) y^{\prime \prime }+\left (2 x +6 \nu -5\right ) y^{\prime }+\left (1-2 \nu \right ) y&=0 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.048 |
|
| \(999\) |
\begin{align*}
2 x y^{\prime \prime \prime }+3 \left (2 a x +k \right ) y^{\prime \prime }+6 \left (a k +b x \right ) y^{\prime }+\left (3 b k +2 c x \right ) y&=0 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
0.046 |
|
| \(1000\) |
\begin{align*}
\left (2 x -1\right ) y^{\prime \prime \prime }-8 y^{\prime } x +8 y&=0 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.036 |
|
| \(1001\) |
\begin{align*}
a \,x^{2} y-6 y^{\prime }+x^{2} y^{\prime \prime \prime }&=0 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.036 |
|
| \(1002\) |
\begin{align*}
x^{2} y^{\prime \prime \prime }+\left (x +1\right ) y^{\prime \prime }-y&=0 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
0.034 |
|
| \(1003\) |
\begin{align*}
x^{2} y^{\prime \prime \prime }-3 \left (x -m \right ) x y^{\prime \prime }+\left (2 x^{2}+4 \left (n -m \right ) x +m \left (2 m -1\right )\right ) y^{\prime }-2 n \left (2 x -2 m +1\right ) y&=0 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.052 |
|
| \(1004\) |
\begin{align*}
x^{2} y^{\prime \prime \prime }+4 y^{\prime \prime } x +\left (x^{2}+2\right ) y^{\prime }+3 y x -f \left (x \right )&=0 \\
\end{align*} |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✗ |
0.042 |
|
| \(1005\) |
\begin{align*}
a \,x^{2} y+6 y^{\prime }+6 y^{\prime \prime } x +x^{2} y^{\prime \prime \prime }&=0 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.040 |
|
| \(1006\) |
\begin{align*}
x^{2} y^{\prime \prime \prime }-3 \left (p +q \right ) x y^{\prime \prime }+3 p \left (3 q +1\right ) y^{\prime }-x^{2} y&=0 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.044 |
|
| \(1007\) |
\begin{align*}
x^{2} y^{\prime \prime \prime }-2 \left (n +1\right ) x y^{\prime \prime }+\left (a \,x^{2}+6 n \right ) y^{\prime }-2 a x y&=0 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.044 |
|
| \(1008\) |
\begin{align*}
x^{2} y^{\prime \prime \prime }-\left (x^{2}-2 x \right ) y^{\prime \prime }-\left (x^{2}+\nu ^{2}-\frac {1}{4}\right ) y^{\prime }+\left (x^{2}-2 x +\nu ^{2}-\frac {1}{4}\right ) y&=0 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.046 |
|
| \(1009\) |
\begin{align*}
x^{2} y^{\prime \prime \prime }-\left (x +\nu \right ) x y^{\prime \prime }+\nu \left (2 x +1\right ) y^{\prime }-\nu \left (x +1\right ) y&=0 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✗ |
✗ |
0.046 |
|
| \(1010\) |
\begin{align*}
x^{2} y^{\prime \prime \prime }-2 \left (x^{2}-x \right ) y^{\prime \prime }+\left (x^{2}-2 x +\frac {1}{4}-\nu ^{2}\right ) y^{\prime }+\left (\nu ^{2}-\frac {1}{4}\right ) y&=0 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.045 |
|
| \(1011\) |
\begin{align*}
x^{2} y^{\prime \prime \prime }-\left (x^{4}-6 x \right ) y^{\prime \prime }-\left (2 x^{3}-6\right ) y^{\prime }+2 x^{2} y&=0 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.043 |
|
| \(1012\) |
\begin{align*}
-2 y x +\left (x^{2}+2\right ) y^{\prime }-2 y^{\prime \prime } x +\left (x^{2}+2\right ) y^{\prime \prime \prime }&=0 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.039 |
|
| \(1013\) |
\begin{align*}
2 x \left (x -1\right ) y^{\prime \prime \prime }+3 \left (2 x -1\right ) y^{\prime \prime }+\left (2 a x +b \right ) y^{\prime }+a y&=0 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.043 |
|
| \(1014\) |
\begin{align*}
x^{3} y^{\prime \prime \prime }+\left (-\nu ^{2}+1\right ) x y^{\prime }+\left (a \,x^{3}+\nu ^{2}-1\right ) y&=0 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.043 |
|
| \(1015\) |
\begin{align*}
x^{3} y^{\prime \prime \prime }+\left (4 x^{3}+\left (-4 \nu ^{2}+1\right ) x \right ) y^{\prime }+\left (4 \nu ^{2}-1\right ) y&=0 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.041 |
|
| \(1016\) |
\begin{align*}
x^{3} y^{\prime \prime \prime }+\left (a \,x^{2 \nu }+1-\nu ^{2}\right ) x y^{\prime }+\left (b \,x^{3 \nu }+a \left (\nu -1\right ) x^{2 \nu }+\nu ^{2}-1\right ) y&=0 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
0.075 |
|
| \(1017\) |
\begin{align*}
-2 \left (x^{2}+4\right ) y+x \left (x^{2}+8\right ) y^{\prime }-4 x^{2} y^{\prime \prime }+x^{3} y^{\prime \prime \prime }&=0 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.043 |
|
| \(1018\) |
\begin{align*}
x^{3} y^{\prime \prime \prime }+3 \left (1-a \right ) x^{2} y^{\prime \prime }+\left (4 b^{2} c^{2} x^{2 c +1}+1-4 \nu ^{2} c^{2}+3 a \left (-1+a \right ) x \right ) y^{\prime }+\left (4 b^{2} c^{2} \left (c -a \right ) x^{2 c}+a \left (4 \nu ^{2} c^{2}-a^{2}\right )\right ) y&=0 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
0.065 |
|
| \(1019\) |
\begin{align*}
x^{3} y^{\prime \prime \prime }+\left (x +3\right ) x^{2} y^{\prime \prime }+5 \left (x -6\right ) x y^{\prime }+\left (4 x +30\right ) y&=0 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.042 |
|
| \(1020\) |
\begin{align*}
-12 y+3 \left (2 x^{2}+1\right ) y^{\prime \prime }+x \left (x^{2}+1\right ) y^{\prime \prime \prime }&=0 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.043 |
|
| \(1021\) |
\begin{align*}
\left (x +3\right ) x^{2} y^{\prime \prime \prime }-3 x \left (2+x \right ) y^{\prime \prime }+6 \left (x +1\right ) y^{\prime }-6 y&=0 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.043 |
|
| \(1022\) |
\begin{align*}
2 \left (x -\operatorname {a1} \right ) \left (x -\operatorname {a2} \right ) \left (x -\operatorname {a3} \right ) y^{\prime \prime \prime }+\left (9 x^{2}-6 \left (\operatorname {a1} +\operatorname {a2} +\operatorname {a3} \right ) x +3 \operatorname {a1} \operatorname {a2} +3 \operatorname {a1} \operatorname {a3} +3 \operatorname {a2} \operatorname {a3} \right ) y^{\prime \prime }-2 \left (\left (n^{2}+n -3\right ) x +b \right ) y^{\prime }-n \left (n +1\right ) y&=0 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.057 |
|
| \(1023\) |
\begin{align*}
x^{3} \left (x +1\right ) y^{\prime \prime \prime }-\left (2+4 x \right ) x^{2} y^{\prime \prime }+\left (4+10 x \right ) x y^{\prime }-4 \left (1+3 x \right ) y&=0 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.045 |
|
| \(1024\) |
\begin{align*}
x^{3} \left (x^{2}+1\right ) y^{\prime \prime \prime }-\left (4 x^{2}+2\right ) x^{2} y^{\prime \prime }+\left (10 x^{2}+4\right ) x y^{\prime }-4 \left (3 x^{2}+1\right ) y&=0 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.048 |
|
| \(1025\) |
\begin{align*}
x^{6} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }-2 y&=0 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.037 |
|
| \(1026\) |
\begin{align*}
x^{6} y^{\prime \prime \prime }+6 x^{5} y^{\prime \prime }+a y&=0 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.034 |
|
| \(1027\) |
\begin{align*}
x^{2} \left (x^{4}+2 x^{2}+2 x +1\right ) y^{\prime \prime \prime }-\left (2 x^{6}+3 x^{4}-6 x^{2}-6 x -1\right ) y^{\prime \prime }+\left (x^{6}-6 x^{3}-15 x^{2}-12 x -2\right ) y^{\prime }+\left (x^{4}+4 x^{3}+8 x^{2}+6 x +1\right ) y&=0 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.053 |
|
| \(1028\) |
\begin{align*}
\left (x -a \right )^{3} \left (-b +x \right )^{3} y^{\prime \prime \prime }-c y&=0 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.043 |
|
| \(1029\) |
\begin{align*}
y^{\prime \prime \prime } \sin \left (x \right )^{2}+3 y^{\prime \prime } \sin \left (x \right ) \cos \left (x \right )+\left (\cos \left (2 x \right )+4 \nu \left (\nu +1\right ) \sin \left (x \right )^{2}\right ) y^{\prime }+2 \nu \left (\nu +1\right ) y \sin \left (2 x \right )&=0 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.065 |
|
| \(1030\) |
\begin{align*}
y^{\prime \prime \prime }+y^{\prime } x +n y&=0 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.036 |
|
| \(1031\) |
\begin{align*}
y^{\prime \prime \prime }-y^{\prime } x -n y&=0 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.033 |
|
| \(1032\) |
\begin{align*}
y^{\prime \prime \prime \prime }+a \left (b x -1\right ) y^{\prime \prime }+a b y^{\prime }+\lambda y&=0 \\
\end{align*} |
[[_high_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
0.042 |
|
| \(1033\) |
\begin{align*}
y^{\prime \prime \prime \prime }+\left (a \,x^{2}+b \lambda +c \right ) y^{\prime \prime }+\left (a \,x^{2}+\beta \lambda +\gamma \right ) y&=0 \\
\end{align*} |
[[_high_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
0.044 |
|
| \(1034\) |
\begin{align*}
a^{4} x^{4} y+4 a^{3} x^{3} y^{\prime }+6 a^{2} x^{2} y^{\prime \prime }+4 a x y^{\prime \prime \prime }+y^{\prime \prime \prime \prime }&=0 \\
\end{align*} |
[[_high_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.051 |
|
| \(1035\) |
\begin{align*}
x y^{\prime \prime \prime \prime }-\left (6 x^{2}+1\right ) y^{\prime \prime \prime }+12 x^{3} y^{\prime \prime }-\left (9 x^{2}-7\right ) x^{2} y^{\prime }+2 \left (x^{2}-3\right ) x^{3} y&=0 \\
\end{align*} |
[[_high_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.053 |
|
| \(1036\) |
\begin{align*}
x^{2} y^{\prime \prime \prime \prime }-2 \left (\nu ^{2} x^{2}+6\right ) y^{\prime \prime }+\nu ^{2} \left (\nu ^{2} x^{2}+4\right ) y&=0 \\
\end{align*} |
[[_high_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.042 |
|
| \(1037\) |
\begin{align*}
x^{2} y^{\prime \prime \prime \prime }+2 x y^{\prime \prime \prime }+a y-b \,x^{2}&=0 \\
\end{align*} |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
✗ |
✗ |
0.042 |
|
| \(1038\) |
\begin{align*}
x^{2} y^{\prime \prime \prime \prime }+6 x y^{\prime \prime \prime }+6 y^{\prime \prime }-\lambda ^{2} y&=0 \\
\end{align*} |
[[_high_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.043 |
|
| \(1039\) |
\begin{align*}
x^{2} y^{\prime \prime \prime \prime }+8 x y^{\prime \prime \prime }+12 y^{\prime \prime }-\lambda ^{2} y&=0 \\
\end{align*} |
[[_high_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.040 |
|
| \(1040\) |
\begin{align*}
x^{2} y^{\prime \prime \prime \prime }+\left (2 n -2 \nu +4\right ) x y^{\prime \prime \prime }+\left (n -\nu +1\right ) \left (n -\nu +2\right ) y^{\prime \prime }-\frac {b^{4} y}{16}&=0 \\
\end{align*} |
[[_high_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.048 |
|
| \(1041\) |
\begin{align*}
x^{3} y^{\prime \prime \prime \prime }+2 x^{2} y^{\prime \prime \prime }-y^{\prime \prime } x +y^{\prime }-a^{4} x^{3} y&=0 \\
\end{align*} |
[[_high_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.045 |
|
| \(1042\) |
\begin{align*}
x^{4} y^{\prime \prime \prime \prime }-2 n \left (n +1\right ) x^{2} y^{\prime \prime }+4 n \left (n +1\right ) x y^{\prime }+\left (a \,x^{4}+n \left (n +1\right ) \left (n +3\right ) \left (-2+n \right )\right ) y&=0 \\
\end{align*} |
[[_high_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.051 |
|
| \(1043\) |
\begin{align*}
x^{4} y^{\prime \prime \prime \prime }+4 x^{3} y^{\prime \prime \prime }-\left (4 n^{2}-1\right ) x^{2} y^{\prime \prime }+\left (4 n^{2}-1\right ) x y^{\prime }-4 x^{4} y&=0 \\
\end{align*} |
[[_high_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.091 |
|
| \(1044\) |
\begin{align*}
x^{4} y^{\prime \prime \prime \prime }+4 x^{3} y^{\prime \prime \prime }-\left (4 n^{2}-1\right ) x^{2} y^{\prime \prime }-\left (4 n^{2}-1\right ) x y^{\prime }+\left (-4 x^{4}+4 n^{2}-1\right ) y&=0 \\
\end{align*} |
[[_high_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.049 |
|
| \(1045\) |
\begin{align*}
x^{4} y^{\prime \prime \prime \prime }+4 x^{3} y^{\prime \prime \prime }-\left (4 n^{2}+3\right ) x^{2} y^{\prime \prime }+\left (12 n^{2}-3\right ) x y^{\prime }-\left (4 x^{4}+12 n^{2}-3\right ) y&=0 \\
\end{align*} |
[[_high_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.052 |
|
| \(1046\) |
\begin{align*}
x^{4} y^{\prime \prime \prime \prime }+6 x^{3} y^{\prime \prime \prime }+\left (4 x^{4}+\left (-\rho ^{2}-\sigma ^{2}+7\right ) x^{2}\right ) y^{\prime \prime }+\left (16 x^{3}+\left (-\rho ^{2}-\sigma ^{2}+1\right ) x \right ) y^{\prime }+\left (\rho ^{2} \sigma ^{2}+8 x^{2}\right ) y&=0 \\
\end{align*} |
[[_high_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.057 |
|
| \(1047\) |
\begin{align*}
x^{4} y^{\prime \prime \prime \prime }+6 x^{3} y^{\prime \prime \prime }+\left (4 x^{4}+\left (-2 \mu ^{2}-2 \nu ^{2}+7\right ) x^{2}\right ) y^{\prime \prime }+\left (16 x^{3}+\left (-2 \mu ^{2}-2 \nu ^{2}+1\right ) x \right ) y^{\prime }+\left (8 x^{2}+\left (\mu ^{2}-\nu ^{2}\right )^{2}\right ) y&=0 \\
\end{align*} |
[[_high_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.058 |
|
| \(1048\) |
\begin{align*}
x^{4} y^{\prime \prime \prime \prime }+\left (6-4 a \right ) x^{3} y^{\prime \prime \prime }+\left (4 x^{2 c} b^{2} c^{2}+6 \left (-1+a \right )^{2}-2 c^{2} \left (\mu ^{2}+\nu ^{2}\right )+1\right ) x^{2} y^{\prime \prime }+\left (4 \left (3 c -2 a +1\right ) b^{2} c^{2} x^{2 c}+\left (2 a -1\right ) \left (2 c^{2} \left (\mu ^{2}+\nu ^{2}\right )-2 a \left (-1+a \right )-1\right )\right ) x y^{\prime }+\left (4 \left (a -c \right ) \left (a -2 c \right ) b^{2} c^{2} x^{2 c}+\left (c \mu +c \nu +a \right ) \left (c \mu +c \nu -a \right ) \left (c \mu -c \nu +a \right ) \left (c \mu -c \nu -a \right )\right ) y&=0 \\
\end{align*} |
[[_high_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.095 |
|
| \(1049\) |
\begin{align*}
x^{4} y^{\prime \prime \prime \prime }+\left (6-4 a -4 c \right ) x^{3} y^{\prime \prime \prime }+\left (-2 \nu ^{2} c^{2}+2 a^{2}+4 \left (a +c -1\right )^{2}+4 \left (-1+a \right ) \left (c -1\right )-1\right ) x^{2} y^{\prime \prime }+\left (2 \nu ^{2} c^{2}-2 a^{2}-\left (2 a -1\right ) \left (2 c -1\right )\right ) \left (2 a +2 c -1\right ) x y^{\prime }+\left (\left (-\nu ^{2} c^{2}+a^{2}\right ) \left (-\nu ^{2} c^{2}+a^{2}+4 a c +4 c^{2}\right )-b^{4} c^{4} x^{4 c}\right ) y&=0 \\
\end{align*} |
[[_high_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.082 |
|
| \(1050\) |
\begin{align*}
\nu ^{4} x^{4} y^{\prime \prime \prime \prime }+\left (4 \nu -2\right ) \nu ^{3} x^{3} y^{\prime \prime \prime }+\left (\nu -1\right ) \left (2 \nu -1\right ) \nu ^{2} x^{2} y^{\prime \prime }-\frac {b^{4} x^{\frac {2}{\nu }} y}{16}&=0 \\
\end{align*} |
[[_high_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.058 |
|
| \(1051\) |
\begin{align*}
\left (x^{2}-1\right )^{2} y^{\prime \prime \prime \prime }+10 x \left (x^{2}-1\right ) y^{\prime \prime \prime }+\left (24 x^{2}-8-2 \left (\mu \left (\mu +1\right )+\nu \left (\nu +1\right )\right ) \left (x^{2}-1\right )\right ) y^{\prime \prime }-6 x \left (\mu \left (\mu +1\right )+\nu \left (\nu +1\right )-2\right ) y^{\prime }+\left (\left (\mu \left (\mu +1\right )-\nu \left (\nu +1\right )\right )^{2}-2 \mu \left (\mu +1\right )-2 \nu \left (\nu +1\right )\right ) y&=0 \\
\end{align*} |
[[_high_order, _with_linear_symmetries]] |
✓ |
✗ |
✗ |
0.063 |
|
| \(1052\) |
\begin{align*}
y^{\prime \prime \prime \prime } \sin \left (x \right )^{4}+2 y^{\prime \prime \prime } \sin \left (x \right )^{3} \cos \left (x \right )+y^{\prime \prime } \sin \left (x \right )^{2} \left (\sin \left (x \right )^{2}-3\right )+y^{\prime } \sin \left (x \right ) \cos \left (x \right ) \left (2 \sin \left (x \right )^{2}+3\right )+\left (a^{4} \sin \left (x \right )^{4}-3\right ) y&=0 \\
\end{align*} |
[[_high_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.088 |
|
| \(1053\) |
\begin{align*}
y^{\prime \prime \prime \prime } \sin \left (x \right )^{6}+4 y^{\prime \prime \prime } \sin \left (x \right )^{5} \cos \left (x \right )-6 y^{\prime \prime } \sin \left (x \right )^{6}-4 y^{\prime } \sin \left (x \right )^{5} \cos \left (x \right )+y \sin \left (x \right )^{6}-f&=0 \\
\end{align*} |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✗ |
0.070 |
|
| \(1054\) |
\begin{align*}
y^{\prime \prime \prime \prime }-2 a^{2} y^{\prime \prime }+a^{4} y-\lambda \left (a x -b \right ) \left (y^{\prime \prime }-a^{2} y\right )&=0 \\
\end{align*} |
[[_high_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.050 |
|
| \(1055\) |
\begin{align*}
y^{\left (5\right )}-a x y-b&=0 \\
\end{align*} |
[[_high_order, _linear, _nonhomogeneous]] |
✗ |
✗ |
✗ |
0.034 |
|
| \(1056\) |
\begin{align*}
y^{\left (5\right )}+a \,x^{\nu } y^{\prime }+a \nu \,x^{\nu -1} y&=0 \\
\end{align*} |
[[_high_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
0.073 |
|
| \(1057\) |
\begin{align*}
x y^{\left (5\right )}-m n y^{\prime \prime \prime \prime }+a x y&=0 \\
\end{align*} |
[[_high_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.039 |
|
| \(1058\) |
\begin{align*}
x y^{\left (5\right )}-\left (a A_{1} -A_{0} \right ) x -A_{1} -\left (\left (a A_{2} -A_{1} \right ) x +A_{2} \right ) y^{\prime }&=0 \\
\end{align*} |
[[_high_order, _missing_y]] |
✗ |
✗ |
✗ |
0.083 |
|
| \(1059\) |
\begin{align*}
x^{2} y^{\prime \prime \prime \prime }-a y&=0 \\
\end{align*} |
[[_high_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.034 |
|
| \(1060\) |
\begin{align*}
x^{10} y^{\left (5\right )}-a y&=0 \\
\end{align*} |
[[_high_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.037 |
|
| \(1061\) |
\begin{align*}
x^{{5}/{2}} y^{\left (5\right )}-a y&=0 \\
\end{align*} |
[[_high_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.043 |
|
| \(1062\) |
\begin{align*}
\left (x -a \right )^{5} \left (-b +x \right )^{5} y^{\left (5\right )}-c y&=0 \\
\end{align*} |
[[_high_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
0.050 |
|
| \(1063\) |
\begin{align*}
y^{\prime \prime }-6 y^{2}-x&=0 \\
\end{align*} |
[[_Painleve, ‘1st‘]] |
✗ |
✗ |
✗ |
0.337 |
|
| \(1064\) |
\begin{align*}
y^{\prime \prime }+a y^{2}+b x +c&=0 \\
\end{align*} |
[NONE] |
✗ |
✗ |
✗ |
0.380 |
|
| \(1065\) |
\begin{align*}
y^{\prime \prime }-2 y^{3}-y x +a&=0 \\
\end{align*} |
[[_Painleve, ‘2nd‘]] |
✗ |
✗ |
✗ |
0.370 |
|
| \(1066\) |
\begin{align*}
y^{\prime \prime }-2 a^{2} y^{3}+2 a b x y-b&=0 \\
\end{align*} |
[NONE] |
✗ |
✗ |
✗ |
0.400 |
|
| \(1067\) |
\begin{align*}
y^{\prime \prime }+d +b x y+c y+a y^{3}&=0 \\
\end{align*} |
[NONE] |
✗ |
✗ |
✗ |
0.423 |
|
| \(1068\) |
\begin{align*}
y^{\prime \prime }+a \,x^{r} y^{2}&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
0.358 |
|
| \(1069\) |
\begin{align*}
y^{\prime \prime }-\frac {1}{\left (a y^{2}+b x y+c \,x^{2}+\alpha y+\beta x +\gamma \right )^{{3}/{2}}}&=0 \\
\end{align*} |
[NONE] |
✓ |
✗ |
✗ |
0.953 |
|
| \(1070\) |
\begin{align*}
y^{\prime \prime }+a \,{\mathrm e}^{x} \sqrt {y}&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
0.371 |
|
| \(1071\) |
\begin{align*}
y^{\prime \prime }+{\mathrm e}^{x} \sin \left (y\right )&=0 \\
\end{align*} |
[NONE] |
✗ |
✗ |
✗ |
0.707 |
|
| \(1072\) |
\begin{align*}
y^{\prime \prime }+a^{2} \sin \left (y\right )-\beta \sin \left (x \right )&=0 \\
\end{align*} |
[NONE] |
✗ |
✗ |
✗ |
1.256 |
|
| \(1073\) |
\begin{align*}
y^{\prime \prime }+a^{2} \sin \left (y\right )-\beta f \left (x \right )&=0 \\
\end{align*} |
[NONE] |
✗ |
✗ |
✗ |
0.908 |
|
| \(1074\) |
\begin{align*}
y^{\prime \prime }&=\frac {f \left (\frac {y}{\sqrt {x}}\right )}{x^{{3}/{2}}} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
16.475 |
|
| \(1075\) |
\begin{align*}
y^{\prime \prime }-3 y^{\prime }-y^{2}-2 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✗ |
✗ |
✗ |
8.794 |
|
| \(1076\) |
\begin{align*}
y^{\prime \prime }-7 y^{\prime }-y^{{3}/{2}}+12 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✗ |
✗ |
✗ |
106.090 |
|
| \(1077\) |
\begin{align*}
y^{\prime \prime }+5 a y^{\prime }-6 y^{2}+6 a^{2} y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✗ |
90.819 |
|
| \(1078\) |
\begin{align*}
y^{\prime \prime }+3 a y^{\prime }-2 y^{3}+2 a^{2} y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✗ |
11.780 |
|
| \(1079\) |
\begin{align*}
y^{\prime \prime }+a y^{\prime }+b \,x^{v} y^{n}&=0 \\
\end{align*} |
[NONE] |
✗ |
✗ |
✗ |
0.402 |
|
| \(1080\) |
\begin{align*}
y^{\prime \prime }+a y^{\prime }+b \,{\mathrm e}^{y}-2 a&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✗ |
✗ |
✗ |
21.361 |
|
| \(1081\) |
\begin{align*}
y^{\prime \prime }+a y^{\prime }+f \left (x \right ) \sin \left (y\right )&=0 \\
\end{align*} |
[NONE] |
✗ |
✗ |
✗ |
1.008 |
|
| \(1082\) |
\begin{align*}
y^{\prime \prime }+y y^{\prime }-y^{3}+a y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✗ |
✗ |
274.637 |
|
| \(1083\) |
\begin{align*}
y^{\prime \prime }+\left (3 a +y\right ) y^{\prime }-y^{3}+a y^{2}+2 a^{2} y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✗ |
42.721 |
|
| \(1084\) |
\begin{align*}
y^{\prime \prime }+\left (y+3 f \left (x \right )\right ) y^{\prime }-y^{3}+f \left (x \right ) y^{2}+y \left (2 f \left (x \right )^{2}+f^{\prime }\left (x \right )\right )&=0 \\
\end{align*} |
[NONE] |
✗ |
✗ |
✗ |
1.259 |
|
| \(1085\) |
\begin{align*}
y^{\prime \prime }+\left (3 y+f \left (x \right )\right ) y^{\prime }+y^{3}+f \left (x \right ) y^{2}&=0 \\
\end{align*} |
[[_2nd_order, _with_potential_symmetries]] |
✓ |
✓ |
✗ |
1.181 |
|
| \(1086\) |
\begin{align*}
y^{\prime \prime }-3 y y^{\prime }-3 a y^{2}-4 a^{2} y-b&=0 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✗ |
51.638 |
|
| \(1087\) |
\begin{align*}
y^{\prime \prime }-\left (3 y+f \left (x \right )\right ) y^{\prime }+y^{3}+f \left (x \right ) y^{2}&=0 \\
\end{align*} |
[[_2nd_order, _with_potential_symmetries]] |
✓ |
✓ |
✗ |
1.316 |
|
| \(1088\) |
\begin{align*}
c y+b y^{\prime }+a {y^{\prime }}^{2}+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✗ |
✗ |
✗ |
44.335 |
|
| \(1089\) |
\begin{align*}
y^{\prime \prime }+a y^{\prime } {| y^{\prime }|}+b \sin \left (y\right )&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✗ |
✗ |
✗ |
19.865 |
|
| \(1090\) |
\begin{align*}
y^{\prime \prime }-a \left (-y+y^{\prime } x \right )^{v}&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.954 |
|
| \(1091\) |
\begin{align*}
y^{\prime \prime }-k \,x^{a} y^{b} {y^{\prime }}^{r}&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
0.636 |
|
| \(1092\) |
\begin{align*}
y^{\prime \prime }&=a \sqrt {b y^{2}+{y^{\prime }}^{2}} \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✗ |
1039.573 |
|
| \(1093\) |
\begin{align*}
y^{\prime \prime }&=2 a \left (c +b x +y\right ) \left (1+{y^{\prime }}^{2}\right )^{{3}/{2}} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
✓ |
✗ |
1.106 |
|
| \(1094\) |
\begin{align*}
y^{\prime \prime } x +2 y^{\prime }-x y^{n}&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
0.663 |
|
| \(1095\) |
\begin{align*}
y^{\prime \prime } x +2 y^{\prime }+a \,x^{v} y^{n}&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
0.665 |
|
| \(1096\) |
\begin{align*}
y^{\prime \prime } x +2 y^{\prime }+x \,{\mathrm e}^{y}&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
0.657 |
|
| \(1097\) |
\begin{align*}
b \,{\mathrm e}^{y} x +a y^{\prime }+y^{\prime \prime } x&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
0.676 |
|
| \(1098\) |
\begin{align*}
y^{\prime \prime } x +a y^{\prime }+b \,x^{5-2 a} {\mathrm e}^{y}&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
0.885 |
|
| \(1099\) |
\begin{align*}
y^{\prime \prime } x -x^{2} {y^{\prime }}^{2}+2 y^{\prime }+y^{2}&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✗ |
0.707 |
|
| \(1100\) |
\begin{align*}
y^{\prime \prime } x +a \left (-y+y^{\prime } x \right )^{2}-b&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.727 |
|
| \(1101\) |
\begin{align*}
x^{2} y^{\prime \prime }&=a \left (y^{n}-y\right ) \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
0.531 |
|
| \(1102\) |
\begin{align*}
x^{2} y^{\prime \prime }+a \left ({\mathrm e}^{y}-1\right )&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
0.572 |
|
| \(1103\) |
\begin{align*}
x^{2} y^{\prime \prime }+a \left (-y+y^{\prime } x \right )^{2}-b \,x^{2}&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.852 |
|
| \(1104\) |
\begin{align*}
b x +a y {y^{\prime }}^{2}+x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
0.487 |
|
| \(1105\) |
\begin{align*}
x^{2} y^{\prime \prime }-\sqrt {b y^{2}+a \,x^{2} {y^{\prime }}^{2}}&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✗ |
✗ |
1.195 |
|
| \(1106\) |
\begin{align*}
4 x^{2} y^{\prime \prime }-x^{4} {y^{\prime }}^{2}+4 y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
0.648 |
|
| \(1107\) |
\begin{align*}
2 y+a y^{3}+9 x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.490 |
|
| \(1108\) |
\begin{align*}
24+12 y x +x^{3} \left (-y^{3}+y y^{\prime }+y^{\prime \prime }\right )&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
1.312 |
|
| \(1109\) |
\begin{align*}
x^{3} y^{\prime \prime }-a \left (-y+y^{\prime } x \right )^{2}&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✗ |
0.937 |
|
| \(1110\) |
\begin{align*}
2 x^{3} y^{\prime \prime }+x^{2} \left (9+2 y x \right ) y^{\prime }+b +x y \left (a +3 y x -2 y^{2} x^{2}\right )&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
1.557 |
|
| \(1111\) |
\begin{align*}
2 \left (-x^{k}+4 x^{3}\right ) \left (-y^{3}+y y^{\prime }+y^{\prime \prime }\right )-\left (-12 x^{2}+k \,x^{-1+k}\right ) \left (y^{2}+3 y^{\prime }\right )+a x y+b&=0 \\
\end{align*} |
[NONE] |
✗ |
✗ |
✗ |
3.419 |
|
| \(1112\) |
\begin{align*}
x^{4} y^{\prime \prime }+a^{2} y^{n}&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
0.535 |
|
| \(1113\) |
\begin{align*}
x^{4} y^{\prime \prime }-x \left (x^{2}+2 y\right ) y^{\prime }+4 y^{2}&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✗ |
0.998 |
|
| \(1114\) |
\begin{align*}
x^{4} y^{\prime \prime }-x^{2} y^{\prime } \left (x +y^{\prime }\right )+4 y^{2}&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✗ |
1.058 |
|
| \(1115\) |
\begin{align*}
\left (-y+y^{\prime } x \right )^{3}+x^{4} y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
1.751 |
|
| \(1116\) |
\begin{align*}
\sqrt {x}\, y^{\prime \prime }-y^{{3}/{2}}&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
0.436 |
|
| \(1117\) |
\begin{align*}
\left (a \,x^{2}+b x +c \right )^{{3}/{2}} y^{\prime \prime }-F \left (\frac {y}{\sqrt {a \,x^{2}+b x +c}}\right )&=0 \\
\end{align*} |
[NONE] |
✓ |
✓ |
✗ |
51.047 |
|
| \(1118\) |
\begin{align*}
y y^{\prime \prime }-a x&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
0.368 |
|
| \(1119\) |
\begin{align*}
y y^{\prime \prime }-a \,x^{2}&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
0.408 |
|
| \(1120\) |
\begin{align*}
y y^{\prime \prime }+y^{2}-a x -b&=0 \\
\end{align*} |
[NONE] |
✗ |
✓ |
✗ |
0.394 |
|
| \(1121\) |
\begin{align*}
y y^{\prime \prime }-{y^{\prime }}^{2}+{\mathrm e}^{x} y \left (c y^{2}+d \right )+{\mathrm e}^{2 x} \left (b +a y^{4}\right )&=0 \\
\end{align*} |
[NONE] |
✗ |
✗ |
✗ |
0.696 |
|
| \(1122\) |
\begin{align*}
y y^{\prime \prime }-{y^{\prime }}^{2}+f \left (x \right ) y^{\prime }-y f^{\prime }\left (x \right )-y^{3}&=0 \\
\end{align*} |
[NONE] |
✗ |
✓ |
✗ |
1.605 |
|
| \(1123\) |
\begin{align*}
y y^{\prime \prime }-{y^{\prime }}^{2}+f^{\prime }\left (x \right ) y^{\prime }-y f^{\prime \prime }\left (x \right )+f \left (x \right ) y^{3}-y^{4}&=0 \\
\end{align*} |
[NONE] |
✗ |
✓ |
✗ |
0.950 |
|
| \(1124\) |
\begin{align*}
y y^{\prime \prime }-{y^{\prime }}^{2}+a y y^{\prime }-2 a y^{2}+y^{3} b&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✗ |
✗ |
✗ |
34.158 |
|
| \(1125\) |
\begin{align*}
y y^{\prime \prime }-{y^{\prime }}^{2}-\left (a y-1\right ) y^{\prime }+2 y^{2} a^{2}-2 b^{2} y^{3}+a y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✗ |
✓ |
✗ |
79.589 |
|
| \(1126\) |
\begin{align*}
y y^{\prime \prime }-{y^{\prime }}^{2}+\left (a y-1\right ) y^{\prime }-y \left (1+y\right ) \left (b^{2} y^{2}-a^{2}\right )&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✗ |
✗ |
✗ |
119.023 |
|
| \(1127\) |
\begin{align*}
y y^{\prime \prime }-{y^{\prime }}^{2}+\left (\tan \left (x \right )+\cot \left (x \right )\right ) y y^{\prime }+\left (\cos \left (x \right )^{2}-n^{2} \cot \left (x \right )^{2}\right ) y^{2} \ln \left (y\right )&=0 \\
\end{align*} |
[[_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✗ |
5.393 |
|
| \(1128\) |
\begin{align*}
y y^{\prime \prime }-{y^{\prime }}^{2}-f \left (x \right ) y y^{\prime }-g \left (x \right ) y^{2}&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✗ |
2.393 |
|
| \(1129\) |
\begin{align*}
y y^{\prime \prime }-{y^{\prime }}^{2}+\left (g \left (x \right )+f \left (x \right ) y^{2}\right ) y^{\prime }-y \left (g^{\prime }\left (x \right )-f^{\prime }\left (x \right ) y^{2}\right )&=0 \\
\end{align*} |
[[_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_xy]] |
✗ |
✓ |
✗ |
3.000 |
|
| \(1130\) |
\begin{align*}
y y^{\prime \prime }+a {y^{\prime }}^{2}+b y y^{\prime }+c y^{2}+d y^{1-a}&=0 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✗ |
363.589 |
|
| \(1131\) |
\begin{align*}
y y^{\prime \prime }-\frac {\left (-1+a \right ) {y^{\prime }}^{2}}{a}-f \left (x \right ) y^{2} y^{\prime }+\frac {a f \left (x \right )^{2} y^{4}}{\left (2+a \right )^{2}}-\frac {a f^{\prime }\left (x \right ) y^{3}}{2+a}&=0 \\
\end{align*} |
[NONE] |
✗ |
✓ |
✗ |
2.945 |
|
| \(1132\) |
\begin{align*}
y y^{\prime \prime }-{y^{\prime }}^{2}-1-2 a y \left (1+{y^{\prime }}^{2}\right )^{{3}/{2}}&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✗ |
366.648 |
|
| \(1133\) |
\begin{align*}
2 y^{\prime } \left (1+y^{\prime }\right )+\left (x -y\right ) y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
✓ |
✗ |
1.291 |
|
| \(1134\) |
\begin{align*}
\left (x -y\right ) y^{\prime \prime }-\left (1+y^{\prime }\right ) \left (1+{y^{\prime }}^{2}\right )&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
✓ |
✗ |
1.077 |
|
| \(1135\) |
\begin{align*}
\left (x -y\right ) y^{\prime \prime }-h \left (y^{\prime }\right )&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
✓ |
✗ |
3.803 |
|
| \(1136\) |
\begin{align*}
2 y y^{\prime \prime }-{y^{\prime }}^{2}+f \left (x \right ) y^{2}+a&=0 \\
\end{align*} |
[NONE] |
✗ |
✗ |
✗ |
0.969 |
|
| \(1137\) |
\begin{align*}
2 y y^{\prime \prime }-{y^{\prime }}^{2}-4 y^{2} \left (x +2 y\right )&=0 \\
\end{align*} |
[NONE] |
✗ |
✗ |
✗ |
0.495 |
|
| \(1138\) |
\begin{align*}
2 y y^{\prime \prime }-{y^{\prime }}^{2}+1+2 x y^{2}+a y^{3}&=0 \\
\end{align*} |
[NONE] |
✗ |
✗ |
✗ |
0.494 |
|
| \(1139\) |
\begin{align*}
2 y y^{\prime \prime }-{y^{\prime }}^{2}+\left (a y+b x \right ) y^{2}&=0 \\
\end{align*} |
[NONE] |
✗ |
✗ |
✗ |
0.457 |
|
| \(1140\) |
\begin{align*}
2 y y^{\prime \prime }-{y^{\prime }}^{2}+b -4 \left (x^{2}+a \right ) y^{2}-8 x y^{3}-3 y^{4}&=0 \\
\end{align*} |
[[_Painleve, ‘4th‘]] |
✗ |
✗ |
✗ |
0.603 |
|
| \(1141\) |
\begin{align*}
2 y y^{\prime \prime }-3 {y^{\prime }}^{2}+f \left (x \right ) y^{2}&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
0.837 |
|
| \(1142\) |
\begin{align*}
3 y y^{\prime \prime }-2 {y^{\prime }}^{2}-a \,x^{2}-b x -c&=0 \\
\end{align*} |
[NONE] |
✓ |
✓ |
✗ |
0.592 |
|
| \(1143\) |
\begin{align*}
f \left (x \right )+a y y^{\prime }+x {y^{\prime }}^{2}+x y y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✗ |
2.007 |
|
| \(1144\) |
\begin{align*}
x y y^{\prime \prime }-x {y^{\prime }}^{2}+y y^{\prime }+x \left (d +a y^{4}\right )+y \left (c +b y^{2}\right )&=0 \\
\end{align*} |
[[_Painleve, ‘3rd‘]] |
✗ |
✗ |
✗ |
1.105 |
|
| \(1145\) |
\begin{align*}
x y y^{\prime \prime }-x {y^{\prime }}^{2}+a y y^{\prime }+y^{3} b x&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
0.967 |
|
| \(1146\) |
\begin{align*}
x y y^{\prime \prime }-2 x {y^{\prime }}^{2}+\left (1+y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✗ |
1.039 |
|
| \(1147\) |
\begin{align*}
x y y^{\prime \prime }+\left (\frac {a x}{\sqrt {b^{2}-x^{2}}}-x \right ) {y^{\prime }}^{2}-y y^{\prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
1.839 |
|
| \(1148\) |
\begin{align*}
x^{2} \left (-1+y\right ) y^{\prime \prime }-2 x^{2} {y^{\prime }}^{2}-2 x \left (-1+y\right ) y^{\prime }-2 y \left (-1+y\right )^{2}&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✗ |
✗ |
33.888 |
|
| \(1149\) |
\begin{align*}
x^{2} \left (x +y\right ) y^{\prime \prime }-\left (-y+y^{\prime } x \right )^{2}&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✗ |
10.340 |
|
| \(1150\) |
\begin{align*}
x^{2} \left (x -y\right ) y^{\prime \prime }+a \left (-y+y^{\prime } x \right )^{2}&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✗ |
8.408 |
|
| \(1151\) |
\begin{align*}
2 x^{2} y y^{\prime \prime }-x^{2} \left (1+{y^{\prime }}^{2}\right )+y^{2}&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
1.378 |
|
| \(1152\) |
\begin{align*}
a \,x^{2} y y^{\prime \prime }+b \,x^{2} {y^{\prime }}^{2}+c x y y^{\prime }+d y^{2}&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✗ |
8.048 |
|
| \(1153\) |
\begin{align*}
x \left (x +1\right )^{2} y y^{\prime \prime }-x \left (x +1\right )^{2} {y^{\prime }}^{2}+2 \left (x +1\right )^{2} y y^{\prime }-a \left (2+x \right ) y^{2}&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✗ |
9.511 |
|
| \(1154\) |
\begin{align*}
8 \left (-x^{3}+1\right ) y y^{\prime \prime }-4 \left (-x^{3}+1\right ) {y^{\prime }}^{2}-12 x^{2} y y^{\prime }+3 x y^{2}&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✗ |
8.595 |
|
| \(1155\) |
\begin{align*}
a x +y {y^{\prime }}^{2}+y^{2} y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✗ |
✗ |
1.060 |
|
| \(1156\) |
\begin{align*}
y^{2} y^{\prime \prime }+y {y^{\prime }}^{2}-a x -b&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
0.968 |
|
| \(1157\) |
\begin{align*}
\left (x +y^{2}\right ) y^{\prime \prime }-2 \left (x -y^{2}\right ) {y^{\prime }}^{3}+y^{\prime } \left (1+4 y y^{\prime }\right )&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
✗ |
✗ |
9.456 |
|
| \(1158\) |
\begin{align*}
\left (x^{2}+y^{2}\right ) y^{\prime \prime }-\left (1+{y^{\prime }}^{2}\right ) \left (-y+y^{\prime } x \right )&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
✓ |
✗ |
8.790 |
|
| \(1159\) |
\begin{align*}
\left (x^{2}+y^{2}\right ) y^{\prime \prime }-2 \left (1+{y^{\prime }}^{2}\right ) \left (-y+y^{\prime } x \right )&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
✓ |
✗ |
8.701 |
|
| \(1160\) |
\begin{align*}
2 \left (1-y\right ) y y^{\prime \prime }-\left (1-2 y\right ) {y^{\prime }}^{2}+f \left (x \right ) \left (1-y\right ) y y^{\prime }&=0 \\
\end{align*} |
[_Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✗ |
47.070 |
|
| \(1161\) |
\begin{align*}
x y^{2} y^{\prime \prime }-a&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
4.533 |
|
| \(1162\) |
\begin{align*}
\left (a^{2}-x^{2}\right ) \left (a^{2}-y^{2}\right ) y^{\prime \prime }+\left (a^{2}-x^{2}\right ) y {y^{\prime }}^{2}-x \left (a^{2}-y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[_Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✗ |
35.170 |
|
| \(1163\) |
\begin{align*}
2 x^{2} y \left (-1+y\right ) y^{\prime \prime }-x^{2} \left (3 y-1\right ) {y^{\prime }}^{2}+2 x y \left (-1+y\right ) y^{\prime }+\left (a y^{2}+b \right ) \left (-1+y\right )^{3}+c x y^{2} \left (-1+y\right )+d \,x^{2} y^{2} \left (1+y\right )&=0 \\
\end{align*} |
[[_Painleve, ‘5th‘]] |
✗ |
✗ |
✗ |
53.074 |
|
| \(1164\) |
\begin{align*}
\left (x +y\right ) \left (-y+y^{\prime } x \right )^{3}+x^{3} y^{2} y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
17.924 |
|
| \(1165\) |
\begin{align*}
2 y^{3} y^{\prime \prime }+y^{4}-a^{2} x y^{2}-1&=0 \\
\end{align*} |
[NONE] |
✗ |
✗ |
✗ |
1.102 |
|
| \(1166\) |
\begin{align*}
2 y^{3} y^{\prime \prime }+y^{2} {y^{\prime }}^{2}-a \,x^{2}-b x -c&=0 \\
\end{align*} |
[NONE] |
✗ |
✗ |
✗ |
1.194 |
|
| \(1167\) |
\begin{align*}
\left (c +2 b x +a \,x^{2}+y^{2}\right )^{2} y^{\prime \prime }+d y&=0 \\
\end{align*} |
[NONE] |
✓ |
✓ |
✗ |
1.693 |
|
| \(1168\) |
\begin{align*}
\sqrt {x^{2}+y^{2}}\, y^{\prime \prime }-a \left (1+{y^{\prime }}^{2}\right )^{{3}/{2}}&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✗ |
✗ |
47.503 |
|
| \(1169\) |
\begin{align*}
y^{\prime } y^{\prime \prime }-x^{2} y y^{\prime }-x y^{2}&=0 \\
\end{align*} |
[[_2nd_order, _exact, _nonlinear], [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_poly_yn]] |
✗ |
✗ |
✗ |
244.703 |
|
| \(1170\) |
\begin{align*}
\left (-y+y^{\prime } x \right ) y^{\prime \prime }+4 {y^{\prime }}^{2}&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
8.965 |
|
| \(1171\) |
\begin{align*}
\left (-y+y^{\prime } x \right ) y^{\prime \prime }-\left (1+{y^{\prime }}^{2}\right )^{2}&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✗ |
✗ |
25.309 |
|
| \(1172\) |
\begin{align*}
a \,x^{3} y^{\prime } y^{\prime \prime }+b y^{2}&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✗ |
✗ |
52.390 |
|
| \(1173\) |
\begin{align*}
\left ({y^{\prime }}^{2}+a \left (-y+y^{\prime } x \right )\right ) y^{\prime \prime }-b&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
63.348 |
|
| \(1174\) |
\begin{align*}
\left (a \sqrt {1+{y^{\prime }}^{2}}-y^{\prime } x \right ) y^{\prime \prime }-{y^{\prime }}^{2}-1&=0 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✗ |
524.511 |
|
| \(1175\) |
\begin{align*}
{y^{\prime \prime }}^{2}-a y-b&=0 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
✗ |
0.063 |
|
| \(1176\) |
\begin{align*}
2 \left (x^{2}+1\right ) {y^{\prime \prime }}^{2}-x \left (x +4 y^{\prime }\right ) y^{\prime \prime }+2 \left (x +y^{\prime }\right ) y^{\prime }-2 y&=0 \\
\end{align*} |
[NONE] |
✓ |
✓ |
✗ |
0.055 |
|
| \(1177\) |
\begin{align*}
4 {y^{\prime }}^{2}-2 \left (y+3 y^{\prime } x \right ) y^{\prime \prime }+3 x^{2} {y^{\prime \prime }}^{2}&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
7.612 |
|
| \(1178\) |
\begin{align*}
\left (2-9 x \right ) x^{2} {y^{\prime \prime }}^{2}-6 \left (1-6 x \right ) x y^{\prime } y^{\prime \prime }+6 y y^{\prime \prime }-36 x {y^{\prime }}^{2}&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
41.745 |
|
| \(1179\) |
\begin{align*}
y {y^{\prime \prime }}^{2}-a \,{\mathrm e}^{2 x}&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
2.725 |
|
| \(1180\) |
\begin{align*}
\left (y^{2}-x^{2} {y^{\prime }}^{2}+x^{2} y y^{\prime \prime }\right )^{2}-4 x y \left (-y+y^{\prime } x \right )^{3}&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
0.068 |
|
| \(1181\) |
\begin{align*}
y^{\prime \prime \prime }+y y^{\prime \prime }-{y^{\prime }}^{2}+1&=0 \\
\end{align*} |
[[_3rd_order, _missing_x], [_3rd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
0.033 |
|
| \(1182\) |
\begin{align*}
y^{\prime \prime \prime }-y y^{\prime \prime }+{y^{\prime }}^{2}&=0 \\
\end{align*} |
[[_3rd_order, _missing_x], [_3rd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
0.035 |
|
| \(1183\) |
\begin{align*}
a y y^{\prime \prime }+y^{\prime \prime \prime }&=0 \\
\end{align*} |
[[_3rd_order, _missing_x], [_3rd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
0.029 |
|
| \(1184\) |
\begin{align*}
x^{2} y^{\prime \prime \prime }+y^{\prime \prime } x +\left (2 y x -1\right ) y^{\prime }+y^{2}-f \left (x \right )&=0 \\
\end{align*} |
[[_3rd_order, _exact, _nonlinear]] |
✗ |
✗ |
✗ |
0.035 |
|
| \(1185\) |
\begin{align*}
x^{2} y^{\prime \prime \prime }+x \left (-1+y\right ) y^{\prime \prime }+x {y^{\prime }}^{2}+\left (1-y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_3rd_order, _exact, _nonlinear], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2]] |
✓ |
✗ |
✗ |
0.040 |
|
| \(1186\) |
\begin{align*}
y^{3} y^{\prime }-y^{\prime } y^{\prime \prime }+y y^{\prime \prime \prime }&=0 \\
\end{align*} |
[[_3rd_order, _missing_x], [_3rd_order, _exact, _nonlinear], [_3rd_order, _with_linear_symmetries]] |
✓ |
✗ |
✗ |
0.036 |
|
| \(1187\) |
\begin{align*}
15 {y^{\prime }}^{3}-18 y y^{\prime } y^{\prime \prime }+4 y^{2} y^{\prime \prime \prime }&=0 \\
\end{align*} |
[[_3rd_order, _missing_x], [_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.038 |
|
| \(1188\) |
\begin{align*}
40 {y^{\prime }}^{3}-45 y y^{\prime } y^{\prime \prime }+9 y^{2} y^{\prime \prime \prime }&=0 \\
\end{align*} |
[[_3rd_order, _missing_x], [_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.049 |
|
| \(1189\) |
\begin{align*}
y^{\prime } y^{\prime \prime \prime \prime }-y^{\prime \prime } y^{\prime \prime \prime }+{y^{\prime }}^{3} y^{\prime \prime \prime }&=0 \\
\end{align*} |
[[_high_order, _missing_x], [_high_order, _missing_y], [_high_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
0.076 |
|
| \(1190\) |
\begin{align*}
9 {y^{\prime \prime }}^{2} y^{\left (5\right )}-45 y^{\prime \prime } y^{\prime \prime \prime } y^{\prime \prime \prime \prime }+40 y^{\prime \prime \prime }&=0 \\
\end{align*} |
[[_high_order, _missing_x], [_high_order, _missing_y], [_high_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.099 |
|
| \(1191\) |
\begin{align*}
y^{\prime \prime \prime }&=f \left (y\right ) \\
\end{align*} |
[[_3rd_order, _missing_x], [_3rd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
0.023 |
|
| \(1192\) |
\begin{align*}
x^{\prime }&=x f \left (t \right )+y g \left (t \right ) \\
y^{\prime }&=-x g \left (t \right )+y f \left (t \right ) \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.032 |
|
| \(1193\) |
\begin{align*}
x^{\prime }+\left (a x+b y\right ) f \left (t \right )&=g \left (t \right ) \\
y^{\prime }+\left (c x+d y\right ) f \left (t \right )&=h \left (t \right ) \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.045 |
|
| \(1194\) |
\begin{align*}
x^{\prime }&=x \cos \left (t \right ) \\
y^{\prime }&=x \,{\mathrm e}^{-\sin \left (t \right )} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.035 |
|
| \(1195\) |
\begin{align*}
t x^{\prime }+y&=0 \\
y^{\prime } t +x&=0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.026 |
|
| \(1196\) |
\begin{align*}
t x^{\prime }+2 x&=t \\
y^{\prime } t -\left (t +2\right ) x-t y&=-t \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.033 |
|
| \(1197\) |
\begin{align*}
t x^{\prime }+2 x-2 y&=t \\
y^{\prime } t +x+5 y&=t^{2} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.032 |
|
| \(1198\) |
\begin{align*}
t^{2} \left (1-\sin \left (t \right )\right ) x^{\prime }&=t \left (1-2 \sin \left (t \right )\right ) x+t^{2} y \\
t^{2} \left (1-\sin \left (t \right )\right ) y^{\prime }&=\left (t \cos \left (t \right )-\sin \left (t \right )\right ) x+t \left (1-t \cos \left (t \right )\right ) y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.048 |
|
| \(1199\) |
\begin{align*}
x^{\prime }+y^{\prime }+y&=f \left (t \right ) \\
x^{\prime \prime }+y^{\prime \prime }+y^{\prime }+x+y&=g \left (t \right ) \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.037 |
|
| \(1200\) |
\begin{align*}
2 x^{\prime }+y^{\prime }-3 x&=0 \\
x^{\prime \prime }+y^{\prime }-2 y&={\mathrm e}^{2 t} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.033 |
|
| \(1201\) |
\begin{align*}
x^{\prime }+x-y^{\prime }&=2 t \\
x^{\prime \prime }+y^{\prime }-9 x+3 y&=\sin \left (2 t \right ) \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.036 |
|
| \(1202\) |
\begin{align*}
x^{\prime }-x+2 y&=0 \\
x^{\prime \prime }-2 y^{\prime }&=2 t -\cos \left (2 t \right ) \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.042 |
|
| \(1203\) |
\begin{align*}
t x^{\prime }-y^{\prime } t -2 y&=0 \\
t x^{\prime \prime }+2 x^{\prime }+t x&=0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.034 |
|
| \(1204\) |
\begin{align*}
x^{\prime \prime }+a y&=0 \\
y^{\prime \prime }-a^{2} y&=0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.025 |
|
| \(1205\) |
\begin{align*}
x^{\prime \prime }&=a x+b y \\
y^{\prime \prime }&=c x+d y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.037 |
|
| \(1206\) |
\begin{align*}
x^{\prime \prime }&=a_{1} x+b_{1} y+c_{1} \\
y^{\prime \prime }&=a_{2} x+b_{2} y+c_{2} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.025 |
|
| \(1207\) |
\begin{align*}
x^{\prime \prime }+x+y&=-5 \\
y^{\prime \prime }-4 x-3 y&=-3 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.036 |
|
| \(1208\) |
\begin{align*}
x^{\prime \prime }&=\left (3 \cos \left (a t +b \right )^{2}-1\right ) c^{2} x+\frac {3 c^{2} y \sin \left (2 a t b \right )}{2} \\
y^{\prime \prime }&=\left (3 \sin \left (a t +b \right )^{2}-1\right ) c^{2} y+\frac {3 c^{2} x \sin \left (2 a t b \right )}{2} \\
\end{align*} |
system_of_ODEs |
✗ |
✗ |
✗ |
0.036 |
|
| \(1209\) |
\begin{align*}
x^{\prime \prime }+6 x+7 y&=0 \\
y^{\prime \prime }+3 x+2 y&=2 t \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.027 |
|
| \(1210\) |
\begin{align*}
x^{\prime \prime }-a y^{\prime }+b x&=0 \\
y^{\prime \prime }+a x^{\prime }+b y&=0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.042 |
|
| \(1211\) |
\begin{align*}
a_{1} x^{\prime \prime }+b_{1} x^{\prime }+c_{1} x-A y^{\prime }&=B \,{\mathrm e}^{i \omega t} \\
a_{2} y^{\prime \prime }+b_{2} y^{\prime }+c_{2} y+A x^{\prime }&=0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.057 |
|
| \(1212\) |
\begin{align*}
x^{\prime \prime }+a \left (x^{\prime }-y^{\prime }\right )+b_{1} x&=c_{1} {\mathrm e}^{i \omega t} \\
y^{\prime \prime }+a \left (y^{\prime }-x^{\prime }\right )+b_{2} y&=c_{2} {\mathrm e}^{i \omega t} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.048 |
|
| \(1213\) |
\begin{align*}
\operatorname {a11} x^{\prime \prime }+\operatorname {b11} x^{\prime }+\operatorname {c11} x+\operatorname {a12} y^{\prime \prime }+\operatorname {b12} y^{\prime }+\operatorname {c12} y&=0 \\
\operatorname {a21} x^{\prime \prime }+\operatorname {b21} x^{\prime }+\operatorname {c21} x+\operatorname {a22} y^{\prime \prime }+\operatorname {b22} y^{\prime }+\operatorname {c22} y&=0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.063 |
|
| \(1214\) |
\begin{align*}
x^{\prime \prime }-2 x^{\prime }-y^{\prime }+y&=0 \\
y^{\prime \prime \prime }-y^{\prime \prime }+2 x^{\prime }-x&=t \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.038 |
|
| \(1215\) |
\begin{align*}
x^{\prime \prime }+y^{\prime \prime }+y^{\prime }&=\sinh \left (2 t \right ) \\
2 x^{\prime \prime }+y^{\prime \prime }&=2 t \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.035 |
|
| \(1216\) |
\begin{align*}
x^{\prime \prime }-x^{\prime }+y^{\prime }&=0 \\
x^{\prime \prime }+y^{\prime \prime }-x&=0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.030 |
|
| \(1217\) |
\begin{align*}
x^{\prime }&=a x+g y+\beta z \\
y^{\prime }&=g x+b y+\alpha z \\
z^{\prime }&=\beta x+\alpha y+c z \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
86.938 |
|
| \(1218\) |
\begin{align*}
t x^{\prime }&=2 x-t \\
t^{3} y^{\prime }&=-x+t^{2} y+t \\
t^{4} z^{\prime }&=-x-t^{2} y+t^{3} z+t \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.050 |
|
| \(1219\) |
\begin{align*}
a t x^{\prime }&=b c \left (y-z\right ) \\
b t y^{\prime }&=c a \left (z-x\right ) \\
c t z^{\prime }&=a b \left (x-y\right ) \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.056 |
|
| \(1220\) |
\begin{align*}
x_{1}^{\prime }&=a x_{2}+b x_{3} \cos \left (c t \right )+b x_{4} \sin \left (c t \right ) \\
x_{2}^{\prime }&=-a x_{1}+b x_{3} \sin \left (c t \right )-b x_{4} \cos \left (c t \right ) \\
x_{3}^{\prime }&=-b x_{1} \cos \left (c t \right )-b x_{2} \sin \left (c t \right )+a x_{4} \\
x_{4}^{\prime }&=-b x_{1} \sin \left (c t \right )+b x_{2} \cos \left (c t \right )-a x_{3} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.080 |
|
| \(1221\) |
\begin{align*}
x^{\prime }&=-x \left (x+y\right ) \\
y^{\prime }&=y \left (x+y\right ) \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.041 |
|
| \(1222\) |
\begin{align*}
x^{\prime }&=\left (a y+b \right ) x \\
y^{\prime }&=\left (c x+d \right ) y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.033 |
|
| \(1223\) |
\begin{align*}
x^{\prime }&=x \left (a \left (p x+q y\right )+\alpha \right ) \\
y^{\prime }&=y \left (\beta +b \left (p x+q y\right )\right ) \\
\end{align*} |
system_of_ODEs |
✗ |
✗ |
✗ |
0.044 |
|
| \(1224\) |
\begin{align*}
x^{\prime }&=h \left (a -x\right ) \left (c -x-y\right ) \\
y^{\prime }&=k \left (b -y\right ) \left (c -x-y\right ) \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.034 |
|
| \(1225\) |
\begin{align*}
x^{\prime }&=y^{2}-\cos \left (x\right ) \\
y^{\prime }&=-y \sin \left (x\right ) \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.042 |
|
| \(1226\) |
\begin{align*}
x^{\prime }&=-x \,y^{2}+x+y \\
y^{\prime }&=y \,x^{2}-x-y \\
\end{align*} |
system_of_ODEs |
✗ |
✗ |
✗ |
0.032 |
|
| \(1227\) |
\begin{align*}
x^{\prime }&=x+y-x \left (x^{2}+y^{2}\right ) \\
y^{\prime }&=-x+y-y \left (x^{2}+y^{2}\right ) \\
\end{align*} |
system_of_ODEs |
✗ |
✗ |
✗ |
0.045 |
|
| \(1228\) |
\begin{align*}
x^{\prime }&=-y+x \left (x^{2}+y^{2}-1\right ) \\
y^{\prime }&=x+y \left (x^{2}+y^{2}-1\right ) \\
\end{align*} |
system_of_ODEs |
✗ |
✗ |
✗ |
0.034 |
|
| \(1229\) |
\begin{align*}
\left (t^{2}+1\right ) x^{\prime }&=-t x+y \\
\left (t^{2}+1\right ) y^{\prime }&=-x-t y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.047 |
|
| \(1230\) |
\begin{align*}
\left (x^{2}+y^{2}-t^{2}\right ) x^{\prime }&=-2 t x \\
\left (x^{2}+y^{2}-t^{2}\right ) y^{\prime }&=-2 t y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.052 |
|
| \(1231\) |
\begin{align*}
{x^{\prime }}^{2}+t x^{\prime }+a y^{\prime }-x&=0 \\
x^{\prime } y^{\prime }+y^{\prime } t -y&=0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.074 |
|
| \(1232\) |
\begin{align*}
x&=t x^{\prime }+f \left (x^{\prime }, y^{\prime }\right ) \\
y&=y^{\prime } t +g \left (x^{\prime }, y^{\prime }\right ) \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.075 |
|
| \(1233\) |
\begin{align*}
x^{\prime \prime }&=a \,{\mathrm e}^{2 x}-{\mathrm e}^{-x}+{\mathrm e}^{-2 x} \cos \left (y\right )^{2} \\
y^{\prime \prime }&={\mathrm e}^{-2 x} \sin \left (y\right ) \cos \left (y\right )-\frac {\sin \left (y\right )}{\cos \left (y\right )^{3}} \\
\end{align*} |
system_of_ODEs |
✗ |
✗ |
✗ |
0.045 |
|
| \(1234\) |
\begin{align*}
x^{\prime \prime }&=\frac {k x}{\left (x^{2}+y^{2}\right )^{{3}/{2}}} \\
y^{\prime \prime }&=\frac {k y}{\left (x^{2}+y^{2}\right )^{{3}/{2}}} \\
\end{align*} |
system_of_ODEs |
✗ |
✗ |
✗ |
0.028 |
|
| \(1235\) |
\begin{align*}
x^{\prime }&=y-z \\
y^{\prime }&=x^{2}+y \\
z^{\prime }&=x^{2}+z \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.049 |
|
| \(1236\) |
\begin{align*}
a x^{\prime }&=\left (b -c \right ) y z \\
b y^{\prime }&=\left (c -a \right ) z x \\
c z^{\prime }&=\left (a -b \right ) x y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.048 |
|
| \(1237\) |
\begin{align*}
x^{\prime }&=x \left (y-z\right ) \\
y^{\prime }&=y \left (z-x\right ) \\
z^{\prime }&=z \left (x-y\right ) \\
\end{align*} |
system_of_ODEs |
✗ |
✗ |
✗ |
0.060 |
|
| \(1238\) |
\begin{align*}
x^{\prime }+y^{\prime }&=x y \\
y^{\prime }+z^{\prime }&=y z \\
x^{\prime }+z^{\prime }&=x z \\
\end{align*} |
system_of_ODEs |
✓ |
✗ |
✗ |
0.051 |
|
| \(1239\) |
\begin{align*}
x^{\prime }&=\frac {x^{2}}{2}-\frac {y}{24} \\
y^{\prime }&=2 x y-3 z \\
z^{\prime }&=3 x z-\frac {y^{2}}{6} \\
\end{align*} |
system_of_ODEs |
✗ |
✗ |
✗ |
0.050 |
|
| \(1240\) |
\begin{align*}
x^{\prime }&=x \left (y^{2}-z^{2}\right ) \\
y^{\prime }&=y \left (z^{2}-x^{2}\right ) \\
z^{\prime }&=z \left (x^{2}-y^{2}\right ) \\
\end{align*} |
system_of_ODEs |
✗ |
✗ |
✗ |
0.040 |
|
| \(1241\) |
\begin{align*}
x^{\prime }&=x \left (y^{2}-z^{2}\right ) \\
y^{\prime }&=-y \left (z^{2}+x^{2}\right ) \\
z^{\prime }&=z \left (x^{2}+y^{2}\right ) \\
\end{align*} |
system_of_ODEs |
✓ |
✗ |
✗ |
0.051 |
|
| \(1242\) |
\begin{align*}
x^{\prime }&=-x \,y^{2}+x+y \\
y^{\prime }&=y \,x^{2}-x-y \\
z^{\prime }&=y^{2}-x^{2} \\
\end{align*} |
system_of_ODEs |
✗ |
✗ |
✗ |
0.039 |
|
| \(1243\) |
\begin{align*}
\left (x-y\right ) \left (x-z\right ) x^{\prime }&=f \left (t \right ) \\
\left (-x+y\right ) \left (y-z\right ) y^{\prime }&=f \left (t \right ) \\
\left (z-x\right ) \left (z-y\right ) z^{\prime }&=f \left (t \right ) \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.060 |
|
| \(1244\) |
\begin{align*}
x^{2} y^{\prime }&=c \,x^{2} y^{2}+\left (a \,x^{2}+b x \right ) y+\alpha \,x^{2}+\beta x +\gamma \\
\end{align*} |
[_rational, _Riccati] |
✓ |
✓ |
✗ |
165.531 |
|
| \(1245\) |
\begin{align*}
x^{2} y^{\prime }&=c \,x^{2} y^{2}+\left (a \,x^{n}+b \right ) x y+\alpha \,x^{2 n}+\beta \,x^{n}+\gamma \\
\end{align*} |
[_rational, _Riccati] |
✓ |
✓ |
✗ |
167.938 |
|
| \(1246\) |
\begin{align*}
x^{2} y^{\prime }&=\left (\alpha \,x^{2 n}+\beta \,x^{n}+\gamma \right ) y^{2}+\left (a \,x^{n}+b \right ) x y+c \,x^{2} \\
\end{align*} |
[_rational, _Riccati] |
✓ |
✓ |
✗ |
186.294 |
|
| \(1247\) |
\begin{align*}
\left (x^{2}-1\right ) y^{\prime }+\lambda \left (1-2 y x +y^{2}\right )&=0 \\
\end{align*} |
[_rational, _Riccati] |
✓ |
✓ |
✗ |
35.184 |
|
| \(1248\) |
\begin{align*}
\left (a \,x^{2}+b \right ) y^{\prime }+\alpha y^{2}+\beta x y+\gamma &=0 \\
\end{align*} |
[_rational, _Riccati] |
✓ |
✓ |
✗ |
597.354 |
|
| \(1249\) |
\begin{align*}
x^{3} y^{\prime }&=a \,x^{3} y^{2}+x \left (b x +c \right ) y+x \alpha +\beta \\
\end{align*} |
[_rational, _Riccati] |
✓ |
✓ |
✗ |
158.733 |
|
| \(1250\) |
\begin{align*}
y^{\prime }&=\sigma y^{2}+a +b \,{\mathrm e}^{\lambda x}+c \,{\mathrm e}^{2 \lambda x} \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✗ |
41.453 |
|
| \(1251\) |
\begin{align*}
y^{\prime }&=y^{2}+a \,{\mathrm e}^{2 \lambda x} \left ({\mathrm e}^{\lambda x}+b \right )^{n}-\frac {\lambda ^{2}}{4} \\
\end{align*} |
[_Riccati] |
✓ |
✗ |
✗ |
173.787 |
|
| \(1252\) |
\begin{align*}
y^{\prime }&=a \,{\mathrm e}^{\mu x} y^{2}+a b \,{\mathrm e}^{\left (\lambda +\mu \right ) x} y-b \lambda \,{\mathrm e}^{\lambda x} \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✗ |
158.951 |
|
| \(1253\) |
\begin{align*}
y^{\prime }&=a \,x^{n} y^{2}-a b \,x^{n} {\mathrm e}^{\lambda x} y+b \lambda \,{\mathrm e}^{\lambda x} \\
\end{align*} |
[_Riccati] |
✗ |
✓ |
✗ |
27.156 |
|
| \(1254\) |
\begin{align*}
y^{\prime }&=a \,x^{n} y^{2}-a \,x^{n} \left (b \,{\mathrm e}^{\lambda x}+c \right ) y+c \,x^{n} \\
\end{align*} |
[_Riccati] |
✗ |
✗ |
✗ |
25.474 |
|
| \(1255\) |
\begin{align*}
y^{\prime }&=a \cosh \left (\lambda x \right ) y^{2}+b \cosh \left (\lambda x \right ) \sinh \left (\lambda x \right )^{n} \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✗ |
205.527 |
|
| \(1256\) |
\begin{align*}
y^{\prime }&=y^{2}+a \lambda -a \left (a +\lambda \right ) \tanh \left (\lambda x \right )^{2} \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✗ |
37.471 |
|
| \(1257\) |
\begin{align*}
y^{\prime }&=y^{2}+3 a \lambda -\lambda ^{2}-a \left (a +\lambda \right ) \tanh \left (\lambda x \right )^{2} \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✗ |
104.952 |
|
| \(1258\) |
\begin{align*}
y^{\prime }&=y^{2}+a \lambda -a \left (a +\lambda \right ) \coth \left (\lambda x \right )^{2} \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✗ |
37.663 |
|
| \(1259\) |
\begin{align*}
y^{\prime }&=y^{2}-\lambda ^{2}+3 a \lambda -a \left (a +\lambda \right ) \coth \left (\lambda x \right )^{2} \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✗ |
66.138 |
|
| \(1260\) |
\begin{align*}
2 y^{\prime }&=\left (\lambda +a -a \sin \left (\lambda x \right )\right ) y^{2}+\lambda -a -a \sin \left (\lambda x \right ) \\
\end{align*} |
[_Riccati] |
✓ |
✗ |
✗ |
244.359 |
|
| \(1261\) |
\begin{align*}
y^{\prime }&=y^{2}+a \lambda +a \left (\lambda -a \right ) \tan \left (\lambda x \right )^{2} \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✗ |
19.038 |
|
| \(1262\) |
\begin{align*}
y^{\prime }&=y^{2}+\lambda ^{2}+3 a \lambda +a \left (\lambda -a \right ) \tan \left (\lambda x \right )^{2} \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✗ |
116.805 |
|
| \(1263\) |
\begin{align*}
y^{\prime }&=y^{2}+a \lambda +a \left (\lambda -a \right ) \cot \left (\lambda x \right )^{2} \\
\end{align*} |
[_Riccati] |
✓ |
✗ |
✗ |
19.838 |
|
| \(1264\) |
\begin{align*}
y^{\prime }&=y^{2}+\lambda ^{2}+3 a \lambda +a \left (\lambda -a \right ) \cot \left (\lambda x \right )^{2} \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✗ |
96.409 |
|
| \(1265\) |
\begin{align*}
y^{\prime }&=y^{2}-2 a b \cot \left (a x \right ) y+b^{2}-a^{2} \\
\end{align*} |
[_Riccati] |
✓ |
✗ |
✗ |
199.721 |
|
| \(1266\) |
\begin{align*}
y^{\prime }&=a \cot \left (\lambda x +\mu \right )^{k} \left (y-b \,x^{n}-c \right )^{2}+b n \,x^{n -1} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
✓ |
✗ |
586.570 |
|
| \(1267\) |
\begin{align*}
y^{\prime }&=a \cos \left (\lambda x \right ) y^{2}+b \cos \left (\lambda x \right ) \sin \left (\lambda x \right )^{n} \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✗ |
203.721 |
|
| \(1268\) |
\begin{align*}
y^{\prime }&=y^{2}-\frac {\lambda ^{2}}{2}-\frac {3 \lambda ^{2} \tan \left (\lambda x \right )^{2}}{4}+a \cos \left (\lambda x \right )^{2} \sin \left (\lambda x \right )^{n} \\
\end{align*} |
[_Riccati] |
✓ |
✗ |
✗ |
219.181 |
|
| \(1269\) |
\begin{align*}
y^{\prime }&=\lambda \arcsin \left (x \right )^{n} \left (y-a \,x^{m}-b \right )^{2}+a m \,x^{m -1} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
✓ |
✗ |
64.296 |
|
| \(1270\) |
\begin{align*}
y^{\prime }&=\lambda \arccos \left (x \right )^{n} \left (y-a \,x^{m}-b \right )^{2}+a m \,x^{m -1} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
✓ |
✗ |
84.066 |
|
| \(1271\) |
\begin{align*}
y^{\prime }&=\lambda \arctan \left (x \right )^{n} \left (y-a \,x^{m}-b \right )^{2}+a m \,x^{m -1} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
✓ |
✗ |
78.755 |
|
| \(1272\) |
\begin{align*}
y^{\prime }&=\lambda \operatorname {arccot}\left (x \right )^{n} \left (y-a \,x^{m}-b \right )^{2}+a m \,x^{m -1} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
✓ |
✗ |
114.627 |
|
| \(1273\) |
\begin{align*}
y^{\prime }&=f \left (x \right ) y^{2}-a \tanh \left (\lambda x \right )^{2} \left (a f \left (x \right )+\lambda \right )+a \lambda \\
\end{align*} |
[_Riccati] |
✗ |
✗ |
✗ |
92.165 |
|
| \(1274\) |
\begin{align*}
y^{\prime }&=f \left (x \right ) y^{2}-a \coth \left (\lambda x \right )^{2} \left (a f \left (x \right )+\lambda \right )+a \lambda \\
\end{align*} |
[_Riccati] |
✗ |
✗ |
✗ |
90.852 |
|
| \(1275\) |
\begin{align*}
y^{\prime }&=f \left (x \right ) y^{2}-a^{2} f \left (x \right )+a \lambda \sinh \left (\lambda x \right )-a^{2} f \left (x \right ) \sinh \left (\lambda x \right )^{2} \\
\end{align*} |
[_Riccati] |
✗ |
✗ |
✗ |
41.761 |
|
| \(1276\) |
\begin{align*}
y^{\prime } x&=f \left (x \right ) y^{2}+a -a^{2} f \left (x \right ) \ln \left (x \right )^{2} \\
\end{align*} |
[_Riccati] |
✗ |
✗ |
✗ |
32.284 |
|
| \(1277\) |
\begin{align*}
y^{\prime } x&=f \left (x \right ) \left (y+a \ln \left (x \right )\right )^{2}-a \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
✓ |
✗ |
37.105 |
|
| \(1278\) |
\begin{align*}
y^{\prime }&=f \left (x \right ) y^{2}-a x \ln \left (x \right ) f \left (x \right ) y+a \ln \left (x \right )+a \\
\end{align*} |
[_Riccati] |
✗ |
✗ |
✗ |
42.078 |
|
| \(1279\) |
\begin{align*}
y^{\prime }&=f \left (x \right ) y^{2}-a^{2} f \left (x \right )+a \lambda \sin \left (\lambda x \right )+a^{2} f \left (x \right ) \sin \left (\lambda x \right )^{2} \\
\end{align*} |
[_Riccati] |
✗ |
✗ |
✗ |
46.079 |
|
| \(1280\) |
\begin{align*}
y^{\prime }&=f \left (x \right ) y^{2}-a^{2} f \left (x \right )+a \lambda \cos \left (\lambda x \right )+a^{2} f \left (x \right ) \cos \left (\lambda x \right )^{2} \\
\end{align*} |
[_Riccati] |
✗ |
✗ |
✗ |
46.503 |
|
| \(1281\) |
\begin{align*}
y^{\prime }&=f \left (x \right ) y^{2}-a \tan \left (\lambda x \right )^{2} \left (a f \left (x \right )-\lambda \right )+a \lambda \\
\end{align*} |
[_Riccati] |
✗ |
✗ |
✗ |
88.500 |
|
| \(1282\) |
\begin{align*}
y^{\prime }&=f \left (x \right ) y^{2}-a \cot \left (\lambda x \right )^{2} \left (a f \left (x \right )-\lambda \right )+a \lambda \\
\end{align*} |
[_Riccati] |
✗ |
✗ |
✗ |
100.441 |
|
| \(1283\) |
\begin{align*}
y^{\prime }&=\frac {y^{2} f^{\prime }\left (x \right )}{g \left (x \right )}-\frac {g^{\prime }\left (x \right )}{f \left (x \right )} \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✗ |
12.420 |
|
| \(1284\) |
\begin{align*}
f \left (x \right )^{2} y^{\prime }-f^{\prime }\left (x \right ) y^{2}+g \left (x \right ) \left (y-f \left (x \right )\right )&=0 \\
\end{align*} |
[_Riccati] |
✗ |
✗ |
✗ |
32.608 |
|
| \(1285\) |
\begin{align*}
y^{\prime }&=y^{2}+a^{2} f \left (a x +b \right ) \\
\end{align*} |
[_Riccati] |
✗ |
✗ |
✗ |
17.164 |
|
| \(1286\) |
\begin{align*}
y^{\prime }&=y^{2}+\frac {f \left (\frac {1}{x}\right )}{x^{4}} \\
\end{align*} |
[_Riccati] |
✗ |
✗ |
✗ |
18.324 |
|
| \(1287\) |
\begin{align*}
x^{2} y^{\prime }&=x^{4} f \left (x \right ) y^{2}+1 \\
\end{align*} |
[_Riccati] |
✗ |
✗ |
✗ |
19.457 |
|
| \(1288\) |
\begin{align*}
x^{2} y^{\prime }&=y^{2} x^{4}+x^{2 n} f \left (a \,x^{n}+b \right )-\frac {n^{2}}{4}+\frac {1}{4} \\
\end{align*} |
[_Riccati] |
✗ |
✗ |
✗ |
81.559 |
|
| \(1289\) |
\begin{align*}
y^{\prime }&=f \left (x \right ) y^{2}+g \left (x \right ) y+h \left (x \right ) \\
\end{align*} |
[_Riccati] |
✗ |
✗ |
✗ |
26.669 |
|
| \(1290\) |
\begin{align*}
x^{2} y^{\prime }&=y^{2} x^{2}+f \left (a \ln \left (x \right )+b \right )+\frac {1}{4} \\
\end{align*} |
[_Riccati] |
✗ |
✗ |
✗ |
49.409 |
|
| \(1291\) |
\begin{align*}
y y^{\prime }-y&=-\frac {2 x}{9}+A +\frac {B}{\sqrt {x}} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✗ |
216.032 |
|
| \(1292\) |
\begin{align*}
y y^{\prime }-y&=2 A \left (\sqrt {x}+4 A +\frac {3 A^{2}}{\sqrt {x}}\right ) \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✗ |
✗ |
173.223 |
|
| \(1293\) |
\begin{align*}
y y^{\prime }-y&=A x +\frac {B}{x}-\frac {B^{2}}{x^{3}} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✗ |
✗ |
64.253 |
|
| \(1294\) |
\begin{align*}
y y^{\prime }-y&=\frac {A}{x}-\frac {A^{2}}{x^{3}} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✗ |
59.261 |
|
| \(1295\) |
\begin{align*}
y y^{\prime }-y&=A +B \,{\mathrm e}^{-\frac {2 x}{A}} \\
\end{align*} |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✗ |
✗ |
68.649 |
|
| \(1296\) |
\begin{align*}
y y^{\prime }-y&=A \left ({\mathrm e}^{\frac {2 x}{A}}-1\right ) \\
\end{align*} |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✗ |
✗ |
83.378 |
|
| \(1297\) |
\begin{align*}
y y^{\prime }-y&=-\frac {2 x}{9}+6 A^{2} \left (1+\frac {2 A}{\sqrt {x}}\right ) \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✗ |
162.005 |
|
| \(1298\) |
\begin{align*}
y y^{\prime }-y&=\frac {\left (2 m +1\right ) x}{4 m^{2}}+\frac {A}{x}-\frac {A^{2}}{x^{3}} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✗ |
✗ |
84.280 |
|
| \(1299\) |
\begin{align*}
y y^{\prime }-y&=\frac {4}{9} x +2 A \,x^{2}+2 A^{2} x^{3} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✗ |
78.524 |
|
| \(1300\) |
\begin{align*}
y y^{\prime }-y&=-\frac {3 x}{16}+\frac {5 A}{x^{{1}/{3}}}-\frac {12 A^{2}}{x^{{5}/{3}}} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
145.663 |
|
| \(1301\) |
\begin{align*}
y y^{\prime }-y&=\frac {A}{x} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✗ |
143.212 |
|
| \(1302\) |
\begin{align*}
y y^{\prime }-y&=-\frac {x}{4}+\frac {A \left (\sqrt {x}+5 A +\frac {3 A^{2}}{\sqrt {x}}\right )}{4} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✗ |
✗ |
215.579 |
|
| \(1303\) |
\begin{align*}
y y^{\prime }-y&=\frac {2 a^{2}}{\sqrt {8 a^{2}+x^{2}}} \\
\end{align*} |
[[_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✗ |
✗ |
952.985 |
|
| \(1304\) |
\begin{align*}
y y^{\prime }-y&=\frac {3 x}{8}+\frac {3 \sqrt {a^{2}+x^{2}}}{8}-\frac {a^{2}}{16 \sqrt {a^{2}+x^{2}}} \\
\end{align*} |
[[_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
235.245 |
|
| \(1305\) |
\begin{align*}
y y^{\prime }-y&=-\frac {4 x}{25}+\frac {A}{\sqrt {x}} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✗ |
✗ |
148.237 |
|
| \(1306\) |
\begin{align*}
y y^{\prime }-y&=-\frac {9 x}{100}+\frac {A}{x^{{5}/{3}}} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✗ |
129.970 |
|
| \(1307\) |
\begin{align*}
y y^{\prime }-y&=-\frac {12 x}{49}+\frac {2 A \left (5 \sqrt {x}+34 A +\frac {15 A^{2}}{\sqrt {x}}\right )}{49} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✗ |
✗ |
220.237 |
|
| \(1308\) |
\begin{align*}
y y^{\prime }-y&=-\frac {12 x}{49}+\frac {A \left (25 \sqrt {x}+41 A +\frac {10 A^{2}}{\sqrt {x}}\right )}{98} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✗ |
✗ |
219.620 |
|
| \(1309\) |
\begin{align*}
y y^{\prime }-y&=-\frac {2 x}{9}+\frac {A}{\sqrt {x}} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✗ |
124.021 |
|
| \(1310\) |
\begin{align*}
y y^{\prime }-y&=-\frac {12 x}{49}+\frac {6 A \left (-3 \sqrt {x}+23 A +\frac {12 A^{2}}{\sqrt {x}}\right )}{49} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
191.872 |
|
| \(1311\) |
\begin{align*}
y y^{\prime }-y&=-\frac {30 x}{121}+\frac {3 A \left (21 \sqrt {x}+35 A +\frac {6 A^{2}}{\sqrt {x}}\right )}{242} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
214.102 |
|
| \(1312\) |
\begin{align*}
y y^{\prime }-y&=-\frac {3 x}{16}+\frac {A}{x^{{5}/{3}}} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
121.730 |
|
| \(1313\) |
\begin{align*}
y y^{\prime }-y&=-\frac {12 x}{49}+\frac {4 A \left (-10 \sqrt {x}+27 A +\frac {10 A^{2}}{\sqrt {x}}\right )}{49} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
209.881 |
|
| \(1314\) |
\begin{align*}
y y^{\prime }-y&=\frac {A}{\sqrt {x}} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✗ |
702.291 |
|
| \(1315\) |
\begin{align*}
y y^{\prime }-y&=A \left (n +2\right ) \left (\sqrt {x}+2 \left (n +2\right ) A +\frac {\left (n +1\right ) \left (n +3\right ) A^{2}}{\sqrt {x}}\right ) \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✗ |
✗ |
1321.608 |
|
| \(1316\) |
\begin{align*}
y y^{\prime }-y&=A \left (n +2\right ) \left (\sqrt {x}+2 \left (n +2\right ) A +\frac {\left (2 n +3\right ) A^{2}}{\sqrt {x}}\right ) \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✗ |
✗ |
1347.311 |
|
| \(1317\) |
\begin{align*}
y y^{\prime }-y&=A \sqrt {x}+2 A^{2}+\frac {B}{\sqrt {x}} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✗ |
✗ |
1173.286 |
|
| \(1318\) |
\begin{align*}
y y^{\prime }-y&=2 A^{2}-A \sqrt {x} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✗ |
✗ |
1461.714 |
|
| \(1319\) |
\begin{align*}
y y^{\prime }-y&=-\frac {x}{4}+\frac {6 A \left (\sqrt {x}+8 A +\frac {5 A^{2}}{\sqrt {x}}\right )}{49} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
1579.085 |
|
| \(1320\) |
\begin{align*}
y y^{\prime }-y&=-\frac {6 x}{25}+\frac {6 A \left (2 \sqrt {x}+7 A +\frac {4 A^{2}}{\sqrt {x}}\right )}{25} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
1594.700 |
|
| \(1321\) |
\begin{align*}
y y^{\prime }-y&=-\frac {3 x}{16}+\frac {3 A}{x^{{1}/{3}}}-\frac {12 A^{2}}{x^{{5}/{3}}} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✗ |
✗ |
1176.888 |
|
| \(1322\) |
\begin{align*}
y y^{\prime }-y&=\frac {9 x}{32}+\frac {15 \sqrt {b^{2}+x^{2}}}{32}+\frac {3 b^{2}}{64 \sqrt {b^{2}+x^{2}}} \\
\end{align*} |
[[_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
264.569 |
|
| \(1323\) |
\begin{align*}
y y^{\prime }-y&=A \,x^{2}-\frac {9}{625 A} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✗ |
73.962 |
|
| \(1324\) |
\begin{align*}
y y^{\prime }-y&=-\frac {6}{25} x -A \,x^{2} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✗ |
85.864 |
|
| \(1325\) |
\begin{align*}
y y^{\prime }-y&=\frac {6}{25} x -A \,x^{2} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✗ |
90.661 |
|
| \(1326\) |
\begin{align*}
y y^{\prime }-y&=\frac {63 x}{4}+\frac {A}{x^{{5}/{3}}} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
126.725 |
|
| \(1327\) |
\begin{align*}
y y^{\prime }-y&=2 x +2 A \left (10 \sqrt {x}+31 A +\frac {30 A^{2}}{\sqrt {x}}\right ) \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✗ |
✗ |
212.048 |
|
| \(1328\) |
\begin{align*}
y y^{\prime }-y&=2 x +2 A \left (-10 \sqrt {x}+19 A +\frac {30 A^{2}}{\sqrt {x}}\right ) \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
212.627 |
|
| \(1329\) |
\begin{align*}
y y^{\prime }-y&=-\frac {12 x}{49}+\frac {A \left (5 \sqrt {x}+262 A +\frac {65 A^{2}}{\sqrt {x}}\right )}{49} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✗ |
✗ |
251.245 |
|
| \(1330\) |
\begin{align*}
y y^{\prime }-y&=-\frac {12 x}{49}+A \sqrt {x} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✗ |
✗ |
151.510 |
|
| \(1331\) |
\begin{align*}
y y^{\prime }-y&=20 x +\frac {A}{\sqrt {x}} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
133.845 |
|
| \(1332\) |
\begin{align*}
y y^{\prime }-y&=-\frac {10 x}{49}+\frac {2 A \left (4 \sqrt {x}+61 A +\frac {12 A^{2}}{\sqrt {x}}\right )}{49} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✗ |
✗ |
241.624 |
|
| \(1333\) |
\begin{align*}
y y^{\prime }-y&=-\frac {12 x}{49}+\frac {2 A \left (\sqrt {x}+166 A +\frac {55 A^{2}}{\sqrt {x}}\right )}{49} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✗ |
✗ |
254.860 |
|
| \(1334\) |
\begin{align*}
y y^{\prime }-y&=-\frac {4 x}{25}+\frac {A \left (7 \sqrt {x}+49 A +\frac {6 A^{2}}{\sqrt {x}}\right )}{50} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
238.873 |
|
| \(1335\) |
\begin{align*}
y y^{\prime }-y&=\frac {15 x}{4}+\frac {6 A}{x^{{1}/{3}}}-\frac {3 A^{2}}{x^{{5}/{3}}} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
157.633 |
|
| \(1336\) |
\begin{align*}
y y^{\prime }-y&=-\frac {3 x}{16}+\frac {A}{x^{{1}/{3}}}+\frac {B}{x^{{5}/{3}}} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
161.342 |
|
| \(1337\) |
\begin{align*}
y y^{\prime }-y&=\frac {k}{\sqrt {A \,x^{2}+B x +c}} \\
\end{align*} |
[[_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
65.332 |
|
| \(1338\) |
\begin{align*}
y y^{\prime }-y&=-\frac {6 x}{25}+\frac {4 B^{2} \left (\left (2-A \right ) x^{{1}/{3}}-\frac {3 B \left (2 A +1\right )}{2}+\frac {B^{2} \left (1-3 A \right )}{x^{{1}/{3}}}-\frac {A \,B^{3}}{x^{{2}/{3}}}\right )}{75} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✗ |
✗ |
313.403 |
|
| \(1339\) |
\begin{align*}
y y^{\prime }-y&=a x +x^{m} b \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
✗ |
✗ |
36.374 |
|
| \(1340\) |
\begin{align*}
y y^{\prime }-y&=a^{2} \lambda \,{\mathrm e}^{2 \lambda x}-a \left (b \lambda +1\right ) {\mathrm e}^{\lambda x}+b \\
\end{align*} |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
✗ |
✗ |
46.910 |
|
| \(1341\) |
\begin{align*}
y y^{\prime }-y&=a^{2} f^{\prime }\left (x \right ) f^{\prime \prime }\left (x \right )-\frac {\left (f \left (x \right )+b \right )^{2} f^{\prime \prime }\left (x \right )}{{f^{\prime }\left (x \right )}^{3}} \\
\end{align*} |
[[_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
11.850 |
|
| \(1342\) |
\begin{align*}
y y^{\prime }&=\left (a x +b \right ) y+1 \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✗ |
20.634 |
|
| \(1343\) |
\begin{align*}
y y^{\prime }&=\frac {y}{\left (a x +b \right )^{2}}+1 \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✗ |
16.443 |
|
| \(1344\) |
\begin{align*}
y y^{\prime }&=\left (a -\frac {1}{a x}\right ) y+1 \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✗ |
46.531 |
|
| \(1345\) |
\begin{align*}
y y^{\prime }&=\frac {3 y}{\sqrt {a \,x^{{3}/{2}}+8 x}}+1 \\
\end{align*} |
[[_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✗ |
✗ |
40.509 |
|
| \(1346\) |
\begin{align*}
y y^{\prime }&=\left (\frac {a}{x^{{2}/{3}}}-\frac {2}{3 a \,x^{{1}/{3}}}\right ) y+1 \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✗ |
✗ |
61.518 |
|
| \(1347\) |
\begin{align*}
y y^{\prime }&=a \,{\mathrm e}^{\lambda x} y+1 \\
\end{align*} |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✗ |
8.262 |
|
| \(1348\) |
\begin{align*}
y y^{\prime }&=\left (a \,{\mathrm e}^{\lambda x}+b \,{\mathrm e}^{-\lambda x}\right ) y+1 \\
\end{align*} |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
✗ |
✗ |
17.622 |
|
| \(1349\) |
\begin{align*}
y y^{\prime }&=a y \cosh \left (x \right )+1 \\
\end{align*} |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
✗ |
✗ |
55.434 |
|
| \(1350\) |
\begin{align*}
y y^{\prime }&=a \cos \left (\lambda x \right ) y+1 \\
\end{align*} |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
✗ |
✗ |
22.851 |
|
| \(1351\) |
\begin{align*}
y y^{\prime }&=a \sin \left (\lambda x \right ) y+1 \\
\end{align*} |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
✗ |
✗ |
32.429 |
|
| \(1352\) |
\begin{align*}
y y^{\prime }&=\left (a x +3 b \right ) y+c \,x^{3}-a b \,x^{2}-2 b^{2} x \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✗ |
✗ |
30.793 |
|
| \(1353\) |
\begin{align*}
2 y y^{\prime }&=\left (7 a x +5 b \right ) y-3 a^{2} x^{3}-2 c \,x^{2}-3 b^{2} x \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✗ |
✗ |
51.910 |
|
| \(1354\) |
\begin{align*}
y y^{\prime }&=\left (\left (3-m \right ) x -1\right ) y-\left (m -1\right ) a x \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
✗ |
✗ |
129.808 |
|
| \(1355\) |
\begin{align*}
y y^{\prime }+x \left (a \,x^{2}+b \right ) y+x&=0 \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✗ |
32.718 |
|
| \(1356\) |
\begin{align*}
y y^{\prime }+a \left (1-\frac {1}{x}\right ) y&=a^{2} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✗ |
49.552 |
|
| \(1357\) |
\begin{align*}
y y^{\prime }-a \left (1-\frac {b}{x}\right ) y&=a^{2} b \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✗ |
54.803 |
|
| \(1358\) |
\begin{align*}
y y^{\prime }&=x^{n -1} \left (\left (2 n +1\right ) x +a n \right ) y-n \,x^{2 n} \left (a +x \right ) \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✗ |
✗ |
91.546 |
|
| \(1359\) |
\begin{align*}
y y^{\prime }&=a \left (-n b +x \right ) x^{n -1} y+c \left (x^{2}-\left (2 n +1\right ) b x +n \left (n +1\right ) b^{2}\right ) x^{2 n -1} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✗ |
188.301 |
|
| \(1360\) |
\begin{align*}
y y^{\prime }-\frac {a \left (x \left (m -1\right )+1\right ) y}{x}&=\frac {a^{2} \left (x m +1\right ) \left (x -1\right )}{x} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✗ |
✗ |
32.128 |
|
| \(1361\) |
\begin{align*}
y y^{\prime }-a \left (1-\frac {b}{\sqrt {x}}\right ) y&=\frac {a^{2} b}{\sqrt {x}} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✗ |
30.812 |
|
| \(1362\) |
\begin{align*}
y y^{\prime }+\frac {a \left (6 x -1\right ) y}{2 x}&=-\frac {a^{2} \left (x -1\right ) \left (4 x -1\right )}{2 x} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✗ |
✗ |
35.618 |
|
| \(1363\) |
\begin{align*}
y y^{\prime }-\frac {a \left (1+\frac {2 b}{x^{2}}\right ) y}{2}&=\frac {a^{2} \left (3 x +\frac {4 b}{x}\right )}{16} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
45.043 |
|
| \(1364\) |
\begin{align*}
y y^{\prime }+\frac {a \left (13 x -18\right ) y}{15 x^{{7}/{5}}}&=-\frac {4 a^{2} \left (x -1\right ) \left (x -6\right )}{15 x^{{9}/{5}}} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
104.345 |
|
| \(1365\) |
\begin{align*}
y y^{\prime }+\frac {a \left (5 x +1\right ) y}{2 \sqrt {x}}&=a^{2} \left (-x^{2}+1\right ) \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
80.315 |
|
| \(1366\) |
\begin{align*}
y y^{\prime }+\frac {a \left (7 x -12\right ) y}{10 x^{{7}/{5}}}&=-\frac {a^{2} \left (x -1\right ) \left (x -16\right )}{10 x^{{9}/{5}}} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✗ |
✗ |
103.098 |
|
| \(1367\) |
\begin{align*}
y y^{\prime }+\frac {3 a \left (13 x -8\right ) y}{20 x^{{7}/{5}}}&=-\frac {a^{2} \left (x -1\right ) \left (27 x -32\right )}{20 x^{{9}/{5}}} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
111.345 |
|
| \(1368\) |
\begin{align*}
y y^{\prime }-\frac {a \left (x +1\right ) y}{2 x^{{7}/{4}}}&=\frac {a^{2} \left (x -1\right ) \left (3 x +5\right )}{4 x^{{5}/{2}}} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✗ |
✗ |
170.769 |
|
| \(1369\) |
\begin{align*}
y y^{\prime }-\frac {a \left (4 x +3\right ) y}{14 x^{{8}/{7}}}&=-\frac {a^{2} \left (x -1\right ) \left (16 x +5\right )}{14 x^{{9}/{7}}} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
125.790 |
|
| \(1370\) |
\begin{align*}
y y^{\prime }+\frac {a \left (13 x -3\right ) y}{6 x^{{2}/{3}}}&=-\frac {a^{2} \left (x -1\right ) \left (5 x -1\right )}{6 x^{{1}/{3}}} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
143.334 |
|
| \(1371\) |
\begin{align*}
y y^{\prime }-\frac {a \left (5 x -4\right ) y}{x^{4}}&=\frac {a^{2} \left (x -1\right ) \left (3 x -1\right )}{x^{7}} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✗ |
✗ |
57.112 |
|
| \(1372\) |
\begin{align*}
y y^{\prime }-\frac {2 a \left (3 x -10\right ) y}{5 x^{4}}&=\frac {a^{2} \left (x -1\right ) \left (8 x -5\right )}{5 x^{7}} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
82.311 |
|
| \(1373\) |
\begin{align*}
y y^{\prime }+\frac {a \left (39 x -4\right ) y}{42 x^{{9}/{7}}}&=-\frac {a^{2} \left (x -1\right ) \left (9 x -1\right )}{42 x^{{11}/{7}}} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
125.867 |
|
| \(1374\) |
\begin{align*}
y y^{\prime }+\frac {a \left (x -2\right ) y}{x}&=\frac {2 a^{2} \left (x -1\right )}{x} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✗ |
✗ |
44.677 |
|
| \(1375\) |
\begin{align*}
y y^{\prime }+\frac {a \left (3 x -2\right ) y}{x}&=-\frac {2 a^{2} \left (x -1\right )^{2}}{x} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
56.972 |
|
| \(1376\) |
\begin{align*}
y y^{\prime }+\frac {a \left (1-\frac {b}{x^{2}}\right ) y}{x}&=\frac {a^{2} b}{x} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
43.968 |
|
| \(1377\) |
\begin{align*}
y y^{\prime }-\frac {a \left (3 x -4\right ) y}{4 x^{{5}/{2}}}&=\frac {a^{2} \left (x -1\right ) \left (2+x \right )}{4 x^{4}} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
74.050 |
|
| \(1378\) |
\begin{align*}
y y^{\prime }+\frac {a \left (33 x +2\right ) y}{30 x^{{6}/{5}}}&=-\frac {a^{2} \left (x -1\right ) \left (9 x -4\right )}{30 x^{{7}/{5}}} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✗ |
✗ |
108.883 |
|
| \(1379\) |
\begin{align*}
y y^{\prime }-\frac {a \left (x -8\right ) y}{8 x^{{5}/{2}}}&=-\frac {a^{2} \left (x -1\right ) \left (3 x -4\right )}{8 x^{4}} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
75.315 |
|
| \(1380\) |
\begin{align*}
y y^{\prime }-\frac {a \left (6 x -13\right ) y}{13 x^{{5}/{2}}}&=-\frac {a^{2} \left (x -1\right ) \left (x -13\right )}{26 x^{4}} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
76.100 |
|
| \(1381\) |
\begin{align*}
y y^{\prime }-\frac {2 a \left (3 x +2\right ) y}{5 x^{{8}/{5}}}&=\frac {a^{2} \left (x -1\right ) \left (8 x +1\right )}{5 x^{{11}/{5}}} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
112.799 |
|
| \(1382\) |
\begin{align*}
y y^{\prime }-\frac {6 a \left (4 x +1\right ) y}{5 x^{{7}/{5}}}&=\frac {a^{2} \left (x -1\right ) \left (27 x +8\right )}{5 x^{{9}/{5}}} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
120.541 |
|
| \(1383\) |
\begin{align*}
y y^{\prime }-\frac {a \left (x +4\right ) y}{5 x^{{8}/{5}}}&=\frac {a^{2} \left (x -1\right ) \left (3 x +7\right )}{5 x^{{3}/{5}}} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
100.614 |
|
| \(1384\) |
\begin{align*}
y y^{\prime }-\frac {a \left (x +4\right ) y}{5 x^{{8}/{5}}}&=\frac {a^{2} \left (x -1\right ) \left (3 x +7\right )}{5 x^{{11}/{5}}} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✗ |
✗ |
109.728 |
|
| \(1385\) |
\begin{align*}
y y^{\prime }-\frac {a \left (2 x -1\right ) y}{x^{{5}/{2}}}&=\frac {a^{2} \left (x -1\right ) \left (1+3 x \right )}{2 x^{4}} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✗ |
✗ |
75.624 |
|
| \(1386\) |
\begin{align*}
y y^{\prime }+\frac {a \left (x -6\right ) y}{5 x^{{7}/{5}}}&=\frac {2 a^{2} \left (x -1\right ) \left (x +4\right )}{5 x^{{9}/{5}}} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✗ |
✗ |
104.141 |
|
| \(1387\) |
\begin{align*}
y y^{\prime }-\frac {3 a y}{x^{{7}/{4}}}&=\frac {a^{2} \left (x -1\right ) \left (x -9\right )}{4 x^{{5}/{2}}} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
113.692 |
|
| \(1388\) |
\begin{align*}
y y^{\prime }-\frac {a \left (\left (1+k \right ) x -1\right ) y}{x^{2}}&=\frac {a^{2} \left (1+k \right ) \left (x -1\right )}{x^{2}} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✗ |
✗ |
159.731 |
|
| \(1389\) |
\begin{align*}
y y^{\prime }-\left (\left (2 n -1\right ) x -a n \right ) x^{-1-n} y&=n \left (x -a \right ) x^{-2 n} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✗ |
✗ |
138.395 |
|
| \(1390\) |
\begin{align*}
y y^{\prime }-a \left (\frac {n +2}{n}+b \,x^{n}\right ) y&=-\frac {a^{2} x \left (\frac {n +1}{n}+b \,x^{n}\right )}{n} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✗ |
✗ |
162.904 |
|
| \(1391\) |
\begin{align*}
y y^{\prime }&=\left (a \,{\mathrm e}^{x}+b \right ) y+c \,{\mathrm e}^{2 x}-a b \,{\mathrm e}^{x}-b^{2} \\
\end{align*} |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✗ |
✗ |
57.426 |
|
| \(1392\) |
\begin{align*}
y y^{\prime }&=\left (a \,{\mathrm e}^{\lambda x}+b \right ) y+c \left (a^{2} {\mathrm e}^{2 \lambda x}+a b \left (\lambda x +1\right ) {\mathrm e}^{\lambda x}+b^{2} \lambda x \right ) \\
\end{align*} |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✗ |
145.084 |
|
| \(1393\) |
\begin{align*}
y y^{\prime }&={\mathrm e}^{\lambda x} \left (2 a \lambda x +a +b \right ) y-{\mathrm e}^{2 \lambda x} \left (a^{2} \lambda \,x^{2}+a b x +c \right ) \\
\end{align*} |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✗ |
✗ |
301.625 |
|
| \(1394\) |
\begin{align*}
y y^{\prime }&={\mathrm e}^{a x} \left (2 a \,x^{2}+b +2 x \right ) y+{\mathrm e}^{2 a x} \left (-a \,x^{4}-b \,x^{2}+c \right ) \\
\end{align*} |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
✗ |
✗ |
157.460 |
|
| \(1395\) |
\begin{align*}
y y^{\prime }+a \left (2 b x +1\right ) {\mathrm e}^{b x} y&=-a^{2} b \,x^{2} {\mathrm e}^{2 b x} \\
\end{align*} |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✗ |
30.835 |
|
| \(1396\) |
\begin{align*}
y y^{\prime }-a \left (1+2 n +2 n \left (n +1\right ) x \right ) {\mathrm e}^{\left (n +1\right ) x} y&=-a^{2} n \left (n +1\right ) \left (x n +1\right ) x \,{\mathrm e}^{2 \left (n +1\right ) x} \\
\end{align*} |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✗ |
✗ |
100.979 |
|
| \(1397\) |
\begin{align*}
y y^{\prime }+a \left (1+2 b \sqrt {x}\right ) {\mathrm e}^{2 b \sqrt {x}} y&=-a^{2} b \,x^{{3}/{2}} {\mathrm e}^{4 b \sqrt {x}} \\
\end{align*} |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✗ |
✗ |
76.557 |
|
| \(1398\) |
\begin{align*}
y y^{\prime }&=\left (2 \ln \left (x \right )+a +1\right ) y+x \left (-\ln \left (x \right )^{2}-a \ln \left (x \right )+b \right ) \\
\end{align*} |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✗ |
✗ |
55.995 |
|
| \(1399\) |
\begin{align*}
y y^{\prime }&=\left (2 \ln \left (x \right )^{2}+2 \ln \left (x \right )+a \right ) y+x \left (-\ln \left (x \right )^{4}-a \ln \left (x \right )^{2}+b \right ) \\
\end{align*} |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
✗ |
✗ |
73.606 |
|
| \(1400\) |
\begin{align*}
y y^{\prime }&=a x \cos \left (\lambda \,x^{2}\right ) y+x \\
\end{align*} |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
✗ |
✗ |
65.520 |
|
| \(1401\) |
\begin{align*}
y y^{\prime } x&=a y^{2}+b y+c \,x^{n}+s \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
95.783 |
|
| \(1402\) |
\begin{align*}
y y^{\prime } x&=-n y^{2}+a \left (2 n +1\right ) x y+b y-a^{2} n \,x^{2}-a b x +c \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✗ |
✗ |
72.283 |
|
| \(1403\) |
\begin{align*}
2 y y^{\prime } x&=\left (1-n \right ) y^{2}+\left (a \left (2 n +1\right ) x +2 n -1\right ) y-a^{2} n \,x^{2}-b x -n \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✗ |
✗ |
170.703 |
|
| \(1404\) |
\begin{align*}
\left (a x y-a k y+b x -b k \right ) y^{\prime }&=c y^{2}+d x y+\left (-d k +b \right ) y \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✗ |
✗ |
77.155 |
|
| \(1405\) |
\begin{align*}
\left (A x y+B \,x^{2}+k x \right ) y^{\prime }&=A y^{2}+c x y+d \,x^{2}+\left (-A \beta +k \right ) y-c \beta x -k \beta \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✗ |
✗ |
111.944 |
|
| \(1406\) |
\begin{align*}
\left (A x y+A k y+B \,x^{2}+B k x \right ) y^{\prime }&=c y^{2}+d x y+k \left (d -B \right ) y \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✗ |
✗ |
128.268 |
|
| \(1407\) |
\begin{align*}
\left (\left (a x +c \right ) y+\left (1-n \right ) x^{2}+\left (2 n -1\right ) x -n \right ) y^{\prime }&=2 a y^{2}+2 y x \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✗ |
✗ |
307.541 |
|
| \(1408\) |
\begin{align*}
x \left (\left (m -1\right ) \left (A x +B \right ) y+m \left (d \,x^{2}+e x +F \right )\right ) y^{\prime }&=\left (A \left (1-n \right ) x -B n \right ) y^{2}+\left (d \left (2-n \right ) x^{2}+e \left (1-n \right ) x -F n \right ) y \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✗ |
490.552 |
|
| \(1409\) |
\begin{align*}
x \left (2 a x y+b \right ) y^{\prime }&=-4 a \,x^{2} y^{2}-3 b x y+c \,x^{2}+k \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
39.179 |
|
| \(1410\) |
\begin{align*}
\left (y x +a \,x^{n}+b \,x^{2}\right ) y^{\prime }&=y^{2}+c \,x^{n}+b x y \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✗ |
282.737 |
|
| \(1411\) |
\begin{align*}
y y^{\prime }&=-n y^{2}+a \left (2 n +1\right ) {\mathrm e}^{x} y+b y-a^{2} n \,{\mathrm e}^{2 x}-a b \,{\mathrm e}^{x}+c \\
\end{align*} |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
✗ |
✗ |
117.459 |
|
| \(1412\) |
\begin{align*}
y^{\prime }&=-y^{3}+3 y a^{2} x^{2}-2 a^{3} x^{3}+a \\
\end{align*} |
[_Abel] |
✓ |
✓ |
✗ |
2.378 |
|
| \(1413\) |
\begin{align*}
y^{\prime }&=-y^{3}+\left (a x +b \right ) y^{2} \\
\end{align*} |
[_Abel] |
✓ |
✓ |
✗ |
8.152 |
|
| \(1414\) |
\begin{align*}
y^{\prime }&=-y^{3}+\frac {y^{2}}{\left (a x +b \right )^{2}} \\
\end{align*} |
[_rational, _Abel] |
✓ |
✓ |
✗ |
10.346 |
|
| \(1415\) |
\begin{align*}
y^{\prime }&=a y^{3} x +2 a b \,x^{2} y^{2}-b -2 a \,b^{3} x^{4} \\
\end{align*} |
[_Abel] |
✗ |
✗ |
✗ |
5.613 |
|
| \(1416\) |
\begin{align*}
9 y^{\prime }&=-x^{m} \left (a \,x^{-m +1}+b \right )^{2 \lambda +1} y^{3}-x^{-2 m} \left (9 a +2+9 b m \,x^{m -1}\right ) \left (a \,x^{-m +1}+b \right )^{-\lambda -2} \\
\end{align*} |
[_Abel] |
✗ |
✗ |
✗ |
13.600 |
|
| \(1417\) |
\begin{align*}
x^{2} y^{\prime }&=y^{3}-3 a^{2} x^{4} y+2 a^{3} x^{6}+2 a \,x^{3} \\
\end{align*} |
[_rational, _Abel] |
✓ |
✓ |
✗ |
2.507 |
|
| \(1418\) |
\begin{align*}
y^{\prime }&=-\left (a x +x^{m} b \right ) y^{3}+y^{2} \\
\end{align*} |
[_Abel] |
✗ |
✗ |
✗ |
39.836 |
|
| \(1419\) |
\begin{align*}
y^{\prime }&=\frac {y^{3}}{\sqrt {a \,x^{2}+b x +c}}+y^{2} \\
\end{align*} |
[_Abel] |
✗ |
✗ |
✗ |
68.627 |
|
| \(1420\) |
\begin{align*}
y^{\prime }&=-y^{3}+a \,{\mathrm e}^{\lambda x} y^{2} \\
\end{align*} |
[_Abel] |
✓ |
✓ |
✗ |
5.733 |
|
| \(1421\) |
\begin{align*}
y^{\prime }&=-y^{3}+3 a^{2} {\mathrm e}^{2 \lambda x} y-2 a^{3} {\mathrm e}^{3 \lambda x}+a \lambda \,{\mathrm e}^{\lambda x} \\
\end{align*} |
[_Abel] |
✓ |
✓ |
✗ |
3.396 |
|
| \(1422\) |
\begin{align*}
y^{\prime \prime }-\left (a \,x^{2}+b \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
2.770 |
|
| \(1423\) |
\begin{align*}
y^{\prime \prime }-\left (a \,x^{2}+b x c \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
2.321 |
|
| \(1424\) |
\begin{align*}
y^{\prime \prime }-a \left (a \,x^{2 n}+n \,x^{n -1}\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
2.120 |
|
| \(1425\) |
\begin{align*}
y^{\prime \prime }-a \,x^{-2+n} \left (a \,x^{n}+n +1\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✗ |
✗ |
2.036 |
|
| \(1426\) |
\begin{align*}
y^{\prime \prime }+\left (a \,x^{2 n}+b \,x^{n -1}\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
2.035 |
|
| \(1427\) |
\begin{align*}
y^{\prime \prime }+a y^{\prime }-\left (b \,x^{2}+c \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
4.582 |
|
| \(1428\) |
\begin{align*}
y^{\prime \prime }+a y^{\prime }+b \left (-b \,x^{2 n}+a \,x^{n}+n \,x^{n -1}\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✗ |
✗ |
4.359 |
|
| \(1429\) |
\begin{align*}
y^{\prime \prime }+a y^{\prime }+b \left (-b \,x^{2 n}-a \,x^{n}+n \,x^{n -1}\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✗ |
✗ |
4.243 |
|
| \(1430\) |
\begin{align*}
y^{\prime \prime }+y^{\prime } x +\left (n -1\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
4.410 |
|
| \(1431\) |
\begin{align*}
2 n y-2 y^{\prime } x +y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
4.336 |
|
| \(1432\) |
\begin{align*}
b y+a x y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
4.539 |
|
| \(1433\) |
\begin{align*}
y^{\prime \prime }+a x y^{\prime }+b x y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
3.159 |
|
| \(1434\) |
\begin{align*}
y^{\prime \prime }+a x y^{\prime }+\left (b x +c \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
3.310 |
|
| \(1435\) |
\begin{align*}
y^{\prime \prime }+2 a x y^{\prime }+\left (b \,x^{4}+a^{2} x^{2}+c x +a \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
6.356 |
|
| \(1436\) |
\begin{align*}
y^{\prime \prime }+\left (a x +b \right ) y^{\prime }+\left (c x +d \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
4.928 |
|
| \(1437\) |
\begin{align*}
y^{\prime \prime }+\left (a x +b \right ) y^{\prime }+c \left (\left (a -c \right ) x^{2}+b x +1\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
5.641 |
|
| \(1438\) |
\begin{align*}
y^{\prime \prime }+\left (a x +b \right ) y^{\prime }+\left (\alpha \,x^{2}+\beta x +\gamma \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
5.973 |
|
| \(1439\) |
\begin{align*}
y^{\prime \prime }+\left (a x +b \right ) y^{\prime }+c \left (-c \,x^{2 n}+a \,x^{n +1}+b \,x^{n}+n \,x^{n -1}\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
6.505 |
|
| \(1440\) |
\begin{align*}
y^{\prime \prime }+\left (a \,x^{2}+b x \right ) y^{\prime }+\left (\alpha \,x^{2}+\beta x +\gamma \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✗ |
✗ |
7.025 |
|
| \(1441\) |
\begin{align*}
y^{\prime \prime }+a \,x^{n} y^{\prime }+b \,x^{n -1} y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
4.842 |
|
| \(1442\) |
\begin{align*}
y^{\prime \prime }+a \,x^{n} y^{\prime }+\left (b \,x^{2 n}+c \,x^{n -1}\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
4.374 |
|
| \(1443\) |
\begin{align*}
y^{\prime \prime }+a \,x^{n} y^{\prime }-b \left (a \,x^{n +m}+b \,x^{2 m}+m \,x^{m -1}\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
5.339 |
|
| \(1444\) |
\begin{align*}
y^{\prime \prime }+2 a \,x^{n} y^{\prime }+\left (a^{2} x^{2 n}+b \,x^{2 m}+x^{n -1} a n +c \,x^{m -1}\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
6.508 |
|
| \(1445\) |
\begin{align*}
y^{\prime \prime }+\left (a \,x^{n}+b \right ) y^{\prime }+c \left (a \,x^{n}+b -c \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
5.601 |
|
| \(1446\) |
\begin{align*}
y^{\prime \prime }+\left (a \,x^{n}+2 b \right ) y^{\prime }+\left (x^{n} a b -a \,x^{n -1}+b^{2}\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✗ |
✗ |
5.749 |
|
| \(1447\) |
\begin{align*}
y^{\prime \prime }+\left (x^{n} a b +b \,x^{n -1}+2 a \right ) y^{\prime }+a^{2} \left (b \,x^{n}+1\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
9.394 |
|
| \(1448\) |
\begin{align*}
y^{\prime \prime }+\left (x^{n} a b +2 b \,x^{n -1}-a^{2} x \right ) y^{\prime }+a \left (x^{n} a b +b \,x^{n -1}-a^{2} x \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
23.318 |
|
| \(1449\) |
\begin{align*}
y^{\prime \prime }+x^{n} \left (a \,x^{2}+\left (a c +b \right ) x +b c \right ) y^{\prime }-x^{n} \left (a x +b \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✗ |
✗ |
25.927 |
|
| \(1450\) |
\begin{align*}
y^{\prime \prime }+\left (a \,x^{n}+x^{m} b \right ) y^{\prime }+c \left (a \,x^{n}+x^{m} b -c \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
6.987 |
|
| \(1451\) |
\begin{align*}
y^{\prime \prime }+\left (a \,x^{n}+x^{m} b \right ) y^{\prime }+\left (x^{n +m} a b +b \left (m +1\right ) x^{m -1}-a \,x^{n -1}\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
5.278 |
|
| \(1452\) |
\begin{align*}
y^{\prime \prime }+\left (a \,x^{n}+x^{m} b +c \right ) y^{\prime }+\left (x^{n +m} a b +x^{m} b c +x^{n -1} a n \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
7.246 |
|
| \(1453\) |
\begin{align*}
y^{\prime \prime } x +a y^{\prime }+\left (b x +c \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
6.082 |
|
| \(1454\) |
\begin{align*}
y^{\prime \prime } x +\left (1-3 n \right ) y^{\prime }-a^{2} n^{2} x^{2 n -1} y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✗ |
5.832 |
|
| \(1455\) |
\begin{align*}
y^{\prime \prime } x +a y^{\prime }+b \,x^{n} \left (-b \,x^{n +1}+a +n \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✗ |
✗ |
5.779 |
|
| \(1456\) |
\begin{align*}
y^{\prime \prime } x +\left (b -x \right ) y^{\prime }-a y&=0 \\
\end{align*} |
[_Laguerre] |
✓ |
✓ |
✗ |
5.635 |
|
| \(1457\) |
\begin{align*}
y^{\prime \prime } x +\left (a x +b \right ) y^{\prime }+c \left (\left (a -c \right ) x +b \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
33.796 |
|
| \(1458\) |
\begin{align*}
\left (a b x +a n +b m \right ) y+\left (m +n +\left (a +b \right ) x \right ) y^{\prime }+y^{\prime \prime } x&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
8.834 |
|
| \(1459\) |
\begin{align*}
y^{\prime \prime } x +\left (a x +b \right ) y^{\prime }+\left (c x +d \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
32.756 |
|
| \(1460\) |
\begin{align*}
y^{\prime \prime } x -\left (2 a x +1\right ) y^{\prime }+b \,x^{3} y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✗ |
✗ |
6.542 |
|
| \(1461\) |
\begin{align*}
y^{\prime \prime } x +\left (a b \,x^{2}+b -5\right ) y^{\prime }+2 a^{2} \left (b -2\right ) x^{3} y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
38.014 |
|
| \(1462\) |
\begin{align*}
y^{\prime \prime } x +\left (a \,x^{2}+b x +c \right ) y^{\prime }+\left (A \,x^{2}+B x +\operatorname {C0} \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✗ |
✗ |
24.050 |
|
| \(1463\) |
\begin{align*}
y^{\prime \prime } x +\left (a \,x^{2}+b x +2\right ) y^{\prime }+\left (c \,x^{2}+d x +b \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
23.521 |
|
| \(1464\) |
\begin{align*}
y^{\prime \prime } x +a \,x^{n} y^{\prime }+\left (x^{n} a b -a \,x^{n -1}-b^{2} x +2 b \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
6.700 |
|
| \(1465\) |
\begin{align*}
y^{\prime \prime } x +\left (x^{n}+1-n \right ) y^{\prime }+b \,x^{2 n -1} y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
8.874 |
|
| \(1466\) |
\begin{align*}
y^{\prime \prime } x +\left (a \,x^{n}+b \right ) y^{\prime }+c \left (a \,x^{n}-c x +b \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
9.065 |
|
| \(1467\) |
\begin{align*}
y^{\prime \prime } x +\left (x^{n} a b +b -3 n +1\right ) y^{\prime }+a^{2} n \left (b -n \right ) x^{2 n -1} y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
7.484 |
|
| \(1468\) |
\begin{align*}
y^{\prime \prime } x +\left (a \,x^{n}+b \right ) y^{\prime }+\left (c \,x^{2 n -1}+d \,x^{n -1}\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
5.301 |
|
| \(1469\) |
\begin{align*}
y^{\prime \prime } x +\left (a \,x^{n}+b \,x^{n -1}+2\right ) y^{\prime }+b \,x^{-2+n} y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✗ |
✗ |
11.496 |
|
| \(1470\) |
\begin{align*}
y^{\prime \prime } x +\left (a \,x^{n}+b x \right ) y^{\prime }+\left (x^{n} a b +x^{n -1} a n -b \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
33.835 |
|
| \(1471\) |
\begin{align*}
y^{\prime \prime } x +\left (x^{n} a b +b \,x^{n -1}+a x -1\right ) y^{\prime }+a^{2} b \,x^{n} y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
29.232 |
|
| \(1472\) |
\begin{align*}
y^{\prime \prime } x +\left (x^{n +m} a b +a n \,x^{n}+x^{m} b +1-2 n \right ) y^{\prime }+a^{2} b n \,x^{2 n +m -1} y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
11.078 |
|
| \(1473\) |
\begin{align*}
\left (a_{1} x +a_{0} \right ) y^{\prime \prime }+\left (b_{1} x +b_{0} \right ) y^{\prime }-m b_{1} y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
25.050 |
|
| \(1474\) |
\begin{align*}
\left (a x +b \right ) y^{\prime \prime }+s \left (c x +d \right ) y^{\prime }-s^{2} \left (\left (a +c \right ) x +b +d \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
30.415 |
|
| \(1475\) |
\begin{align*}
\left (a_{2} x +b_{2} \right ) y^{\prime \prime }+\left (a_{1} x +b_{1} \right ) y^{\prime }+\left (a_{0} x +b_{0} \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
30.850 |
|
| \(1476\) |
\begin{align*}
x^{2} y^{\prime \prime }+\left (a \,x^{2}+b x +c \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
3.469 |
|
| \(1477\) |
\begin{align*}
x^{2} y^{\prime \prime }-\left (a^{2} x^{2 n}+a \left (2 b +n -1\right ) x^{n}+b \left (b -1\right )\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✗ |
✗ |
4.288 |
|
| \(1478\) |
\begin{align*}
x^{2} y^{\prime \prime }+\left (a \,x^{2 n}+b \,x^{n}+c \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
2.795 |
|
| \(1479\) |
\begin{align*}
x^{2} y^{\prime \prime }+\left (a \,x^{3 n}+b \,x^{2 n}+\frac {1}{4}-\frac {n^{2}}{4}\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✗ |
✗ |
3.130 |
|
| \(1480\) |
\begin{align*}
x^{2} y^{\prime \prime }+\left (a \,x^{2 n} \left (b \,x^{n}+c \right )^{m}+\frac {1}{4}-\frac {n^{2}}{4}\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
3.965 |
|
| \(1481\) |
\begin{align*}
x^{2} y^{\prime \prime }+\lambda x y^{\prime }+\left (a \,x^{2}+b x +c \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
11.979 |
|
| \(1482\) |
\begin{align*}
x^{2} y^{\prime \prime }+a x y^{\prime }+x^{n} \left (b \,x^{n}+c \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
9.997 |
|
| \(1483\) |
\begin{align*}
x^{2} y^{\prime \prime }+\left (a x +b \right ) y^{\prime }+c y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
21.666 |
|
| \(1484\) |
\begin{align*}
x^{2} y^{\prime \prime }+a \,x^{2} y^{\prime }+\left (b \,x^{2}+c x +d \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
5.527 |
|
| \(1485\) |
\begin{align*}
x^{2} y^{\prime \prime }+\left (a \,x^{2}+b \right ) y^{\prime }+c \left (\left (a -c \right ) x^{2}+b \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
25.119 |
|
| \(1486\) |
\begin{align*}
x^{2} y^{\prime \prime }+\left (a \,x^{2}+b x \right ) y^{\prime }+\left (k \left (a -k \right ) x^{2}+\left (a n +b k -2 k n \right ) x +n \left (b -n -1\right )\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
27.791 |
|
| \(1487\) |
\begin{align*}
a_{2} x^{2} y^{\prime \prime }+\left (a_{1} x^{2}+b_{1} x \right ) y^{\prime }+\left (a_{0} x^{2}+b_{0} x +c_{0} \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
25.543 |
|
| \(1488\) |
\begin{align*}
x^{2} y^{\prime \prime }-2 x \left (x^{2}-a \right ) y^{\prime }+\left (2 n \,x^{2}+\left (\left (-1\right )^{n}-1\right ) a \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
27.372 |
|
| \(1489\) |
\begin{align*}
x^{2} y^{\prime \prime }+x \left (a \,x^{2}+b x +c \right ) y^{\prime }+\left (A \,x^{3}+B \,x^{2}+C x +d \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✗ |
✗ |
42.863 |
|
| \(1490\) |
\begin{align*}
x^{2} y^{\prime \prime }+a \,x^{n} y^{\prime }-\left (x^{n} a b +a c \,x^{n -1}+b^{2} x^{2}+2 b x c +c^{2}-c \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
13.371 |
|
| \(1491\) |
\begin{align*}
x^{2} y^{\prime \prime }+a \,x^{n} y^{\prime }+\left (a b \,x^{n +2 m}-b^{2} x^{4 m +2}+a m \,x^{n -1}-m^{2}-m \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
7.994 |
|
| \(1492\) |
\begin{align*}
x^{2} y^{\prime \prime }+\left (a \,x^{n}+b \right ) y^{\prime } x +\left (\alpha \,x^{2 n}+\beta \,x^{n}+\gamma \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
13.732 |
|
| \(1493\) |
\begin{align*}
x^{2} y^{\prime \prime }+x \left (2 a \,x^{n}+b \right ) y^{\prime }+\left (a^{2} x^{2 n}+a \left (b +n -1\right ) x^{n}+\alpha \,x^{2 m}+\beta \,x^{m}+\gamma \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
15.622 |
|
| \(1494\) |
\begin{align*}
x^{2} y^{\prime \prime }+\left (a \,x^{n +2}+b \,x^{2}+c \right ) y^{\prime }+\left (a n \,x^{n +1}+a c \,x^{n}+b c \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
26.660 |
|
| \(1495\) |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }+n \left (n -1\right ) y&=0 \\
\end{align*} |
[_Gegenbauer] |
✓ |
✓ |
✓ |
4.703 |
|
| \(1496\) |
\begin{align*}
\left (-a^{2}+x^{2}\right ) y^{\prime \prime }+b y^{\prime }-6 y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
12.107 |
|
| \(1497\) |
\begin{align*}
n \left (n +1\right ) y-2 y^{\prime } x +\left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
[_Gegenbauer] |
✓ |
✓ |
✗ |
119.593 |
|
| \(1498\) |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +\nu \left (\nu +1\right ) y&=0 \\
\end{align*} |
[_Gegenbauer] |
✓ |
✓ |
✗ |
102.308 |
|
| \(1499\) |
\begin{align*}
\left (x^{2}-1\right ) y^{\prime \prime }+2 \left (n +1\right ) x y^{\prime }-\left (\nu +n +1\right ) \left (\nu -n \right ) y&=0 \\
\end{align*} |
[_Gegenbauer] |
✓ |
✓ |
✗ |
91.958 |
|
| \(1500\) |
\begin{align*}
\left (x^{2}-1\right ) y^{\prime \prime }-2 \left (n -1\right ) x y^{\prime }-\left (\nu -n +1\right ) \left (\nu +n \right ) y&=0 \\
\end{align*} |
[_Gegenbauer] |
✓ |
✓ |
✗ |
78.437 |
|
| \(1501\) |
\begin{align*}
\left (x^{2}-1\right ) y^{\prime \prime }+\left (2 a +1\right ) y^{\prime }-b \left (2 a +b \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
125.034 |
|
| \(1502\) |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }+\left (2 a -3\right ) x y^{\prime }+\left (n +1\right ) \left (n +2 a -1\right ) y&=0 \\
\end{align*} |
[_Gegenbauer] |
✓ |
✓ |
✗ |
76.258 |
|
| \(1503\) |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }+\left (\beta -\alpha -\left (\alpha +\beta +2\right ) x \right ) y^{\prime }+n \left (n +\alpha +\beta +1\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
173.881 |
|
| \(1504\) |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }+\left (\alpha -\beta +\left (\alpha +\beta -2\right ) x \right ) y^{\prime }+\left (n +1\right ) \left (n +\alpha +\beta \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
161.027 |
|
| \(1505\) |
\begin{align*}
\left (a \,x^{2}+b \right ) y^{\prime \prime }+\left (2 n +1\right ) a x y^{\prime }+c y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
651.777 |
|
| \(1506\) |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }-y^{\prime } x +\left (2 a \,x^{2}+b \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
41.449 |
|
| \(1507\) |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }+\left (a x +b \right ) y^{\prime }+c y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
166.384 |
|
| \(1508\) |
\begin{align*}
\left (a \,x^{2}+b \right ) y^{\prime \prime }+\left (c \,x^{2}+d \right ) y^{\prime }+\lambda \left (\left (-a \lambda +c \right ) x^{2}+d -b \lambda \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
30.699 |
|
| \(1509\) |
\begin{align*}
\left (a \,x^{2}+b \right ) y^{\prime \prime }+\left (\lambda \left (a +c \right ) x^{2}+\left (c -a \right ) x +2 b \lambda \right ) y^{\prime }+\lambda ^{2} \left (c \,x^{2}+b \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
197.935 |
|
| \(1510\) |
\begin{align*}
x \left (x -1\right ) y^{\prime \prime }+\left (\left (\alpha +\beta +1\right ) x -\gamma \right ) y^{\prime }+\alpha \beta y&=0 \\
\end{align*} |
[_Jacobi] |
✓ |
✓ |
✗ |
186.735 |
|
| \(1511\) |
\begin{align*}
x \left (a +x \right ) y^{\prime \prime }+\left (b x +c \right ) y^{\prime }+d y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
118.862 |
|
| \(1512\) |
\begin{align*}
2 x \left (x -1\right ) y^{\prime \prime }+\left (2 x -1\right ) y^{\prime }+\left (a x +b \right ) y&=0 \\
\end{align*} |
[_Jacobi] |
✓ |
✓ |
✗ |
88.241 |
|
| \(1513\) |
\begin{align*}
\left (a_{2} x^{2}+b_{2} x +c_{2} \right ) y^{\prime \prime }+\left (b_{1} x +c_{1} \right ) y^{\prime }+c_{0} y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
187.433 |
|
| \(1514\) |
\begin{align*}
\left (a \,x^{2}+b x +c \right ) y^{\prime \prime }-\left (-k^{2}+x^{2}\right ) y^{\prime }+\left (k +x \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
197.411 |
|
| \(1515\) |
\begin{align*}
\left (a \,x^{2}+b x +c \right ) y^{\prime \prime }+\left (k^{3}+x^{3}\right ) y^{\prime }-\left (k^{2}-k x +x^{2}\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
206.548 |
|
| \(1516\) |
\begin{align*}
x^{3} y^{\prime \prime }+\left (a \,x^{2}+b \right ) y^{\prime }+c x y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
49.990 |
|
| \(1517\) |
\begin{align*}
x^{3} y^{\prime \prime }+\left (a \,x^{2}+b x \right ) y^{\prime }+b y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
47.314 |
|
| \(1518\) |
\begin{align*}
x^{3} y^{\prime \prime }+\left (a \,x^{2}+b x \right ) y^{\prime }+c y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
32.063 |
|
| \(1519\) |
\begin{align*}
x^{3} y^{\prime \prime }+\left (a \,x^{2}+b x \right ) y^{\prime }+\left (c x +d \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
71.230 |
|
| \(1520\) |
\begin{align*}
x^{3} y^{\prime \prime }+\left (a \,x^{3}+a b x -x^{2}+b \right ) y^{\prime }+a^{2} b x y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
127.324 |
|
| \(1521\) |
\begin{align*}
x^{3} y^{\prime \prime }+\left (a \,x^{n}+b \right ) y^{\prime } x -\left (a \,x^{n}-a b \,x^{n -1}+b \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
116.247 |
|
| \(1522\) |
\begin{align*}
x \left (x^{2}+a \right ) y^{\prime \prime }+\left (b \,x^{2}+c \right ) y^{\prime }+s x y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
171.925 |
|
| \(1523\) |
\begin{align*}
x^{2} \left (a x +b \right ) y^{\prime \prime }+\left (c \,x^{2}+\left (a \lambda +2 b \right ) x +b \lambda \right ) y^{\prime }+\lambda \left (c -2 a \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
226.386 |
|
| \(1524\) |
\begin{align*}
x^{2} \left (x +a_{2} \right ) y^{\prime \prime }+x \left (b_{1} x +a_{1} \right ) y^{\prime }+\left (b_{0} x +a_{0} \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
178.273 |
|
| \(1525\) |
\begin{align*}
\left (a \,x^{3}+b \,x^{2}+c x \right ) y^{\prime \prime }+\left (\alpha \,x^{2}+\beta x +2 c \right ) y^{\prime }+\left (\beta -2 b \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
291.890 |
|
| \(1526\) |
\begin{align*}
\left (a \,x^{3}+b \,x^{2}+c x \right ) y^{\prime \prime }+\left (\alpha \,x^{2}+\beta x +2 c \right ) y^{\prime }-\left (x \alpha +2 b -\beta \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
271.757 |
|
| \(1527\) |
\begin{align*}
\left (a \,x^{3}+b \,x^{2}+c x \right ) y^{\prime \prime }+\left (-2 a \,x^{2}-\left (b +1\right ) x +k \right ) y^{\prime }+2 \left (a x +1\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
282.276 |
|
| \(1528\) |
\begin{align*}
\left (a \,x^{3}+b \,x^{2}+c x \right ) y^{\prime \prime }+\left (n \,x^{2}+x m +k \right ) y^{\prime }+\left (-1+k \right ) \left (\left (-a k +n \right ) x +m -b k \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
321.124 |
|
| \(1529\) |
\begin{align*}
\left (a \,x^{3}+b \,x^{2}+c x \right ) y^{\prime \prime }+\left (n \,x^{2}+x m +k \right ) y^{\prime }+\left (-2 \left (a +n \right ) x +1\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
356.434 |
|
| \(1530\) |
\begin{align*}
\left (a \,x^{3}+x^{2}+b \right ) y^{\prime \prime }+a^{2} x \left (x^{2}-b \right ) y^{\prime }-a^{3} b x y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✗ |
✗ |
207.125 |
|
| \(1531\) |
\begin{align*}
x \left (a \,x^{2}+b x +1\right ) y^{\prime \prime }+\left (\alpha \,x^{2}+\beta x +\gamma \right ) y^{\prime }+\left (x n +m \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
342.944 |
|
| \(1532\) |
\begin{align*}
x \left (x -1\right ) \left (x -a \right ) y^{\prime \prime }+\left (\left (\alpha +\beta +1\right ) x^{2}-\left (\alpha +\beta +1+a \left (\gamma +d \right )-a \right ) x +a \gamma \right ) y^{\prime }+\left (\alpha \beta x -q \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
382.410 |
|
| \(1533\) |
\begin{align*}
\left (a \,x^{3}+b \,x^{2}+c x +d \right ) y^{\prime \prime }-\left (-\lambda ^{2}+x^{2}\right ) y^{\prime }+\left (x +\lambda \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✗ |
✗ |
473.723 |
|
| \(1534\) |
\begin{align*}
2 \left (a \,x^{3}+b \,x^{2}+c x +d \right ) y^{\prime \prime }+3 \left (3 a \,x^{2}+2 b x +c \right ) y^{\prime }+\left (6 a x +2 b +\lambda \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✗ |
✗ |
416.360 |
|
| \(1535\) |
\begin{align*}
\left (a \,x^{3}+b \,x^{2}+c x +d \right ) y^{\prime \prime }+\left (\alpha \,x^{2}+\left (\alpha \gamma +\beta \right ) x +\beta \lambda \right ) y^{\prime }-\left (x \alpha +\beta \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
885.732 |
|
| \(1536\) |
\begin{align*}
\left (a \,x^{3}+b \,x^{2}+c x +d \right ) y^{\prime \prime }+\left (\lambda ^{3}+x^{3}\right ) y^{\prime }-\left (\lambda ^{2}-\lambda x +x^{2}\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
1133.063 |
|
| \(1537\) |
\begin{align*}
x^{4} y^{\prime \prime }+\left (a \,x^{2}+b x +c \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✗ |
✗ |
3.706 |
|
| \(1538\) |
\begin{align*}
x^{4} y^{\prime \prime }+a \,x^{n} y^{\prime }-\left (a \,x^{n -1}+a b \,x^{-2+n}+b^{2}\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
19.677 |
|
| \(1539\) |
\begin{align*}
a \,x^{2} \left (x -1\right )^{2} y^{\prime \prime }+\left (b \,x^{2}+c x +d \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
7.861 |
|
| \(1540\) |
\begin{align*}
x^{2} \left (x^{2}+a \right ) y^{\prime \prime }+\left (b \,x^{2}+c \right ) x y^{\prime }+d y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
141.715 |
|
| \(1541\) |
\begin{align*}
\left (x^{2}-1\right )^{2} y^{\prime \prime }+2 x \left (x^{2}-1\right ) y^{\prime }-\left (\nu \left (\nu +1\right ) \left (x^{2}-1\right )+n^{2}\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
108.167 |
|
| \(1542\) |
\begin{align*}
\left (-x^{2}+1\right )^{2} y^{\prime \prime }-2 x \left (-x^{2}+1\right ) y^{\prime }+\left (\nu \left (\nu +1\right ) \left (-x^{2}+1\right )-\mu ^{2}\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
93.520 |
|
| \(1543\) |
\begin{align*}
a \left (x^{2}-1\right )^{2} y^{\prime \prime }+b x \left (x^{2}-1\right ) y^{\prime }+\left (c \,x^{2}+d x +e \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
148.688 |
|
| \(1544\) |
\begin{align*}
\left (x^{2}+a \right )^{2} y^{\prime \prime }+b \,x^{n} \left (x^{2}+a \right ) y^{\prime }-\left (b \,x^{n +1}+a \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
35.269 |
|
| \(1545\) |
\begin{align*}
\left (x^{2}+a \right )^{2} y^{\prime \prime }+b \,x^{n} \left (x^{2}+a \right ) y^{\prime }-m \left (b \,x^{n +1}+\left (m -1\right ) x^{2}+a \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
30.920 |
|
| \(1546\) |
\begin{align*}
\left (x^{2}-1\right )^{2} y^{\prime \prime }+2 x \left (x^{2}-1\right ) y^{\prime }+\left (\left (x^{2}-1\right ) \left (a^{2} x^{2}-\lambda \right )-m^{2}\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
97.529 |
|
| \(1547\) |
\begin{align*}
\left (x^{2}+1\right )^{2} y^{\prime \prime }+2 x \left (x^{2}+1\right ) y^{\prime }+\left (\left (x^{2}+1\right ) \left (a^{2} x^{2}-\lambda \right )+m^{2}\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
119.592 |
|
| \(1548\) |
\begin{align*}
x^{n} y^{\prime \prime }+c \left (a x +b \right )^{n -4} y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
4.633 |
|
| \(1549\) |
\begin{align*}
x^{n} y^{\prime \prime }+a x y^{\prime }-\left (b^{2} x^{n}+2 b \,x^{n -1}+a b x +a \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
8.356 |
|
| \(1550\) |
\begin{align*}
x^{n} y^{\prime \prime }+\left (a \,x^{n -1}+b x \right ) y^{\prime }+\left (-1+a \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✗ |
✗ |
10.758 |
|
| \(1551\) |
\begin{align*}
x^{n} y^{\prime \prime }+\left (2 x^{n -1}+a \,x^{2}+b x \right ) y^{\prime }+b y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✗ |
✗ |
35.841 |
|
| \(1552\) |
\begin{align*}
x^{n} y^{\prime \prime }+\left (a \,x^{n}+b \right ) y^{\prime }+c \left (\left (a -c \right ) x^{n}+b \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
8.535 |
|
| \(1553\) |
\begin{align*}
x^{n} y^{\prime \prime }+\left (a \,x^{n}-x^{n -1}+a b x +b \right ) y^{\prime }+a^{2} b x y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
49.899 |
|
| \(1554\) |
\begin{align*}
x^{n} y^{\prime \prime }+\left (a \,x^{n +m}+1\right ) y^{\prime }+a \,x^{m} \left (1+m \,x^{n -1}\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
9.422 |
|
| \(1555\) |
\begin{align*}
\left (a \,x^{n}+b \right ) y^{\prime \prime }+\left (c \,x^{n}+d \right ) y^{\prime }+\lambda \left (\left (-a \lambda +c \right ) x^{n}+d -b \lambda \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
16.100 |
|
| \(1556\) |
\begin{align*}
x \left (x^{n}+1\right ) y^{\prime \prime }+\left (\left (a -b \right ) x^{n}+a -n \right ) y^{\prime }+b \left (1-a \right ) x^{n -1} y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
40.000 |
|
| \(1557\) |
\begin{align*}
x \left (x^{2 n}+a \right ) y^{\prime \prime }+\left (x^{2 n}+a -a n \right ) y^{\prime }-b^{2} x^{2 n -1} y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✗ |
172.263 |
|
| \(1558\) |
\begin{align*}
x^{2} \left (a^{2} x^{2 n}-1\right ) y^{\prime \prime }+x \left (a^{2} \left (n +1\right ) x^{2 n}+n -1\right ) y^{\prime }-\nu \left (\nu +1\right ) a^{2} n^{2} x^{2 n} y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
94.691 |
|
| \(1559\) |
\begin{align*}
x^{2} \left (a^{2} x^{2 n}-1\right ) y^{\prime \prime }+x \left (a p \,x^{n}+q \right ) y^{\prime }+\left (a r \,x^{n}+s \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✗ |
✗ |
111.360 |
|
| \(1560\) |
\begin{align*}
\left (x^{n}+a \right )^{2} y^{\prime \prime }-b \,x^{-2+n} \left (\left (b -1\right ) x^{n}+a \left (n -1\right )\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✗ |
✗ |
3.270 |
|
| \(1561\) |
\begin{align*}
\left (a \,x^{n}+b \right )^{2} y^{\prime \prime }+\left (a \,x^{n}+b \right ) \left (c \,x^{n}+d \right ) y^{\prime }+n \left (-a d +b c \right ) x^{n -1} y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
16.275 |
|
| \(1562\) |
\begin{align*}
\left (x^{n}+a \right )^{2} y^{\prime \prime }+b \,x^{m} \left (x^{n}+a \right ) y^{\prime }-x^{-2+n} \left (b \,x^{m +1}+a n -a \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
52.357 |
|
| \(1563\) |
\begin{align*}
\left (a \,x^{n}+b \right )^{2} y^{\prime \prime }+c \,x^{m} \left (a \,x^{n}+b \right ) y^{\prime }+\left (c \,x^{m}-x^{n -1} a n -1\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
29.662 |
|
| \(1564\) |
\begin{align*}
x^{2} \left (a \,x^{n}+b \right )^{2} y^{\prime \prime }+\left (n +1\right ) x \left (a^{2} x^{2 n}-b^{2}\right ) y^{\prime }+c y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
146.770 |
|
| \(1565\) |
\begin{align*}
\left (a \,x^{n +1}+b \,x^{n}+c \right )^{2} y^{\prime \prime }+\left (\alpha \,x^{n}+\beta \,x^{n -1}+\gamma \right ) y^{\prime }+\left (n \left (-a n -a +\alpha \right ) x^{n -1}+\left (n -1\right ) \left (-n b +\beta \right ) x^{-2+n}\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
336.962 |
|
| \(1566\) |
\begin{align*}
\left (a \,x^{n}+x^{m} b +c \right ) y^{\prime \prime }+\left (\lambda ^{2}-x^{2}\right ) y^{\prime }+\left (x +\lambda \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✗ |
✗ |
74.984 |
|
| \(1567\) |
\begin{align*}
2 \left (a \,x^{n}+x^{m} b +c \right ) y^{\prime \prime }+a n \,x^{n -1} b m \,x^{m -1} y^{\prime }+d y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
99.291 |
|
| \(1568\) |
\begin{align*}
y^{\prime \prime }+a \left (\lambda \,{\mathrm e}^{\lambda x}-a \,{\mathrm e}^{2 \lambda x}\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
1.593 |
|
| \(1569\) |
\begin{align*}
y^{\prime \prime }-\left (a^{2} {\mathrm e}^{2 x}+a \left (2 b +1\right ) {\mathrm e}^{x}+b^{2}\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
1.776 |
|
| \(1570\) |
\begin{align*}
y^{\prime \prime }-\left (a \,{\mathrm e}^{2 \lambda x}+b \,{\mathrm e}^{\lambda x}+c \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
1.541 |
|
| \(1571\) |
\begin{align*}
y^{\prime \prime }+\left (a \,{\mathrm e}^{4 \lambda x}+b \,{\mathrm e}^{3 \lambda x}+c \,{\mathrm e}^{2 \lambda x}-\frac {\lambda ^{2}}{4}\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
1.997 |
|
| \(1572\) |
\begin{align*}
y^{\prime \prime }+\left (a \,{\mathrm e}^{2 \lambda x} \left (b \,{\mathrm e}^{\lambda x}+c \right )^{n}-\frac {\lambda ^{2}}{4}\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✗ |
✗ |
2.007 |
|
| \(1573\) |
\begin{align*}
y^{\prime \prime }-y^{\prime }+\left (a \,{\mathrm e}^{3 \lambda x}+b \,{\mathrm e}^{2 \lambda x}+\frac {1}{4}-\frac {\lambda ^{2}}{4}\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
3.351 |
|
| \(1574\) |
\begin{align*}
y^{\prime \prime }-y^{\prime }+\left (a \,{\mathrm e}^{2 \lambda x} \left (b \,{\mathrm e}^{\lambda x}+c \right )^{n}+\frac {1}{4}-\frac {\lambda ^{2}}{4}\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✗ |
✗ |
3.517 |
|
| \(1575\) |
\begin{align*}
y^{\prime \prime }+\left (a +b \right ) {\mathrm e}^{\lambda x} y^{\prime }+a \,{\mathrm e}^{\lambda x} \left (b \,{\mathrm e}^{\lambda x}+\lambda \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
3.587 |
|
| \(1576\) |
\begin{align*}
y^{\prime \prime }+a \,{\mathrm e}^{\lambda x} y^{\prime }-b \,{\mathrm e}^{\mu x} \left (a \,{\mathrm e}^{\lambda x}+b \,{\mathrm e}^{\mu x}+\mu \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✗ |
✗ |
4.135 |
|
| \(1577\) |
\begin{align*}
y^{\prime \prime }+2 k \,{\mathrm e}^{\mu x} y^{\prime }+\left (a \,{\mathrm e}^{2 \lambda x}+b \,{\mathrm e}^{\lambda x}+k^{2} {\mathrm e}^{2 \mu x}+k \mu \,{\mathrm e}^{\mu x}+c \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
4.276 |
|
| \(1578\) |
\begin{align*}
y^{\prime \prime }+\left (a \,{\mathrm e}^{2 \lambda x}+\lambda \right ) y^{\prime }-a \lambda \,{\mathrm e}^{2 \lambda x} y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
3.064 |
|
| \(1579\) |
\begin{align*}
y^{\prime \prime }+\left (a \,{\mathrm e}^{\lambda x}+b \right ) y^{\prime }+c \left (a \,{\mathrm e}^{\lambda x}+b -c \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
3.446 |
|
| \(1580\) |
\begin{align*}
y^{\prime \prime }+\left (a +b \,{\mathrm e}^{2 \lambda x}\right ) y^{\prime }+\lambda \left (a -\lambda -b \,{\mathrm e}^{2 \lambda x}\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
3.383 |
|
| \(1581\) |
\begin{align*}
y^{\prime \prime }+\left (a +b \,{\mathrm e}^{\lambda x}+b -3 \lambda \right ) y^{\prime }+a^{2} \lambda \left (b -\lambda \right ) {\mathrm e}^{2 \lambda x} y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
4.324 |
|
| \(1582\) |
\begin{align*}
y^{\prime \prime }+\left (2 a \,{\mathrm e}^{\lambda x}-\lambda \right ) y^{\prime }+\left (a^{2} {\mathrm e}^{2 \lambda x}+c \,{\mathrm e}^{\mu x}\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
3.725 |
|
| \(1583\) |
\begin{align*}
y^{\prime \prime }+\left (a \,{\mathrm e}^{\lambda x}+2 b -\lambda \right ) y^{\prime }+\left (c \,{\mathrm e}^{2 \lambda x}+a b \,{\mathrm e}^{\lambda x}+b^{2}-b \lambda \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
4.285 |
|
| \(1584\) |
\begin{align*}
y^{\prime \prime }+\left (a \,{\mathrm e}^{x}+b \right ) y^{\prime }+\left (c \left (a -c \right ) {\mathrm e}^{2 x}+\left (a k +b c -2 c k +c \right ) {\mathrm e}^{x}+k \left (b -k \right )\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
5.092 |
|
| \(1585\) |
\begin{align*}
y^{\prime \prime }+\left (a \,{\mathrm e}^{\lambda x}+b \right ) y^{\prime }+\left (\alpha \,{\mathrm e}^{2 \lambda x}+\beta \,{\mathrm e}^{\lambda x}+\gamma \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
3.320 |
|
| \(1586\) |
\begin{align*}
y^{\prime \prime }+\left (2 a \,{\mathrm e}^{\lambda x}-\lambda \right ) y^{\prime }+\left (a^{2} {\mathrm e}^{2 \lambda x}+b \,{\mathrm e}^{2 \mu x}+c \,{\mathrm e}^{\mu x}+k \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
3.738 |
|
| \(1587\) |
\begin{align*}
y^{\prime \prime }+\left (2 a \,{\mathrm e}^{\lambda x}+b -\lambda \right ) y^{\prime }+\left (a^{2} {\mathrm e}^{2 \lambda x}+a b \,{\mathrm e}^{\lambda x}+c \,{\mathrm e}^{2 \mu x}+d \,{\mathrm e}^{\mu x}+k \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
5.018 |
|
| \(1588\) |
\begin{align*}
y^{\prime \prime }+\left (a \,{\mathrm e}^{\lambda x}+b \,{\mathrm e}^{\mu x}\right ) y^{\prime }+a \,{\mathrm e}^{\lambda x} \left (b \,{\mathrm e}^{\mu x}+\lambda \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
3.931 |
|
| \(1589\) |
\begin{align*}
y^{\prime \prime }+{\mathrm e}^{\lambda x} \left (a \,{\mathrm e}^{2 \mu x}+b \right ) y^{\prime }+\mu \left ({\mathrm e}^{\lambda x} \left (b -a \,{\mathrm e}^{2 \mu x}\right )-\mu \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✗ |
✗ |
5.640 |
|
| \(1590\) |
\begin{align*}
y^{\prime \prime }+\left (a \,{\mathrm e}^{\lambda x}+b \,{\mathrm e}^{\mu x}+c \right ) y^{\prime }+\left (a b \,{\mathrm e}^{\left (\lambda +\mu \right ) x}+{\mathrm e}^{\lambda x} a c +{\mathrm e}^{\mu x} b \mu \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
4.449 |
|
| \(1591\) |
\begin{align*}
y^{\prime \prime }+\left (a \,{\mathrm e}^{\lambda x}+2 b \,{\mathrm e}^{\mu x}-\lambda \right ) y^{\prime }+\left (a b \,{\mathrm e}^{\left (\lambda +\mu \right ) x}+c \,{\mathrm e}^{2 \lambda x}+{\mathrm e}^{2 \mu x} b^{2}+b \left (\mu -\lambda \right ) {\mathrm e}^{\mu x}\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
5.727 |
|
| \(1592\) |
\begin{align*}
y^{\prime \prime }+\left (a \,{\mathrm e}^{\left (\lambda +\mu \right ) x}+a \lambda \,{\mathrm e}^{\lambda x}+b \,{\mathrm e}^{\mu x}-2 \lambda \right ) y^{\prime }+a^{2} b \lambda \,{\mathrm e}^{\left (2 \lambda +\mu \right ) x} y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
6.572 |
|
| \(1593\) |
\begin{align*}
y^{\prime \prime }+a \,{\mathrm e}^{b \,x^{n}} y^{\prime }+c \left (a \,{\mathrm e}^{b \,x^{n}}-c \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✗ |
✗ |
4.713 |
|
| \(1594\) |
\begin{align*}
\left (a \,{\mathrm e}^{\lambda x}+b \right ) y^{\prime \prime }+\left (c \,{\mathrm e}^{\lambda x}+d \right ) y^{\prime }+k \left (\left (-a k +c \right ) {\mathrm e}^{\lambda x}+d -b k \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
7.085 |
|
| \(1595\) |
\begin{align*}
\left (a \,{\mathrm e}^{\lambda x}+b \right ) y^{\prime \prime }+\left (c \,{\mathrm e}^{\lambda x}+d \right ) y^{\prime }+\left (n \,{\mathrm e}^{\lambda x}+m \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
4.936 |
|
| \(1596\) |
\begin{align*}
\left (x^{2}+y^{2}\right ) \left (x +y y^{\prime }\right )&=\left (x^{2}+y^{2}+x \right ) \left (-y+y^{\prime } x \right ) \\
\end{align*} |
[_rational] |
✓ |
✓ |
✗ |
5.239 |
|
| \(1597\) |
\begin{align*}
x^{3} y^{4}+x^{2} y^{3}+x y^{2}+y+\left (y^{3} x^{4}-x^{3} y^{2}-x^{3} y+x \right ) y^{\prime }&=0 \\
\end{align*} |
[_rational] |
✗ |
✗ |
✗ |
3.338 |
|
| \(1598\) |
\begin{align*}
\left (x -y^{\prime }-y\right )^{2}&=x^{2} \left (2 y x -x^{2} y^{\prime }\right ) \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
66.469 |
|
| \(1599\) |
\begin{align*}
4 x^{2} y^{\prime \prime }+4 x^{3} y^{\prime }+\left (x^{2}+1\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
10.722 |
|
| \(1600\) |
\begin{align*}
x^{2} y^{\prime \prime }-2 n x \left (x +1\right ) y^{\prime }+\left (a^{2} x^{2}+n^{2}+n \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✗ |
✗ |
12.832 |
|
| \(1601\) |
\begin{align*}
x^{4} y^{\prime \prime }+2 x^{3} \left (x +1\right ) y^{\prime }+n^{2} y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✗ |
✗ |
20.143 |
|
| \(1602\) |
\begin{align*}
-2 y+2 y^{\prime } x -x^{2} y^{\prime \prime }+\left (x^{2}-2 x +2\right ) y^{\prime \prime \prime }&=0 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.042 |
|
| \(1603\) |
\begin{align*}
y-y^{\prime } x -y^{\prime \prime }+x y^{\prime \prime \prime }&=-x^{2}+1 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.039 |
|
| \(1604\) |
\begin{align*}
2 x^{3} y y^{\prime \prime \prime }+6 x^{3} y^{\prime } y^{\prime \prime }+18 x^{2} y y^{\prime \prime }+18 x^{2} {y^{\prime }}^{2}+36 y y^{\prime } x +6 y^{2}&=0 \\
\end{align*} |
[[_3rd_order, _exact, _nonlinear], [_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.044 |
|
| \(1605\) |
\begin{align*}
x^{2} y^{\prime \prime \prime }-5 y^{\prime \prime } x +\left (4 x^{4}+5\right ) y^{\prime }-8 x^{3} y&=0 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.041 |
|
| \(1606\) |
\begin{align*}
\left (-y+y^{\prime } x \right )^{2}+x^{2} y y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✗ |
0.594 |
|
| \(1607\) |
\begin{align*}
x^{3} y^{\prime \prime }-\left (-y+y^{\prime } x \right )^{2}&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✗ |
0.735 |
|
| \(1608\) |
\begin{align*}
y y^{\prime \prime }-{y^{\prime }}^{2}&=\ln \left (y\right ) y^{2}-y^{2} x^{2} \\
\end{align*} |
[[_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✗ |
0.488 |
|
| \(1609\) |
\begin{align*}
x x^{\prime }&=1-t x \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✗ |
15.672 |
|
| \(1610\) |
\begin{align*}
{x^{\prime }}^{2}+t x&=\sqrt {1+t} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
60.183 |
|
| \(1611\) |
\begin{align*}
3 x^{2} y+2-\left (x^{3}+y\right ) y^{\prime }&=0 \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
✗ |
✗ |
8.102 |
|
| \(1612\) |
\begin{align*}
y^{\prime \prime }+y^{\prime } x +x^{2} y&=0 \\
y \left (1\right ) &= 0 \\
y^{\prime }\left (1\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
3.460 |
|
| \(1613\) |
\begin{align*}
\left (x^{4}-2 x^{3}+x^{2}\right ) y^{\prime \prime }+2 \left (x -1\right ) y^{\prime }+x^{2} y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
0.217 |
|
| \(1614\) |
\begin{align*}
\left (x^{5}+x^{4}-6 x^{3}\right ) y^{\prime \prime }+x^{2} y^{\prime }+\left (x -2\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
0.109 |
|
| \(1615\) |
\begin{align*}
t^{3} x^{\prime \prime \prime }-\left (t +3\right ) t^{2} x^{\prime \prime }+2 t \left (t +3\right ) x^{\prime }-2 \left (t +3\right ) x&=0 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.038 |
|
| \(1616\) |
\begin{align*}
\left (2 t +1\right ) x^{\prime \prime }+t^{3} x^{\prime }+x&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
63.505 |
|
| \(1617\) |
\begin{align*}
\sin \left (t \right ) x^{\prime \prime }+\cos \left (t \right ) x^{\prime }+2 x&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✗ |
✗ |
2.339 |
|
| \(1618\) |
\begin{align*}
\left (t^{4}+t^{2}\right ) x^{\prime \prime }+2 t^{3} x^{\prime }+3 x&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
53.603 |
|
| \(1619\) |
\begin{align*}
x^{\prime \prime }-\tan \left (t \right ) x^{\prime }+x&=0 \\
\end{align*} |
[_Lienard] |
✓ |
✓ |
✗ |
2.736 |
|
| \(1620\) |
\begin{align*}
f \left (t \right ) x^{\prime \prime }+x g \left (t \right )&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
1.315 |
|
| \(1621\) |
\begin{align*}
x^{\prime }&=4 x-4 y-x \left (x^{2}+y^{2}\right ) \\
y^{\prime }&=4 x+4 y-y \left (x^{2}+y^{2}\right ) \\
\end{align*} |
system_of_ODEs |
✗ |
✗ |
✗ |
0.038 |
|
| \(1622\) |
\begin{align*}
x^{\prime }&=y+\frac {x \left (1-x^{2}-y^{2}\right )}{\sqrt {x^{2}+y^{2}}} \\
y^{\prime }&=-x+\frac {y \left (1-x^{2}-y^{2}\right )}{\sqrt {x^{2}+y^{2}}} \\
\end{align*} |
system_of_ODEs |
✗ |
✗ |
✗ |
0.053 |
|
| \(1623\) |
\begin{align*}
x^{\prime \prime }+x^{4} x^{\prime }-x^{\prime }+x&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✗ |
✗ |
✗ |
53.254 |
|
| \(1624\) |
\begin{align*}
x^{\prime \prime }+x^{\prime }+{x^{\prime }}^{3}+x&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✗ |
✗ |
✗ |
34.396 |
|
| \(1625\) |
\begin{align*}
x^{\prime \prime }+\left (x^{4}+x^{2}\right ) x^{\prime }+x^{3}+x&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✗ |
✗ |
✗ |
26.088 |
|
| \(1626\) |
\begin{align*}
x^{\prime \prime }+\left (5 x^{4}-6 x^{2}\right ) x^{\prime }+x^{3}&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✗ |
✗ |
✗ |
73.322 |
|
| \(1627\) |
\begin{align*}
x^{\prime \prime }+\left (x^{2}+1\right ) x^{\prime }+x^{3}&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✗ |
✗ |
✗ |
17.647 |
|
| \(1628\) |
\begin{align*}
x^{\prime }&=x-x^{2} \\
y^{\prime }&=2 y-y^{2} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.026 |
|
| \(1629\) |
\begin{align*}
\left (t \cos \left (t \right )-\sin \left (t \right )\right ) x^{\prime \prime }-x^{\prime } t \sin \left (t \right )-x \sin \left (t \right )&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
2.122 |
|
| \(1630\) |
\begin{align*}
y^{\prime }&=x y^{3}+x^{2} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_Abel] |
✗ |
✗ |
✗ |
7.918 |
|
| \(1631\) |
\begin{align*}
x^{\prime }&=y \\
y^{\prime }&=\frac {y^{2}}{x} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.029 |
|
| \(1632\) |
\begin{align*}
y^{\prime }&=\sin \left (y x \right ) \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
1.782 |
|
| \(1633\) |
\begin{align*}
y^{\prime }&=t \ln \left (y^{2 t}\right )+t^{2} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✓ |
✗ |
20.394 |
|
| \(1634\) |
\begin{align*}
y^{\prime }&=\ln \left (y x \right ) \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
2.298 |
|
| \(1635\) |
\begin{align*}
y^{\prime \prime \prime }+y x&=\sin \left (x \right ) \\
\end{align*} |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✗ |
0.035 |
|
| \(1636\) |
\begin{align*}
y y^{\prime }+y^{\prime \prime }&=1 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✗ |
71.711 |
|
| \(1637\) |
\begin{align*}
y^{\prime \prime }+y y^{\prime \prime \prime \prime }&=1 \\
\end{align*} |
[[_high_order, _missing_x], [_high_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
0.039 |
|
| \(1638\) |
\begin{align*}
y^{\prime \prime \prime }+y x&=\cosh \left (x \right ) \\
\end{align*} |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✗ |
0.037 |
|
| \(1639\) |
\begin{align*}
y^{\prime \prime \prime }+y x&=\cosh \left (x \right ) \\
\end{align*} |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✗ |
0.030 |
|
| \(1640\) |
\begin{align*}
2 y^{\prime \prime }+3 y^{\prime }+4 x^{2} y&=1 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✗ |
8.295 |
|
| \(1641\) |
\begin{align*}
y^{\prime \prime \prime }+y^{\prime \prime } x -y^{2}&=\sin \left (x \right ) \\
\end{align*} |
[NONE] |
✗ |
✗ |
✗ |
0.034 |
|
| \(1642\) |
\begin{align*}
{y^{\prime }}^{2}+x y {y^{\prime }}^{2}&=\ln \left (x \right ) \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
41.583 |
|
| \(1643\) |
\begin{align*}
\sin \left (y^{\prime \prime }\right )+y y^{\prime \prime \prime \prime }&=1 \\
\end{align*} |
[[_high_order, _missing_x], [_high_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
0.031 |
|
| \(1644\) |
\begin{align*}
\sinh \left (x \right ) {y^{\prime }}^{2}+y^{\prime \prime }&=y x \\
\end{align*} |
[NONE] |
✗ |
✗ |
✗ |
1.239 |
|
| \(1645\) |
\begin{align*}
{y^{\prime \prime \prime }}^{2}+\sqrt {y}&=\sin \left (x \right ) \\
\end{align*} |
[NONE] |
✗ |
✗ |
✗ |
0.058 |
|
| \(1646\) |
\begin{align*}
\left (x -3\right ) y^{\prime \prime }+y \ln \left (x \right )&=x^{2} \\
y \left (1\right ) &= 1 \\
y^{\prime }\left (1\right ) &= 2 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
✗ |
✗ |
27.014 |
|
| \(1647\) |
\begin{align*}
y^{\prime \prime }+\tan \left (x \right ) y^{\prime }+\cot \left (x \right ) y&=0 \\
y \left (\frac {\pi }{4}\right ) &= 1 \\
y^{\prime }\left (\frac {\pi }{4}\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✗ |
✗ |
6.833 |
|
| \(1648\) |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime \prime }+\left (x -1\right ) y^{\prime }+y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✗ |
✗ |
60.009 |
|
| \(1649\) |
\begin{align*}
y^{\prime \prime } x +2 x^{2} y^{\prime }+\sin \left (x \right ) y&=\sinh \left (x \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
✗ |
✗ |
54.867 |
|
| \(1650\) |
\begin{align*}
\sin \left (x \right ) y^{\prime \prime }+y^{\prime } x +7 y&=1 \\
y \left (1\right ) &= 1 \\
y^{\prime }\left (1\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
21.411 |
|
| \(1651\) |
\begin{align*}
y^{\prime \prime }-\left (x -1\right ) y^{\prime }+x^{2} y&=\tan \left (x \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✗ |
10.687 |
|
| \(1652\) |
\begin{align*}
x^{2} y^{\prime \prime }-4 x^{2} y^{\prime }+\left (x^{2}+1\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
9.649 |
|
| \(1653\) |
\begin{align*}
y^{\prime \prime }+\frac {k x}{y^{4}}&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _with_linear_symmetries]] |
✓ |
✗ |
✗ |
0.635 |
|
| \(1654\) |
\begin{align*}
x^{2} y^{\prime \prime }+x^{2} y^{\prime }+2 \left (1-x \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
8.841 |
|
| \(1655\) |
\begin{align*}
\ln \left (x^{2}+1\right ) y^{\prime \prime }+\frac {4 x y^{\prime }}{x^{2}+1}+\frac {\left (-x^{2}+1\right ) y}{\left (x^{2}+1\right )^{2}}&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
308.815 |
|
| \(1656\) |
\begin{align*}
y^{\prime \prime } x +\left (6 x y^{2}+1\right ) y^{\prime }+2 y^{3}+1&=0 \\
\end{align*} |
[[_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_xy]] |
✗ |
✗ |
✗ |
15.494 |
|
| \(1657\) |
\begin{align*}
y^{\prime \prime }+\frac {\left (x -1\right ) y^{\prime }}{x}+\frac {y}{x^{3}}&=\frac {{\mathrm e}^{-\frac {1}{x}}}{x^{3}} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
✗ |
✗ |
8.987 |
|
| \(1658\) |
\begin{align*}
t^{2} y^{\prime \prime }-6 y^{\prime } t +\sin \left (2 t \right ) y&=\ln \left (t \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
✗ |
✗ |
12.681 |
|
| \(1659\) |
\begin{align*}
y^{\prime \prime }+3 y^{\prime }+\frac {y}{t}&=t \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✗ |
31.183 |
|
| \(1660\) |
\begin{align*}
y^{\prime \prime }+y^{\prime } t -y \ln \left (t \right )&=\cos \left (2 t \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
✗ |
✗ |
4.796 |
|
| \(1661\) |
\begin{align*}
t^{3} y^{\prime \prime }-2 y^{\prime } t +y&=t^{4} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✗ |
42.055 |
|
| \(1662\) |
\begin{align*}
x^{3} y^{\prime \prime }+x^{2} y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_Emden, _Fowler]] |
✗ |
✓ |
✗ |
0.106 |
|
| \(1663\) |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime }-2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✗ |
✓ |
✗ |
0.200 |
|
| \(1664\) |
\begin{align*}
n \left (n +1\right ) y-2 y^{\prime } x +\left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
[_Gegenbauer] |
✓ |
✓ |
✗ |
115.567 |
|
| \(1665\) |
\begin{align*}
x^{\prime \prime }+x^{\prime }+x-x^{3}&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✗ |
✗ |
✗ |
31.415 |
|
| \(1666\) |
\begin{align*}
x^{\prime \prime }+x^{\prime }+x+x^{3}&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✗ |
✗ |
✗ |
31.896 |
|
| \(1667\) |
\begin{align*}
x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y&=0 \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (2\right ) &= -1 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✗ |
✗ |
✓ |
17.623 |
|
| \(1668\) |
\begin{align*}
y^{\prime }&=x^{3}+y^{3} \\
\end{align*} |
[_Abel] |
✗ |
✗ |
✗ |
3.108 |
|
| \(1669\) |
\begin{align*}
y^{\prime }&=\frac {1}{\sqrt {15-x^{2}-y^{2}}} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
5.828 |
|
| \(1670\) |
\begin{align*}
\sqrt {1-x}\, y^{\prime \prime }-4 y&=\sin \left (x \right ) \\
y \left (-2\right ) &= 3 \\
y^{\prime }\left (-2\right ) &= -1 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✗ |
✗ |
4.717 |
|
| \(1671\) |
\begin{align*}
\left (x^{2}-4\right ) y^{\prime \prime }+y \ln \left (x \right )&=x \,{\mathrm e}^{x} \\
y \left (1\right ) &= 1 \\
y^{\prime }\left (1\right ) &= 2 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
✗ |
✗ |
4.214 |
|
| \(1672\) |
\begin{align*}
y_{1}^{\prime }&=\frac {2 y_{1}}{x}-\frac {y_{2}}{x^{2}}-3+\frac {1}{x}-\frac {1}{x^{2}} \\
y_{2}^{\prime }&=2 y_{1}+1-6 x \\
\end{align*} With initial conditions \begin{align*}
y_{1} \left (1\right ) &= -2 \\
y_{2} \left (1\right ) &= -5 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.040 |
|
| \(1673\) |
\begin{align*}
y_{1}^{\prime }&=\frac {5 y_{1}}{x}+\frac {4 y_{2}}{x}-2 x \\
y_{2}^{\prime }&=-\frac {6 y_{1}}{x}-\frac {5 y_{2}}{x}+5 x \\
\end{align*} With initial conditions \begin{align*}
y_{1} \left (-1\right ) &= 3 \\
y_{2} \left (-1\right ) &= -3 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.047 |
|
| \(1674\) |
\begin{align*}
y_{1}^{\prime }&=\sin \left (x \right ) y_{1}+\sqrt {x}\, y_{2}+\ln \left (x \right ) \\
y_{2}^{\prime }&=\tan \left (x \right ) y_{1}-{\mathrm e}^{x} y_{2}+1 \\
\end{align*} With initial conditions \begin{align*}
y_{1} \left (1\right ) &= 1 \\
y_{2} \left (1\right ) &= -1 \\
\end{align*} |
system_of_ODEs |
✗ |
✗ |
✗ |
0.047 |
|
| \(1675\) |
\begin{align*}
y_{1}^{\prime }&=\sin \left (x \right ) y_{1}+\sqrt {x}\, y_{2}+\ln \left (x \right ) \\
y_{2}^{\prime }&=\tan \left (x \right ) y_{1}-{\mathrm e}^{x} y_{2}+1 \\
\end{align*} With initial conditions \begin{align*}
y_{1} \left (2\right ) &= 1 \\
y_{2} \left (2\right ) &= -1 \\
\end{align*} |
system_of_ODEs |
✗ |
✗ |
✗ |
0.049 |
|
| \(1676\) |
\begin{align*}
y_{1}^{\prime }&={\mathrm e}^{-x} y_{1}-\sqrt {x +1}\, y_{2}+x^{2} \\
y_{2}^{\prime }&=\frac {y_{1}}{\left (x -2\right )^{2}} \\
\end{align*} With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 0 \\
y_{2} \left (0\right ) &= 1 \\
\end{align*} |
system_of_ODEs |
✗ |
✗ |
✗ |
0.045 |
|
| \(1677\) |
\begin{align*}
y_{1}^{\prime }&={\mathrm e}^{-x} y_{1}-\sqrt {x +1}\, y_{2}+x^{2} \\
y_{2}^{\prime }&=\frac {y_{1}}{\left (x -2\right )^{2}} \\
\end{align*} With initial conditions \begin{align*}
y_{1} \left (3\right ) &= 1 \\
y_{2} \left (3\right ) &= 0 \\
\end{align*} |
system_of_ODEs |
✗ |
✗ |
✗ |
0.045 |
|
| \(1678\) |
\begin{align*}
y_{1}^{\prime }&=2 x y_{1}-x^{2} y_{2}+4 x \\
y_{2}^{\prime }&={\mathrm e}^{x} y_{1}+3 \,{\mathrm e}^{-x} y_{2}-\cos \left (3 x \right ) \\
\end{align*} |
system_of_ODEs |
✗ |
✗ |
✗ |
0.042 |
|
| \(1679\) |
\begin{align*}
y_{1}^{\prime }&=\frac {5 y_{1}}{x}+\frac {4 y_{2}}{x} \\
y_{2}^{\prime }&=-\frac {6 y_{1}}{x}-\frac {5 y_{2}}{x} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.039 |
|
| \(1680\) |
\begin{align*}
y_{1}^{\prime }&=\frac {5 y_{1}}{x}+\frac {4 y_{2}}{x}-2 x \\
y_{2}^{\prime }&=-\frac {6 y_{1}}{x}-\frac {5 y_{2}}{x}+5 x \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.039 |
|
| \(1681\) |
\begin{align*}
y^{\prime }&=2 y^{3}+t^{2} \\
y \left (0\right ) &= -{\frac {1}{2}} \\
\end{align*} |
[_Abel] |
✗ |
✗ |
✗ |
3.229 |
|
| \(1682\) |
\begin{align*}
y^{\prime }&=\left (y-3\right ) \left (\sin \left (y\right ) \sin \left (t \right )+\cos \left (t \right )+1\right ) \\
y \left (0\right ) &= 4 \\
\end{align*} |
[‘x=_G(y,y’)‘] |
✗ |
✗ |
✗ |
16.783 |
|
| \(1683\) |
\begin{align*}
y^{\prime }&=\left (y-1\right ) \left (y-2\right ) \left (y-{\mathrm e}^{\frac {t}{2}}\right ) \\
\end{align*} |
[_Abel] |
✗ |
✗ |
✗ |
12.544 |
|
| \(1684\) |
\begin{align*}
y^{2} y^{\prime \prime }&=8 x^{2} \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
0.469 |
|
| \(1685\) |
\begin{align*}
\sin \left (x +y\right )-y y^{\prime }&=0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
62.884 |
|
| \(1686\) |
\begin{align*}
y^{2} y^{\prime }+3 x^{2} y&=\sin \left (x \right ) \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
45.574 |
|
| \(1687\) |
\begin{align*}
y^{\prime \prime }+x^{2} y^{\prime }-4 y&=x^{3} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✗ |
11.780 |
|
| \(1688\) |
\begin{align*}
y^{\prime \prime }+x^{2} y^{\prime }-4 y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
7.955 |
|
| \(1689\) |
\begin{align*}
y^{\prime \prime }+x^{2} y^{\prime }&=4 y \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
7.815 |
|
| \(1690\) |
\begin{align*}
y^{\prime \prime }+x^{2} y^{\prime }+4 y&=y^{3} \\
\end{align*} |
[NONE] |
✗ |
✗ |
✗ |
1.152 |
|
| \(1691\) |
\begin{align*}
y y^{\prime \prime \prime }+6 y^{\prime \prime }+3 y^{\prime }&=y \\
\end{align*} |
[[_3rd_order, _missing_x], [_3rd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
0.032 |
|
| \(1692\) |
\begin{align*}
x^{3} y^{\prime \prime \prime }-4 y^{\prime \prime }+10 y^{\prime }-12 y&=0 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
0.036 |
|
| \(1693\) |
\begin{align*}
t x^{\prime }+2 x&=15 y \\
y^{\prime } t&=x \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.032 |
|
| \(1694\) |
\begin{align*}
x^{\prime }&=x y-6 y \\
y^{\prime }&=x-y-5 \\
\end{align*} |
system_of_ODEs |
✗ |
✗ |
✗ |
0.037 |
|
| \(1695\) |
\begin{align*}
x {y^{\prime \prime }}^{2}+2 y&=2 x \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
0.098 |
|
| \(1696\) |
\begin{align*}
x^{\prime \prime }+2 \sin \left (x\right )&=\sin \left (2 t \right ) \\
\end{align*} |
[NONE] |
✗ |
✗ |
✗ |
2.485 |
|
| \(1697\) |
\begin{align*}
4 \left (x^{2}+y^{2}\right ) x -5 y+4 y \left (x^{2}+y^{2}-5 x \right ) y^{\prime }&=0 \\
\end{align*} |
[_rational] |
✗ |
✗ |
✗ |
60.570 |
|
| \(1698\) |
\begin{align*}
y^{\prime }+t^{2}&=\frac {1}{y^{2}} \\
\end{align*} |
[_rational] |
✗ |
✗ |
✗ |
13.817 |
|
| \(1699\) |
\begin{align*}
1-y^{2} \cos \left (t y\right )+\left (t y \cos \left (t y\right )+\sin \left (t y\right )\right ) y^{\prime }&=0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
10.402 |
|
| \(1700\) |
\begin{align*}
\frac {1}{t^{2}+1}-y^{2}-2 t y y^{\prime }&=0 \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_exact, _rational, _Bernoulli] |
✗ |
✗ |
✗ |
71.054 |
|
| \(1701\) |
\begin{align*}
y^{\prime \prime }+b \left (t \right ) y^{\prime }+c \left (t \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
4.191 |
|
| \(1702\) |
\begin{align*}
{y^{\prime \prime }}^{2}-5 y^{\prime \prime } y^{\prime }+4 y^{2}&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✗ |
✗ |
0.109 |
|
| \(1703\) |
\begin{align*}
{y^{\prime \prime }}^{2}-2 y^{\prime \prime } y^{\prime }+y^{2}&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✗ |
✗ |
0.043 |
|
| \(1704\) |
\begin{align*}
x \left (x +1\right ) y^{\prime \prime }+\frac {y^{\prime }}{x^{2}}+5 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
0.188 |
|
| \(1705\) |
\begin{align*}
x^{\prime }&=x^{2} \\
y^{\prime }&={\mathrm e}^{t} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.025 |
|
| \(1706\) |
\begin{align*}
y^{\prime }&=\sin \left (y\right )-\cos \left (x \right ) \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
3.239 |
|
| \(1707\) |
\begin{align*}
y^{\prime }&=\sin \left (y x \right ) \\
y \left (0\right ) &= 0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✗ |
1.558 |
|
| \(1708\) |
\begin{align*}
x^{2} y^{\prime } \cos \left (y\right )+1&=0 \\
y \left (\infty \right ) &= \frac {16 \pi }{3} \\
\end{align*} |
[_separable] |
✓ |
✗ |
✗ |
123.111 |
|
| \(1709\) |
\begin{align*}
x^{2} y^{\prime }+\cos \left (2 y\right )&=1 \\
y \left (\infty \right ) &= \frac {10 \pi }{3} \\
\end{align*} |
[_separable] |
✓ |
✗ |
✗ |
59.645 |
|
| \(1710\) |
\begin{align*}
x^{2} y^{\prime }+\sin \left (2 y\right )&=1 \\
y \left (\infty \right ) &= \frac {11 \pi }{4} \\
\end{align*} |
[_separable] |
✓ |
✗ |
✓ |
72.735 |
|
| \(1711\) |
\begin{align*}
y^{\prime }-2 \,{\mathrm e}^{x} y&=2 \sqrt {{\mathrm e}^{x} y} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✗ |
11.263 |
|
| \(1712\) |
\begin{align*}
y^{\prime }&=y \left ({\mathrm e}^{x}+\ln \left (y\right )\right ) \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
8.025 |
|
| \(1713\) |
\begin{align*}
y^{\prime }+x \sin \left (2 y\right )&=2 x \,{\mathrm e}^{-x^{2}} \cos \left (y\right )^{2} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✗ |
23.944 |
|
| \(1714\) |
\begin{align*}
y^{\prime \prime \prime }&=3 y y^{\prime } \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 1 \\
y^{\prime \prime }\left (0\right ) &= {\frac {3}{2}} \\
\end{align*} |
[[_3rd_order, _missing_x], [_3rd_order, _exact, _nonlinear], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2]] |
✓ |
✗ |
✗ |
0.065 |
|
| \(1715\) |
\begin{align*}
y^{\prime \prime }-2 y^{\prime }+y&=4 \,{\mathrm e}^{-x} \\
y \left (\infty \right ) &= 0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
24.101 |
|
| \(1716\) |
\begin{align*}
y^{\prime \prime }+4 y^{\prime }+3 y&=8 \,{\mathrm e}^{x}+9 \\
y \left (-\infty \right ) &= 3 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✗ |
✓ |
20.605 |
|
| \(1717\) |
\begin{align*}
y^{\prime \prime }+4 y^{\prime }+4 y&=2 \,{\mathrm e}^{x} \left (\sin \left (x \right )+7 \cos \left (x \right )\right ) \\
y \left (-\infty \right ) &= 0 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✗ |
✓ |
29.085 |
|
| \(1718\) |
\begin{align*}
y^{\prime \prime }-5 y^{\prime }+6 y&=2 \,{\mathrm e}^{-2 x} \left (9 \sin \left (2 x \right )+4 \cos \left (2 x \right )\right ) \\
y \left (\infty \right ) &= 0 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✗ |
✓ |
23.891 |
|
| \(1719\) |
\begin{align*}
y^{\prime \prime }-4 y^{\prime }+4 y&={\mathrm e}^{-x} \left (9 x^{2}+5 x -12\right ) \\
y \left (\infty \right ) &= 0 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✗ |
✗ |
45.793 |
|
| \(1720\) |
\begin{align*}
4 y^{\prime \prime } x +2 y^{\prime }+y&=\frac {6+x}{x^{2}} \\
y \left (\infty \right ) &= 0 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✗ |
✗ |
509.012 |
|
| \(1721\) |
\begin{align*}
2 x^{2} \left (2-\ln \left (x \right )\right ) y^{\prime \prime }+x \left (4-\ln \left (x \right )\right ) y^{\prime }-y&=\frac {\left (2-\ln \left (x \right )\right )^{2}}{\sqrt {x}} \\
y \left (\infty \right ) &= 0 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✗ |
✗ |
73.719 |
|
| \(1722\) |
\begin{align*}
x^{3} \left (\ln \left (x \right )-1\right ) y^{\prime \prime }-x^{2} y^{\prime }+y x&=2 \ln \left (x \right ) \\
y \left (\infty \right ) &= 0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✗ |
✗ |
143.861 |
|
| \(1723\) |
\begin{align*}
\left (x^{2}-2 x \right ) y^{\prime \prime }+\left (-x^{2}+2\right ) y^{\prime }-2 \left (1-x \right ) y&=2 x -2 \\
y \left (\infty \right ) &= 1 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✗ |
✗ |
104.433 |
|
| \(1724\) |
\begin{align*}
x^{\prime \prime }-2 {x^{\prime }}^{2}+x^{\prime }-2 x&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✗ |
✗ |
✗ |
152.345 |
|
| \(1725\) |
\begin{align*}
x^{\prime \prime }+{\mathrm e}^{-x^{\prime }}-x&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✗ |
✗ |
✗ |
127.523 |
|
| \(1726\) |
\begin{align*}
x^{\prime \prime }-x^{\prime }+x-x^{2}&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✗ |
✗ |
✗ |
123.835 |
|
| \(1727\) |
\begin{align*}
y^{\prime \prime }+y&=0 \\
y \left (0\right ) &= 0 \\
y \left (2 \pi \right ) &= 1 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✗ |
✗ |
✗ |
29.577 |
|
| \(1728\) |
\begin{align*}
y^{\prime \prime \prime }+x \sin \left (y\right )&=0 \\
y \left (0\right ) &= \frac {\pi }{2} \\
y^{\prime }\left (0\right ) &= 0 \\
y^{\prime \prime }\left (0\right ) &= 0 \\
\end{align*} Series expansion around \(x=0\). |
[NONE] |
✓ |
✗ |
✗ |
0.138 |
|
| \(1729\) |
\begin{align*}
x_{1}^{\prime }&=-2 t x_{1}^{2} \\
x_{2}^{\prime }&=\frac {x_{2}+t}{t} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.041 |
|
| \(1730\) |
\begin{align*}
x_{1}^{\prime }&={\mathrm e}^{t -x_{1}} \\
x_{2}^{\prime }&=2 \,{\mathrm e}^{x_{1}} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.087 |
|
| \(1731\) |
\begin{align*}
x^{\prime }&=y \\
y^{\prime }&=\frac {y^{2}}{x} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.041 |
|
| \(1732\) |
\begin{align*}
x_{1}^{\prime }&=\frac {x_{1}^{2}}{x_{2}} \\
x_{2}^{\prime }&=x_{2}-x_{1} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.080 |
|
| \(1733\) |
\begin{align*}
x^{\prime }&=\frac {{\mathrm e}^{-x}}{t} \\
y^{\prime }&=\frac {x \,{\mathrm e}^{-y}}{t} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.042 |
|
| \(1734\) |
\begin{align*}
x^{\prime }&=\frac {y+t}{x+y} \\
y^{\prime }&=\frac {x-t}{x+y} \\
\end{align*} |
system_of_ODEs |
✓ |
✗ |
✗ |
0.044 |
|
| \(1735\) |
\begin{align*}
x^{\prime }&=\frac {t -y}{-x+y} \\
y^{\prime }&=\frac {x-t}{-x+y} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.045 |
|
| \(1736\) |
\begin{align*}
x^{\prime }&=\frac {y+t}{x+y} \\
y^{\prime }&=\frac {t +x}{x+y} \\
\end{align*} |
system_of_ODEs |
✓ |
✗ |
✗ |
0.067 |
|
| \(1737\) |
\begin{align*}
x^{\prime \prime }&=y \\
y^{\prime \prime }&=x \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.040 |
|
| \(1738\) |
\begin{align*}
x^{\prime \prime }+y^{\prime }+x&=0 \\
x^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.048 |
|
| \(1739\) |
\begin{align*}
x^{\prime \prime }&=3 x+y \\
y^{\prime }&=-2 x \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.035 |
|
| \(1740\) |
\begin{align*}
x^{\prime \prime }&=x^{2}+y \\
y^{\prime }&=-2 x x^{\prime }+x \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
x^{\prime }\left (0\right ) &= 1 \\
y \left (0\right ) &= 0 \\
\end{align*} |
system_of_ODEs |
✓ |
✗ |
✗ |
0.026 |
|
| \(1741\) |
\begin{align*}
x^{\prime }&=x^{2}+y^{2} \\
y^{\prime }&=2 x y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.088 |
|
| \(1742\) |
\begin{align*}
x^{\prime }&=-\frac {1}{y} \\
y^{\prime }&=\frac {1}{x} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.040 |
|
| \(1743\) |
\begin{align*}
x^{\prime }&=\frac {x}{y} \\
y^{\prime }&=\frac {y}{x} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.048 |
|
| \(1744\) |
\begin{align*}
x^{\prime }&=\frac {y}{x-y} \\
y^{\prime }&=\frac {x}{x-y} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.042 |
|
| \(1745\) |
\begin{align*}
x^{\prime }&=\sin \left (x\right ) \cos \left (y\right ) \\
y^{\prime }&=\cos \left (x\right ) \sin \left (y\right ) \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.046 |
|
| \(1746\) |
\begin{align*}
{\mathrm e}^{t} x^{\prime }&=\frac {1}{y} \\
{\mathrm e}^{t} y^{\prime }&=\frac {1}{x} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.058 |
|
| \(1747\) |
\begin{align*}
x^{\prime }&=\cos \left (x\right )^{2} \cos \left (y\right )^{2}+\sin \left (x\right )^{2} \cos \left (y\right )^{2} \\
y^{\prime }&=-\frac {\sin \left (2 x\right ) \sin \left (2 y\right )}{2} \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 0 \\
\end{align*} |
system_of_ODEs |
✗ |
✗ |
✗ |
0.053 |
|
| \(1748\) |
\begin{align*}
x^{\prime }&=-4 x-2 y+\frac {2}{{\mathrm e}^{t}-1} \\
y^{\prime }&=6 x+3 y-\frac {3}{{\mathrm e}^{t}-1} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.041 |
|
| \(1749\) |
\begin{align*}
y^{\prime }&=\sqrt {1-t^{2}-y^{2}} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
16.949 |
|
| \(1750\) |
\begin{align*}
y^{\prime }&=\frac {\ln \left (t y\right )}{1-t^{2}+y^{2}} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
27.565 |
|
| \(1751\) |
\begin{align*}
y^{\prime }&=\left (t^{2}+y^{2}\right )^{{3}/{2}} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
15.624 |
|
| \(1752\) |
\begin{align*}
{\mathrm e}^{x} \sin \left (y\right )+3 y-\left (3 x -{\mathrm e}^{x} \sin \left (y\right )\right ) y^{\prime }&=0 \\
\end{align*} |
[‘x=_G(y,y’)‘] |
✗ |
✗ |
✗ |
26.735 |
|
| \(1753\) |
\begin{align*}
\frac {4 x^{3}}{y^{2}}+\frac {12}{y}+3 \left (\frac {x}{y^{2}}+4 y\right ) y^{\prime }&=0 \\
\end{align*} |
[_rational] |
✗ |
✗ |
✗ |
12.285 |
|
| \(1754\) |
\begin{align*}
x^{\prime }&=-2 t x+y \\
y^{\prime }&=3 x-y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.038 |
|
| \(1755\) |
\begin{align*}
x^{\prime }&=-x+t y \\
y^{\prime }&=t x-y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.037 |
|
| \(1756\) |
\begin{align*}
x^{\prime }&=x+y+4 \\
y^{\prime }&=-2 x+\sin \left (t \right ) y \\
\end{align*} |
system_of_ODEs |
✓ |
✗ |
✗ |
0.041 |
|
| \(1757\) |
\begin{align*}
x^{\prime }&=-x+y+x^{2} \\
y^{\prime }&=y-2 x y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.037 |
|
| \(1758\) |
\begin{align*}
x^{\prime }&=2 y \,x^{2}-3 x^{2}-4 y \\
y^{\prime }&=-2 x \,y^{2}+6 x y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.042 |
|
| \(1759\) |
\begin{align*}
x^{\prime }&=3 x-x^{2} \\
y^{\prime }&=2 x y-3 y+2 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.037 |
|
| \(1760\) |
\begin{align*}
x^{\prime }&=x-x y \\
y^{\prime }&=y+2 x y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.044 |
|
| \(1761\) |
\begin{align*}
x^{\prime }&=2-y \\
y^{\prime }&=y-x^{2} \\
\end{align*} |
system_of_ODEs |
✗ |
✗ |
✗ |
0.041 |
|
| \(1762\) |
\begin{align*}
x^{\prime }&=x-x^{2}-x y \\
y^{\prime }&=\frac {y}{2}-\frac {y^{2}}{4}-\frac {3 x y}{4} \\
\end{align*} |
system_of_ODEs |
✗ |
✗ |
✗ |
0.044 |
|
| \(1763\) |
\begin{align*}
x^{\prime }&=-\left (x-y\right ) \left (1-x-y\right ) \\
y^{\prime }&=x \left (2+y\right ) \\
\end{align*} |
system_of_ODEs |
✗ |
✗ |
✗ |
0.037 |
|
| \(1764\) |
\begin{align*}
x^{\prime }&=y \left (2-x-y\right ) \\
y^{\prime }&=-x-y-2 x y \\
\end{align*} |
system_of_ODEs |
✗ |
✗ |
✗ |
0.050 |
|
| \(1765\) |
\begin{align*}
x^{\prime }&=\left (2+x\right ) \left (-x+y\right ) \\
y^{\prime }&=y-x^{2}-y^{2} \\
\end{align*} |
system_of_ODEs |
✗ |
✗ |
✗ |
0.040 |
|
| \(1766\) |
\begin{align*}
x^{\prime }&=-x+2 x y \\
y^{\prime }&=y-x^{2}-y^{2} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.037 |
|
| \(1767\) |
\begin{align*}
x^{\prime }&=y \\
y^{\prime }&=x-\frac {x^{3}}{5}-\frac {y}{5} \\
\end{align*} |
system_of_ODEs |
✗ |
✗ |
✗ |
0.036 |
|
| \(1768\) |
\begin{align*}
x^{\prime }&=x \left (1-x-y\right ) \\
y^{\prime }&=y \left (\frac {3}{4}-y-\frac {x}{2}\right ) \\
\end{align*} |
system_of_ODEs |
✗ |
✗ |
✗ |
0.061 |
|
| \(1769\) |
\begin{align*}
y^{\prime \prime }+y^{\prime }+y+y^{3}&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✗ |
✗ |
✗ |
80.112 |
|
| \(1770\) |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +\alpha \left (\alpha +1\right ) y&=0 \\
\end{align*} |
[_Gegenbauer] |
✓ |
✓ |
✗ |
117.312 |
|
| \(1771\) |
\begin{align*}
y^{\prime \prime }+\mu \left (1-y^{2}\right ) y^{\prime }+y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x], _Van_der_Pol] |
✗ |
✗ |
✗ |
91.937 |
|
| \(1772\) |
\begin{align*}
\left (t -1\right ) y^{\prime \prime }-3 y^{\prime } t +4 y&=\sin \left (t \right ) \\
y \left (-2\right ) &= 2 \\
y^{\prime }\left (-2\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✗ |
50.931 |
|
| \(1773\) |
\begin{align*}
t \left (t -4\right ) y^{\prime \prime }+3 y^{\prime } t +4 y&=2 \\
y \left (3\right ) &= 0 \\
y^{\prime }\left (3\right ) &= -1 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
142.413 |
|
| \(1774\) |
\begin{align*}
y^{\prime \prime }+\cos \left (t \right ) y^{\prime }+3 y \ln \left (t \right )&=0 \\
y \left (2\right ) &= 3 \\
y^{\prime }\left (2\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
19.705 |
|
| \(1775\) |
\begin{align*}
\left (x +3\right ) y^{\prime \prime }+y^{\prime } x +y \ln \left (x \right )&=0 \\
y \left (1\right ) &= 0 \\
y^{\prime }\left (1\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
46.302 |
|
| \(1776\) |
\begin{align*}
\left (x -2\right ) y^{\prime \prime }+y^{\prime }+\left (x -2\right ) \tan \left (x \right ) y&=0 \\
y \left (3\right ) &= 1 \\
y^{\prime }\left (3\right ) &= 2 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
49.062 |
|
| \(1777\) |
\begin{align*}
y^{\prime \prime }-\frac {t}{y}&=\frac {1}{\pi } \\
y \left (0\right ) &= y_{0} \\
y^{\prime }\left (0\right ) &= y_{1} \\
\end{align*} |
[NONE] |
✗ |
✓ |
✗ |
1.062 |
|
| \(1778\) |
\begin{align*}
y^{\prime \prime }+y+\frac {y^{3}}{5}&=\cos \left (w t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[NONE] |
✗ |
✗ |
✗ |
2.541 |
|
| \(1779\) |
\begin{align*}
y^{\prime \prime }+\frac {y^{\prime }}{5}+y+\frac {y^{3}}{5}&=\cos \left (w t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[NONE] |
✗ |
✗ |
✗ |
3.069 |
|
| \(1780\) |
\begin{align*}
t y^{\prime \prime \prime }+\sin \left (t \right ) y^{\prime \prime }+8 y&=\cos \left (t \right ) \\
\end{align*} |
[[_3rd_order, _linear, _nonhomogeneous]] |
✗ |
✗ |
✗ |
0.065 |
|
| \(1781\) |
\begin{align*}
t \left (t -1\right ) y^{\prime \prime \prime \prime }+{\mathrm e}^{t} y^{\prime \prime }+4 t^{2} y&=0 \\
\end{align*} |
[[_high_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
0.060 |
|
| \(1782\) |
\begin{align*}
y^{\prime \prime \prime }+t y^{\prime \prime }+t^{2} y^{\prime }+t^{2} y&=\ln \left (t \right ) \\
\end{align*} |
[[_3rd_order, _linear, _nonhomogeneous]] |
✗ |
✗ |
✗ |
0.060 |
|
| \(1783\) |
\begin{align*}
\left (x -4\right ) y^{\prime \prime \prime \prime }+\left (x +1\right ) y^{\prime \prime }+\tan \left (x \right ) y&=0 \\
\end{align*} |
[[_high_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
0.081 |
|
| \(1784\) |
\begin{align*}
\left (x^{2}-2\right ) y^{\left (6\right )}+x^{2} y^{\prime \prime }+3 y&=0 \\
\end{align*} |
[[_high_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
0.061 |
|
| \(1785\) |
\begin{align*}
t y^{\prime \prime \prime }+\sin \left (t \right ) y^{\prime \prime }+4 y&=\cos \left (t \right ) \\
\end{align*} |
[[_3rd_order, _linear, _nonhomogeneous]] |
✗ |
✗ |
✗ |
0.059 |
|
| \(1786\) |
\begin{align*}
t \left (t -1\right ) y^{\prime \prime \prime \prime }+{\mathrm e}^{t} y^{\prime \prime }+7 t^{2} y&=0 \\
\end{align*} |
[[_high_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
0.062 |
|
| \(1787\) |
\begin{align*}
y^{\prime \prime \prime }+t y^{\prime \prime }+5 t^{2} y^{\prime }+2 y t^{3}&=\ln \left (t \right ) \\
\end{align*} |
[[_3rd_order, _linear, _nonhomogeneous]] |
✗ |
✗ |
✗ |
0.061 |
|
| \(1788\) |
\begin{align*}
\left (x -1\right ) y^{\prime \prime \prime \prime }+\left (x +5\right ) y^{\prime \prime }+\tan \left (x \right ) y&=0 \\
\end{align*} |
[[_high_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
0.055 |
|
| \(1789\) |
\begin{align*}
\left (x^{2}-25\right ) y^{\left (6\right )}+x^{2} y^{\prime \prime }+5 y&=0 \\
\end{align*} |
[[_high_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
0.066 |
|
| \(1790\) |
\begin{align*}
x^{\prime }&=-2 y+x y \\
y^{\prime }&=x+4 x y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.041 |
|
| \(1791\) |
\begin{align*}
x^{\prime }&=1+5 y \\
y^{\prime }&=1-6 x^{2} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.045 |
|
| \(1792\) |
\begin{align*}
\left (x^{2}-x^{3}+3 x y^{2}+2 y^{3}\right ) y^{\prime }+2 x^{3}+3 x^{2} y+y^{2}-y^{3}&=0 \\
\end{align*} |
[_rational] |
✓ |
✓ |
✗ |
17.619 |
|
| \(1793\) |
\begin{align*}
y&={y^{\prime }}^{2}-y^{\prime } x +\frac {x^{3}}{2} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
77.798 |
|
| \(1794\) |
\begin{align*}
n \,x^{3} y^{\prime \prime }&=\left (-y^{\prime } x +y\right )^{2} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✗ |
2.335 |
|
| \(1795\) |
\begin{align*}
y^{2} \left (x^{2} y^{\prime \prime }-y^{\prime } x +y\right )&=x^{3} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
2.166 |
|
| \(1796\) |
\begin{align*}
x^{2} y^{2} y^{\prime \prime }-3 y^{2} y^{\prime } x +4 y^{3}+x^{6}&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
2.103 |
|
| \(1797\) |
\begin{align*}
y^{\prime } y^{\prime \prime }-x^{2} y y^{\prime }-x y^{2}&=0 \\
\end{align*} |
[[_2nd_order, _exact, _nonlinear], [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_poly_yn]] |
✗ |
✗ |
✗ |
76.959 |
|
| \(1798\) |
\begin{align*}
x \left (x^{2} y^{\prime }+2 y x \right ) y^{\prime \prime }+4 x {y^{\prime }}^{2}+8 y y^{\prime } x +4 y^{2}-1&=0 \\
\end{align*} |
[NONE] |
✗ |
✗ |
✗ |
10.712 |
|
| \(1799\) |
\begin{align*}
x^{2} y y^{\prime \prime }+x^{2} {y^{\prime }}^{2}-5 y y^{\prime } x&=4 y^{2} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✗ |
2.048 |
|
| \(1800\) |
\begin{align*}
40 {y^{\prime \prime \prime }}^{3}-45 y^{\prime \prime } y^{\prime \prime \prime } y^{\prime \prime \prime \prime }+9 {y^{\prime \prime }}^{2} y^{\left (5\right )}&=0 \\
\end{align*} |
[[_high_order, _missing_x], [_high_order, _missing_y], [_high_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.176 |
|
| \(1801\) |
\begin{align*}
n \left (n +1\right ) y-2 y^{\prime } x +\left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
[_Gegenbauer] |
✓ |
✓ |
✗ |
113.899 |
|
| \(1802\) |
\begin{align*}
-y+y^{\prime } x -y^{\prime \prime }+x y^{\prime \prime \prime }&=0 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.048 |
|
| \(1803\) |
\begin{align*}
-2 y x +\left (x^{2}+2\right ) y^{\prime }-2 y^{\prime \prime } x +\left (x^{2}+2\right ) y^{\prime \prime \prime }&=x^{4}+12 \\
\end{align*} |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✗ |
0.057 |
|
| \(1804\) |
\begin{align*}
y^{\prime \prime }+\frac {y}{\ln \left (x \right ) x^{2}}&={\mathrm e}^{x} \left (\frac {2}{x}+\ln \left (x \right )\right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✗ |
7.435 |
|
| \(1805\) |
\begin{align*}
y^{\prime }&=\frac {y^{2}}{z} \\
z^{\prime }&=\frac {y}{2} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.035 |
|
| \(1806\) |
\begin{align*}
y^{\prime }&=1-\frac {1}{z} \\
z^{\prime }&=\frac {1}{-x +y} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.045 |
|
| \(1807\) |
\begin{align*}
y^{\prime \prime }&=x +y^{2} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
[NONE] |
✗ |
✗ |
✗ |
0.642 |
|
| \(1808\) |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }+y^{2}&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _missing_x], [_Emden, _modified]] |
✗ |
✗ |
✗ |
79.006 |
|
| \(1809\) |
\begin{align*}
y^{\prime }&=\frac {z^{2}}{y} \\
z^{\prime }&=\frac {y^{2}}{z} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.038 |
|
| \(1810\) |
\begin{align*}
y^{\prime }&=\frac {y^{2}}{z} \\
z^{\prime }&=\frac {z^{2}}{y} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.040 |
|
| \(1811\) |
\begin{align*}
y^{\prime \prime }+z^{\prime }-2 z&={\mathrm e}^{2 x} \\
z^{\prime }+2 y^{\prime }-3 y&=0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.048 |
|
| \(1812\) |
\begin{align*}
y^{\prime }+\frac {2 z}{x^{2}}&=1 \\
z^{\prime }+y&=x \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.038 |
|
| \(1813\) |
\begin{align*}
t x^{\prime }-x-3 y&=t \\
y^{\prime } t -x+y&=0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.040 |
|
| \(1814\) |
\begin{align*}
t x^{\prime }+6 x-y-3 z&=0 \\
y^{\prime } t +23 x-6 y-9 z&=0 \\
t z^{\prime }+x+y-2 z&=0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.052 |
|
| \(1815\) |
\begin{align*}
\left (x \,{\mathrm e}^{y}+y-x^{2}\right ) y^{\prime \prime }&=2 y x -{\mathrm e}^{y}-x \\
\end{align*} |
[NONE] |
✗ |
✗ |
✗ |
1.460 |
|
| \(1816\) |
\begin{align*}
y^{\prime \prime }-f \left (x \right ) y^{\prime }+\left (f \left (x \right )-1\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✗ |
✗ |
34.577 |
|
| \(1817\) |
\begin{align*}
y^{\prime \prime }+3 y^{\prime } x +x^{2} y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
35.390 |
|
| \(1818\) |
\begin{align*}
x^{2} y^{\prime }&=y \\
\end{align*} Series expansion around \(x=0\). |
[_separable] |
✗ |
✓ |
✗ |
0.293 |
|
| \(1819\) |
\begin{align*}
x^{3} \left (x -1\right ) y^{\prime \prime }-2 \left (x -1\right ) y^{\prime }+3 y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
0.239 |
|
| \(1820\) |
\begin{align*}
x^{2} y^{\prime \prime }+\left (-x +2\right ) y^{\prime }&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _missing_y]] |
✗ |
✓ |
✗ |
0.410 |
|
| \(1821\) |
\begin{align*}
x^{4} y^{\prime \prime }+\sin \left (x \right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
0.214 |
|
| \(1822\) |
\begin{align*}
y^{\prime \prime }+\frac {y^{\prime }}{x^{2}}-\frac {y}{x^{3}}&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✗ |
✓ |
✗ |
0.218 |
|
| \(1823\) |
\begin{align*}
y^{\prime \prime }+\frac {n y^{\prime }}{x^{2}}+\frac {q y}{x^{3}}&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
0.275 |
|
| \(1824\) |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (-n^{2}+x^{2}\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[_Bessel] |
✗ |
✓ |
✓ |
0.437 |
|
| \(1825\) |
\begin{align*}
x^{\prime \prime }+\left (5 x^{4}-9 x^{2}\right ) x^{\prime }+x^{5}&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✗ |
✗ |
✗ |
198.194 |
|
| \(1826\) |
\begin{align*}
x^{2} y^{\prime \prime }-\frac {x^{2} {y^{\prime }}^{2}}{2 y}+4 y^{\prime } x +4 y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✗ |
3.573 |
|
| \(1827\) |
\begin{align*}
\cos \left (x \right ) y^{\prime }+\sin \left (x \right ) y^{\prime \prime }+n y \sin \left (x \right )&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
35.298 |
|
| \(1828\) |
\begin{align*}
v^{\prime \prime }&=\left (\frac {1}{v}+{v^{\prime }}^{4}\right )^{{1}/{3}} \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✗ |
✗ |
✗ |
58.293 |
|
| \(1829\) |
\begin{align*}
\sqrt {y^{\prime }+y}&=\left (y^{\prime \prime }+2 x \right )^{{1}/{4}} \\
\end{align*} |
[NONE] |
✗ |
✗ |
✗ |
28.725 |
|
| \(1830\) |
\begin{align*}
y^{\prime \prime \prime } y^{\prime }-3 {y^{\prime \prime }}^{2}+3 y^{\prime \prime } {y^{\prime }}^{2}-2 {y^{\prime }}^{4}-x {y^{\prime }}^{5}&=0 \\
\end{align*} |
[[_3rd_order, _missing_y], [_3rd_order, _with_exponential_symmetries], [_3rd_order, _with_linear_symmetries]] |
✓ |
✗ |
✗ |
0.396 |
|
| \(1831\) |
\begin{align*}
\left (1+y^{2}\right ) y^{\prime \prime }-2 y {y^{\prime }}^{2}-2 \left (1+y^{2}\right ) y^{\prime }&=y^{2} \left (1+y^{2}\right ) \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✗ |
✗ |
✗ |
142.660 |
|
| \(1832\) |
\begin{align*}
y^{2} y^{\prime \prime \prime }-\left (3 y y^{\prime }+2 x y^{2}\right ) y^{\prime \prime }+\left (2 {y^{\prime }}^{2}+2 y y^{\prime } x +3 y^{2} x^{2}\right ) y^{\prime }+x^{3} y^{3}&=0 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✗ |
✗ |
0.060 |
|
| \(1833\) |
\begin{align*}
\left (-y+y^{\prime } x \right )^{2}&=a \left (1+{y^{\prime }}^{2}\right ) \left (x^{2}+y^{2}\right )^{{3}/{2}} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
204.188 |
|
| \(1834\) |
\begin{align*}
\left (-y+y^{\prime } x \right )^{2}&={y^{\prime }}^{2}-\frac {2 y y^{\prime }}{x}+1 \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✗ |
98.914 |
|
| \(1835\) |
\begin{align*}
\left (1-y^{2}+\frac {y^{4}}{x^{2}}\right ) {y^{\prime }}^{2}-\frac {2 y y^{\prime }}{x}+\frac {y^{2}}{x^{2}}&=0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✗ |
✗ |
299.332 |
|
| \(1836\) |
\begin{align*}
\left (5+2 x \right )^{2} y^{\prime \prime }-6 \left (5-2 x \right ) y^{\prime }+8 y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
81.977 |
|
| \(1837\) |
\begin{align*}
16 \left (x +1\right )^{4} y^{\prime \prime \prime \prime }+96 \left (x +1\right )^{3} y^{\prime \prime \prime }+104 \left (x +1\right )^{2} y^{\prime \prime }+8 \left (x +1\right ) y^{\prime }+y&=x^{2}+4 x +3 \\
\end{align*} |
[[_high_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.075 |
|
| \(1838\) |
\begin{align*}
\sqrt {x}\, y^{\prime \prime }+2 y^{\prime } x +3 y&=x \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
20.802 |
|
| \(1839\) |
\begin{align*}
y^{\prime } y^{\prime \prime }-x^{2} y y^{\prime }&=x y^{2} \\
\end{align*} |
[[_2nd_order, _exact, _nonlinear], [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_poly_yn]] |
✗ |
✗ |
✗ |
74.581 |
|
| \(1840\) |
\begin{align*}
x^{4} y^{\prime \prime }+y^{\prime } x +y&=\frac {1}{x} \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
✓ |
✗ |
0.278 |
|
| \(1841\) |
\begin{align*}
\left (y^{2}+2 x^{2} y^{\prime }\right ) y^{\prime \prime }+2 \left (x +y\right ) {y^{\prime }}^{2}+y^{\prime } x +y&=0 \\
\end{align*} |
[[_2nd_order, _exact, _nonlinear], [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_poly_yn]] |
✗ |
✗ |
✗ |
123.480 |
|
| \(1842\) |
\begin{align*}
\left (x^{3}+x +1\right ) y^{\prime \prime \prime }+\left (3+6 x \right ) y^{\prime \prime }+6 y&=0 \\
\end{align*} |
[[_3rd_order, _exact, _linear, _homogeneous]] |
✗ |
✗ |
✗ |
22.926 |
|
| \(1843\) |
\begin{align*}
y^{\prime \prime }+\frac {y^{\prime }}{x^{{1}/{3}}}+\left (\frac {1}{4 x^{{2}/{3}}}-\frac {1}{6 x^{{1}/{3}}}-\frac {6}{x^{2}}\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
24.334 |
|
| \(1844\) |
\begin{align*}
y^{\prime \prime }-2 b y^{\prime }+b^{2} x^{2} y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
32.770 |
|
| \(1845\) |
\begin{align*}
x^{2} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y&=0 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.059 |
|
| \(1846\) |
\begin{align*}
\left (-y+y^{\prime } x \right )^{2}+x^{2} y y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✗ |
0.719 |
|
| \(1847\) |
\begin{align*}
x^{\prime \prime }-3 x-4 y&=0 \\
x+y^{\prime \prime }+y&=0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.052 |
|
| \(1848\) |
\begin{align*}
y^{\prime }-\frac {\tan \left (y\right )}{x +1}&=\left (x +1\right ) {\mathrm e}^{x} \sec \left (y\right ) \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✓ |
33.743 |
|
| \(1849\) |
\begin{align*}
y^{\prime }+\frac {y \ln \left (y\right )}{x}&=\frac {y}{x^{2}}-\ln \left (y\right )^{2} \\
\end{align*} |
[‘x=_G(y,y’)‘] |
✗ |
✗ |
✗ |
24.520 |
|
| \(1850\) |
\begin{align*}
y^{\prime }&={\mathrm e}^{x -y} \left ({\mathrm e}^{x}-{\mathrm e}^{y}\right ) \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
✓ |
✓ |
9.343 |
|
| \(1851\) |
\begin{align*}
\left (-y+y^{\prime } x \right )^{2}&=a \left (1+{y^{\prime }}^{2}\right ) \left (x^{2}+y^{2}\right )^{{3}/{2}} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
168.915 |
|
| \(1852\) |
\begin{align*}
\left (-y+y^{\prime } x \right )^{2}&={y^{\prime }}^{2}-\frac {2 y y^{\prime }}{x}+1 \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✗ |
97.241 |
|
| \(1853\) |
\begin{align*}
x y {y^{\prime }}^{2}+\left (x^{2}+y^{2}-h^{2}\right ) y^{\prime }-y x&=0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
133.563 |
|
| \(1854\) |
\begin{align*}
\left (x^{2} y^{\prime }+y^{2}\right ) \left (y^{\prime } x +y\right )&=\left (1+y^{\prime }\right )^{2} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
58.789 |
|
| \(1855\) |
\begin{align*}
3 y x +\left (x^{2}+2\right ) y^{\prime }+4 y^{\prime \prime } x +x^{2} y^{\prime \prime \prime }&=2 \\
\end{align*} |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✗ |
0.052 |
|
| \(1856\) |
\begin{align*}
x^{5} y^{\left (6\right )}+x^{4} y^{\left (5\right )}+y^{\prime } x +y&=\ln \left (x \right ) \\
\end{align*} |
[[_high_order, _exact, _linear, _nonhomogeneous]] |
✗ |
✗ |
✗ |
0.784 |
|
| \(1857\) |
\begin{align*}
y^{2}+\left (2 y x -1\right ) y^{\prime }+y^{\prime \prime } x +x^{2} y^{\prime \prime \prime }&=0 \\
\end{align*} |
[[_3rd_order, _exact, _nonlinear], [_3rd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
0.054 |
|
| \(1858\) |
\begin{align*}
2 x^{2} y y^{\prime \prime }+y^{2}&=x^{2} {y^{\prime }}^{2} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✗ |
0.965 |
|
| \(1859\) |
\begin{align*}
x^{2} y^{\prime \prime }&=\sqrt {m \,x^{2} {y^{\prime }}^{3}+n y^{2}} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
2.374 |
|
| \(1860\) |
\begin{align*}
x^{4} y^{\prime \prime }&=\left (x^{3}+2 y x \right ) y^{\prime }-4 y^{2} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✗ |
4.647 |
|
| \(1861\) |
\begin{align*}
x^{4} y^{\prime \prime }-x^{3} y^{\prime }&=x^{2} {y^{\prime }}^{2}-4 y^{2} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✗ |
5.927 |
|
| \(1862\) |
\begin{align*}
x^{2} y^{\prime \prime }+4 y^{2}-6 y&=x^{4} {y^{\prime }}^{2} \\
\end{align*} |
[NONE] |
✗ |
✗ |
✗ |
0.984 |
|
| \(1863\) |
\begin{align*}
y^{\prime \prime \prime }-y^{\prime \prime } x -y^{\prime }+y x&=0 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.053 |
|
| \(1864\) |
\begin{align*}
4 x^{2} y^{\prime \prime }+4 x^{5} y^{\prime }+\left (x^{3}+6 x^{2}+4\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
79.628 |
|
| \(1865\) |
\begin{align*}
\left (-y+y^{\prime } x \right )^{2}+x^{2} y y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✗ |
0.718 |
|
| \(1866\) |
\begin{align*}
y^{\prime \prime } x +\left (x^{2}+1\right ) y^{\prime }+2 y x&=2 x \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✗ |
71.210 |
|
| \(1867\) |
\begin{align*}
t x^{\prime }+y&=0 \\
y^{\prime } t +x&=0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.039 |
|
| \(1868\) |
\begin{align*}
\left (x y \sin \left (y x \right )+\cos \left (y x \right )\right ) y+\left (x y \sin \left (y x \right )-\cos \left (y x \right )\right ) y^{\prime }&=0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
19.892 |
|
| \(1869\) |
\begin{align*}
3 x^{2} y^{4}+2 y x +\left (2 x^{3} y^{2}-x^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[_rational] |
✗ |
✗ |
✗ |
34.928 |
|
| \(1870\) |
\begin{align*}
3 y {y^{\prime }}^{2}-2 y y^{\prime } x +4 y^{2}-x^{2}&=0 \\
\end{align*} |
[_rational] |
✗ |
✗ |
✗ |
255.404 |
|
| \(1871\) |
\begin{align*}
\left (1-y^{2}+\frac {y^{4}}{x^{2}}\right ) {y^{\prime }}^{2}-\frac {2 y y^{\prime }}{x}+\frac {y^{2}}{x^{2}}&=0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✗ |
✗ |
293.472 |
|
| \(1872\) |
\begin{align*}
\left (2 x^{2}+1\right ) {y^{\prime }}^{2}+\left (y^{2}+2 y x +x^{2}+2\right ) y^{\prime }+2 y^{2}+1&=0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✓ |
✗ |
120.121 |
|
| \(1873\) |
\begin{align*}
\left (2 x -1\right )^{3} y^{\prime \prime \prime }+\left (2 x -1\right ) y^{\prime }-2 y&=0 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.056 |
|
| \(1874\) |
\begin{align*}
16 \left (x +1\right )^{4} y^{\prime \prime \prime \prime }+96 \left (x +1\right )^{3} y^{\prime \prime \prime }+104 \left (x +1\right )^{2} y^{\prime \prime }+8 \left (x +1\right ) y^{\prime }+y&=x^{2}+4 x +3 \\
\end{align*} |
[[_high_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.076 |
|
| \(1875\) |
\begin{align*}
2 x^{2} y y^{\prime \prime }+4 y^{2}&=x^{2} {y^{\prime }}^{2}+2 y y^{\prime } x \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✗ |
2.361 |
|
| \(1876\) |
\begin{align*}
\sqrt {x}\, y^{\prime \prime }+2 y^{\prime } x +3 y&=x \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
14.022 |
|
| \(1877\) |
\begin{align*}
2 x^{2} \cos \left (y\right ) y^{\prime \prime }-2 x^{2} \sin \left (y\right ) {y^{\prime }}^{2}+x \cos \left (y\right ) y^{\prime }-\sin \left (y\right )&=\ln \left (x \right ) \\
\end{align*} |
[[_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✗ |
30.802 |
|
| \(1878\) |
\begin{align*}
y+3 y^{\prime } x +2 y {y^{\prime }}^{2}+\left (x^{2}+2 y^{2} y^{\prime }\right ) y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
5.251 |
|
| \(1879\) |
\begin{align*}
\left (y^{2}+2 x^{2} y^{\prime }\right ) y^{\prime \prime }+2 \left (x +y\right ) {y^{\prime }}^{2}+y^{\prime } x +y&=0 \\
\end{align*} |
[[_2nd_order, _exact, _nonlinear], [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_poly_yn]] |
✗ |
✗ |
✗ |
116.104 |
|
| \(1880\) |
\begin{align*}
y^{\prime }-y y^{\prime \prime }&=n \sqrt {{y^{\prime }}^{2}+a^{2} y^{\prime \prime }} \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✗ |
✗ |
✗ |
1118.642 |
|
| \(1881\) |
\begin{align*}
x^{4} y^{\prime \prime }&=\left (-y^{\prime } x +y\right )^{3} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
7.864 |
|
| \(1882\) |
\begin{align*}
y^{\prime \prime } x +2 y^{\prime }&=x^{2} y^{\prime }-y^{2} \\
\end{align*} |
[NONE] |
✗ |
✗ |
✗ |
4.851 |
|
| \(1883\) |
\begin{align*}
y^{\prime \prime }-\cot \left (x \right ) y^{\prime }-\left (1-\cot \left (x \right )\right ) y&={\mathrm e}^{x} \sin \left (x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✗ |
17.523 |
|
| \(1884\) |
\begin{align*}
y^{\prime \prime }+\left (1+\frac {2 \cot \left (x \right )}{x}-\frac {2}{x^{2}}\right ) y&=\cos \left (x \right ) x \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✗ |
✗ |
15.822 |
|
| \(1885\) |
\begin{align*}
y^{\prime \prime }+\left (1-\cot \left (x \right )\right ) y^{\prime }-\cot \left (x \right ) y&=\sin \left (x \right )^{2} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✗ |
13.114 |
|
| \(1886\) |
\begin{align*}
t x^{\prime }&=t -2 x \\
y^{\prime } t&=t x+t y+2 x-t \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.044 |
|
| \(1887\) |
\begin{align*}
3 x^{2}+6 x y^{2}+\left (6 x^{2}+4 y^{3}\right ) y^{\prime }&=0 \\
\end{align*} |
[_rational] |
✗ |
✗ |
✗ |
26.129 |
|
| \(1888\) |
\begin{align*}
y^{\prime \prime } x -y^{\prime } x +y&={\mathrm e}^{x} \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
54.022 |
|
| \(1889\) |
\begin{align*}
x^{2} \left (x -2\right ) y^{\prime \prime }+4 \left (x -2\right ) y^{\prime }+3 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
0.828 |
|
| \(1890\) |
\begin{align*}
y^{\prime \prime }+y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_Emden, _Fowler]] |
✗ |
✓ |
✓ |
0.254 |
|
| \(1891\) |
\begin{align*}
y^{\prime }&=x^{3}+y^{3} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_Abel] |
✗ |
✗ |
✗ |
12.630 |
|
| \(1892\) |
\begin{align*}
y^{\prime }&=x +\sqrt {1+y^{2}} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✓ |
✗ |
45.546 |
|
| \(1893\) |
\begin{align*}
x^{\prime }&=x \cos \left (t \right )-\sin \left (t \right ) y \\
y^{\prime }&=x \sin \left (t \right )+y \cos \left (t \right ) \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.042 |
|
| \(1894\) |
\begin{align*}
x^{\prime }&=\left (3 t -1\right ) x-\left (1-t \right ) y+t \,{\mathrm e}^{t^{2}} \\
y^{\prime }&=-\left (t +2\right ) x+\left (-2+t \right ) y-{\mathrm e}^{t^{2}} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.048 |
|
| \(1895\) |
\begin{align*}
w_{1}^{\prime }&=w_{2} \\
w_{2}^{\prime }&=\frac {a w_{1}}{z^{2}} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.041 |
|
| \(1896\) |
\begin{align*}
x^{\prime }&=t^{2} x^{4}+1 \\
x \left (0\right ) &= 0 \\
\end{align*} |
[_Chini] |
✗ |
✗ |
✗ |
13.087 |
|
| \(1897\) |
\begin{align*}
x^{\prime }&=\sin \left (t x\right ) \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
4.378 |
|
| \(1898\) |
\begin{align*}
x^{\prime }&=\arctan \left (x\right )+t \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
39.113 |
|
| \(1899\) |
\begin{align*}
x^{2}+y^{2}+\left (a x y+y^{4}\right ) y^{\prime }&=0 \\
\end{align*} |
[_rational] |
✗ |
✗ |
✗ |
59.565 |
|
| \(1900\) |
\begin{align*}
{x^{\prime }}^{2}&=x^{2}+t^{2}-1 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
44.142 |
|
| \(1901\) |
\begin{align*}
x^{\prime \prime }+p \left (t \right ) x^{\prime }+q \left (t \right ) x&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
59.761 |
|
| \(1902\) |
\begin{align*}
x^{\prime \prime }+\frac {x^{\prime }}{t}+q \left (t \right ) x&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
44.109 |
|
| \(1903\) |
\begin{align*}
x^{\prime \prime }+2 x^{\prime }&=0 \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (\infty \right ) &= a \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✗ |
✓ |
18.523 |
|
| \(1904\) |
\begin{align*}
x^{\prime \prime }+\frac {\left (t^{5}+1\right ) x}{t^{4}+5}&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
15.306 |
|
| \(1905\) |
\begin{align*}
x^{\prime \prime }+\sqrt {t^{6}+3 t^{5}+1}\, x&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✗ |
✗ |
✗ |
7.269 |
|
| \(1906\) |
\begin{align*}
x^{\prime \prime }-p \left (t \right ) x&=q \left (t \right ) \\
x \left (a \right ) &= 0 \\
x \left (b \right ) &= 0 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
✗ |
✗ |
10.412 |
|
| \(1907\) |
\begin{align*}
x^{\prime \prime }+p \left (t \right ) x^{\prime }+q \left (t \right ) x&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
30.873 |
|
| \(1908\) |
\begin{align*}
x x^{\prime \prime }-{x^{\prime }}^{2}+{\mathrm e}^{t} x^{2}&=0 \\
x \left (0\right ) &= 1 \\
x^{\prime }\left (0\right ) &= -1 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✗ |
0.850 |
|
| \(1909\) |
\begin{align*}
x x^{\prime \prime }-{x^{\prime }}^{2}+{\mathrm e}^{t} x^{2}&=0 \\
x \left (0\right ) &= -1 \\
x^{\prime }\left (0\right ) &= -1 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✗ |
0.540 |
|
| \(1910\) |
\begin{align*}
x^{\prime \prime \prime }-x^{\prime }&=0 \\
x \left (0\right ) &= 1 \\
x \left (\infty \right ) &= 0 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
1.766 |
|
| \(1911\) |
\begin{align*}
x^{\prime \prime \prime }+a x^{\prime \prime }+b x^{\prime }+c x&=0 \\
x \left (\infty \right ) &= 0 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✗ |
✗ |
10.998 |
|
| \(1912\) |
\begin{align*}
x^{\prime \prime \prime }-3 x^{\prime }+k x&=0 \\
x \left (0\right ) &= 1 \\
x \left (\infty \right ) &= 0 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✗ |
✗ |
8.073 |
|
| \(1913\) |
\begin{align*}
x^{\prime \prime \prime \prime }-4 x^{\prime \prime }+x&=0 \\
x \left (0\right ) &= 0 \\
x \left (\infty \right ) &= 0 \\
x^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
0.886 |
|
| \(1914\) |
\begin{align*}
x^{\prime \prime \prime \prime }-8 x^{\prime \prime \prime }+23 x^{\prime \prime }-28 x^{\prime }+12 x&=0 \\
x \left (\infty \right ) &= 0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
0.443 |
|
| \(1915\) |
\begin{align*}
x^{\left (5\right )}+x&=0 \\
x \left (\infty \right ) &= 0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✗ |
✗ |
✗ |
8.886 |
|
| \(1916\) |
\begin{align*}
x^{\prime }+t y&=-1 \\
x^{\prime }+y^{\prime }&=2 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.039 |
|
| \(1917\) |
\begin{align*}
x^{\prime }+y&=3 t \\
y^{\prime }-t x^{\prime }&=0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.044 |
|
| \(1918\) |
\begin{align*}
x^{\prime }-t y&=1 \\
y^{\prime }-t x^{\prime }&=3 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.040 |
|
| \(1919\) |
\begin{align*}
t^{2} x^{\prime }-y&=1 \\
y^{\prime }-2 x&=0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.038 |
|
| \(1920\) |
\begin{align*}
t x^{\prime }+y^{\prime }&=1 \\
y^{\prime }+x+{\mathrm e}^{x^{\prime }}&=1 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.133 |
|
| \(1921\) |
\begin{align*}
x x^{\prime }+y&=2 t \\
y^{\prime }+2 x^{2}&=1 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.039 |
|
| \(1922\) |
\begin{align*}
x^{\prime }&=x-x y \\
y^{\prime }&=-y+x y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.046 |
|
| \(1923\) |
\begin{align*}
x^{\prime }&=2 x-7 x y-a x \\
y^{\prime }&=-y+4 x y-a y \\
\end{align*} |
system_of_ODEs |
✓ |
✗ |
✗ |
0.039 |
|
| \(1924\) |
\begin{align*}
x^{\prime }&=2 x-2 x y \\
y^{\prime }&=-y+x y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.048 |
|
| \(1925\) |
\begin{align*}
x^{\prime }&=x-4 x y \\
y^{\prime }&=-2 y+x y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.038 |
|
| \(1926\) |
\begin{align*}
x^{\prime }&=x \left (3-y\right ) \\
y^{\prime }&=y \left (x-5\right ) \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.038 |
|
| \(1927\) |
\begin{align*}
t x^{\prime \prime }&=t x+1 \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 1 \\
\end{align*} Series expansion around \(t=0\). |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
✗ |
✗ |
0.900 |
|
| \(1928\) |
\begin{align*}
t^{2} x^{\prime \prime }+t x^{\prime }+t^{2} x&=0 \\
x^{\prime }\left (0\right ) &= a \\
\end{align*} |
[_Lienard] |
✗ |
✗ |
✓ |
38.700 |
|
| \(1929\) |
\begin{align*}
t^{2} x^{\prime \prime }+t x^{\prime }+\left (t^{2}-1\right ) x&=0 \\
x^{\prime }\left (0\right ) &= a \\
\end{align*} |
[_Bessel] |
✓ |
✓ |
✗ |
43.345 |
|
| \(1930\) |
\begin{align*}
t^{2} x^{\prime \prime }+t x^{\prime }+\left (-m^{2}+t^{2}\right ) x&=0 \\
x \left (0\right ) &= 0 \\
\end{align*} |
[_Bessel] |
✗ |
✓ |
✓ |
46.713 |
|
| \(1931\) |
\begin{align*}
t^{2} x^{\prime \prime }+t x^{\prime }+t^{2} x&=\lambda x \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
28.497 |
|
| \(1932\) |
\begin{align*}
x^{\prime }&=-x+y+y^{2} \\
y^{\prime }&=-2 y-x^{2} \\
\end{align*} |
system_of_ODEs |
✗ |
✗ |
✗ |
0.049 |
|
| \(1933\) |
\begin{align*}
x^{\prime }&=-x^{3} \\
y^{\prime }&=-y^{3} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.037 |
|
| \(1934\) |
\begin{align*}
x^{\prime \prime }+4 x^{3}&=0 \\
x \left (0\right ) &= 0 \\
x \left (b \right ) &= 1 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✗ |
✗ |
48.170 |
|
| \(1935\) |
\begin{align*}
-x^{\prime \prime }&=1-x-x^{2} \\
x \left (a \right ) &= 0 \\
x \left (b \right ) &= 0 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✗ |
✗ |
✗ |
93.271 |
|
| \(1936\) |
\begin{align*}
-x^{\prime \prime }+x&={\mathrm e}^{-x} \\
x \left (a \right ) &= 0 \\
x \left (b \right ) &= 0 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✗ |
✗ |
✗ |
67.083 |
|
| \(1937\) |
\begin{align*}
-x^{\prime \prime }+x&={\mathrm e}^{-x^{2}} \\
x \left (a \right ) &= 0 \\
x \left (b \right ) &= 0 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✗ |
✗ |
✗ |
59.008 |
|
| \(1938\) |
\begin{align*}
-x^{\prime \prime }&=\frac {1}{\sqrt {x^{2}+1}}-x \\
x \left (a \right ) &= 0 \\
x \left (b \right ) &= 0 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✗ |
✗ |
✗ |
62.753 |
|
| \(1939\) |
\begin{align*}
-x^{\prime \prime }&=2 x-x^{2} \\
x \left (0\right ) &= 0 \\
x \left (\pi \right ) &= 0 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✗ |
✗ |
28.095 |
|
| \(1940\) |
\begin{align*}
-x^{\prime \prime }&=\arctan \left (x\right ) \\
x \left (0\right ) &= 0 \\
x \left (b \right ) &= 0 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✗ |
✗ |
616.861 |
|
| \(1941\) |
\begin{align*}
\frac {x^{2}}{y}+y^{2}-\left (\frac {x^{3}}{y^{2}}+y x +y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[_rational] |
✓ |
✗ |
✗ |
20.517 |
|
| \(1942\) |
\begin{align*}
y^{\prime }&=1+x +x^{2} \cos \left (x \right )-\left (1+4 \cos \left (x \right ) x \right ) y+2 y^{2} \cos \left (x \right ) \\
\end{align*} |
[_Riccati] |
✗ |
✗ |
✗ |
137.664 |
|
| \(1943\) |
\begin{align*}
a_{0} \left (x \right ) y^{\prime \prime }+a_{1} \left (x \right ) y^{\prime }+a_{2} \left (x \right ) y&=f \left (x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
✗ |
✗ |
70.091 |
|
| \(1944\) |
\begin{align*}
y^{\prime \prime }-2 s y^{\prime }-2 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
17.576 |
|
| \(1945\) |
\begin{align*}
\frac {x^{2}}{y}+y^{2}-\left (\frac {x^{3}}{y^{2}}+y x +y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[_rational] |
✓ |
✗ |
✗ |
20.091 |
|
| \(1946\) |
\begin{align*}
n \left (n +1\right ) y-2 y^{\prime } x +\left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
[_Gegenbauer] |
✓ |
✓ |
✗ |
195.343 |
|
| \(1947\) |
\begin{align*}
x^{2} y^{\prime \prime }+2 y^{\prime }+y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
0.551 |
|
| \(1948\) |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
0.450 |
|
| \(1949\) |
\begin{align*}
\left (x^{2}+2\right ) y^{\prime \prime }+\left (2 x +\frac {2}{x}\right ) y^{\prime }+2 x^{2} y&=\frac {4 x^{2}+2 x +10}{x^{4}} \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
✓ |
✗ |
1.012 |
|
| \(1950\) |
\begin{align*}
x^{2} y^{\prime \prime }-\left (x +4\right ) y^{\prime }+2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
0.492 |
|
| \(1951\) |
\begin{align*}
x^{3} y^{\prime \prime \prime }-4 x^{2} y^{\prime \prime }+8 y^{\prime } x -8 y&=4 \ln \left (x \right ) \\
\end{align*} Series expansion around \(x=0\). |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
0.039 |
|
| \(1952\) |
\begin{align*}
x^{4} y^{\prime \prime \prime \prime }+4 x^{3} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }+y^{\prime } x -y&=-\ln \left (x \right ) \\
\end{align*} Series expansion around \(x=0\). |
[[_high_order, _exact, _linear, _nonhomogeneous]] |
✗ |
✓ |
✗ |
0.042 |
|
| \(1953\) |
\begin{align*}
y^{\prime }&=-\sqrt {1-y^{2}} \\
x^{\prime }&=x+2 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.042 |
|
| \(1954\) |
\begin{align*}
y^{\prime \prime } \cos \left (y\right )+\left (\cos \left (y\right )-y^{\prime } \sin \left (y\right )\right ) y^{\prime }-2 y x&=0 \\
\end{align*} |
[NONE] |
✗ |
✗ |
✗ |
9.501 |
|
| \(1955\) |
\begin{align*}
x^{\prime }&=x+4 y-y^{2} \\
y^{\prime }&=6 x-y+2 x y \\
\end{align*} |
system_of_ODEs |
✗ |
✗ |
✗ |
0.056 |
|
| \(1956\) |
\begin{align*}
x^{\prime }&=\sin \left (x\right )-4 y \\
y^{\prime }&=\sin \left (2 x\right )-5 y \\
\end{align*} |
system_of_ODEs |
✗ |
✗ |
✗ |
0.043 |
|
| \(1957\) |
\begin{align*}
x^{\prime }&=8 x-y^{2} \\
y^{\prime }&=6 x^{2}-6 y \\
\end{align*} |
system_of_ODEs |
✗ |
✗ |
✗ |
0.051 |
|
| \(1958\) |
\begin{align*}
x^{\prime }&=-x^{2}-y \\
y^{\prime }&=x \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.049 |
|
| \(1959\) |
\begin{align*}
x^{\prime }&=-x^{3}-y \\
y^{\prime }&=x \\
\end{align*} |
system_of_ODEs |
✗ |
✗ |
✗ |
0.043 |
|
| \(1960\) |
\begin{align*}
x^{\prime }&=2 x y \\
y^{\prime }&=3 y^{2}-x^{2} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.052 |
|
| \(1961\) |
\begin{align*}
x^{\prime }&=x^{2} \\
y^{\prime }&=2 y^{2}-x y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.040 |
|
| \(1962\) |
\begin{align*}
x^{\prime }&=-x+y^{2} \\
y^{\prime }&=x^{2}-y \\
\end{align*} |
system_of_ODEs |
✓ |
✗ |
✗ |
0.039 |
|
| \(1963\) |
\begin{align*}
-y+y^{\prime } x&=x^{2} \sqrt {x^{2}-y^{2}} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✗ |
52.347 |
|
| \(1964\) |
\begin{align*}
a x y-b +\left (c x y-d \right ) x y^{\prime }&=0 \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
86.265 |
|
| \(1965\) |
\begin{align*}
x^{\prime \prime }-x+y&={\mathrm e}^{t} \\
x^{\prime }+x-y^{\prime }-y&=3 \,{\mathrm e}^{t} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.063 |
|
| \(1966\) |
\begin{align*}
y^{\prime }+y-x^{\prime \prime }+x&={\mathrm e}^{t} \\
y^{\prime }-x^{\prime }+x&={\mathrm e}^{-t} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.050 |
|
| \(1967\) |
\begin{align*}
2 y^{\prime \prime \prime }+y^{\prime \prime } x +2 y^{\prime }+y x&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
y^{\prime \prime }\left (0\right ) &= -1 \\
\end{align*} Series expansion around \(x=0\). |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.082 |
|
| \(1968\) |
\begin{align*}
x^{\prime \prime }&=1 \\
x^{\prime }+x+y^{\prime \prime }-9 y+z^{\prime }+z&=0 \\
5 x+z^{\prime \prime }-4 z&=2 \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 0 \\
z \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
z^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.051 |
|
| \(1969\) |
\begin{align*}
s^{2} t^{\prime \prime }+s t t^{\prime }&=s \\
\end{align*} |
[[_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✗ |
2.386 |
|
| \(1970\) |
\begin{align*}
5 {b^{\prime \prime \prime \prime }}^{5}+7 {b^{\prime }}^{10}+b^{7}-b^{5}&=p \\
\end{align*} |
|
✗ |
✗ |
✗ |
0.309 |
|
| \(1971\) |
\begin{align*}
{y^{\prime \prime }}^{2}-3 y y^{\prime }+y x&=0 \\
\end{align*} |
[NONE] |
✗ |
✗ |
✗ |
0.096 |
|
| \(1972\) |
\begin{align*}
y^{\prime \prime \prime \prime }+x y^{\prime \prime \prime }+x^{2} y^{\prime \prime }-y^{\prime } x +\sin \left (y\right )&=0 \\
\end{align*} |
[NONE] |
✗ |
✗ |
✗ |
0.065 |
|
| \(1973\) |
\begin{align*}
{r^{\prime \prime }}^{2}+r^{\prime \prime }+y r^{\prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✗ |
✗ |
✗ |
127.533 |
|
| \(1974\) |
\begin{align*}
{y^{\prime \prime }}^{{3}/{2}}+y&=x \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
✓ |
✗ |
0.365 |
|
| \(1975\) |
\begin{align*}
y^{\prime \prime }+4 y&=0 \\
y \left (0\right ) &= 1 \\
y \left (\frac {\pi }{2}\right ) &= 2 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✗ |
✗ |
✗ |
46.419 |
|
| \(1976\) |
\begin{align*}
y^{\prime }&=x \sin \left (y\right )+{\mathrm e}^{x} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
16.209 |
|
| \(1977\) |
\begin{align*}
1+y x +y y^{\prime }&=0 \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✗ |
142.749 |
|
| \(1978\) |
\begin{align*}
2 y^{\prime \prime } x +x^{2} y^{\prime }-\sin \left (x \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
63.063 |
|
| \(1979\) |
\begin{align*}
y y^{\prime \prime \prime }+y^{\prime } x +y&=x^{2} \\
\end{align*} |
[[_3rd_order, _exact, _nonlinear]] |
✗ |
✗ |
✗ |
0.048 |
|
| \(1980\) |
\begin{align*}
y^{\prime \prime }+{\mathrm e}^{x} y^{\prime }+\left (x +1\right ) y&=0 \\
y \left (1\right ) &= 0 \\
y^{\prime }\left (1\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
30.376 |
|
| \(1981\) |
\begin{align*}
y^{\prime \prime \prime \prime }+x^{2} y^{\prime \prime \prime }+y^{\prime \prime } x -{\mathrm e}^{x} y^{\prime }+2 y&=x^{2}+x +1 \\
\end{align*} |
[[_high_order, _linear, _nonhomogeneous]] |
✗ |
✗ |
✗ |
0.081 |
|
| \(1982\) |
\begin{align*}
y^{\prime \prime }+2 y^{\prime } x +y&=4 x y^{2} \\
\end{align*} |
[NONE] |
✗ |
✗ |
✗ |
2.089 |
|
| \(1983\) |
\begin{align*}
y y^{\prime }+y^{\prime \prime }&=x^{2} \\
\end{align*} |
[[_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_xy]] |
✗ |
✗ |
✗ |
146.366 |
|
| \(1984\) |
\begin{align*}
y^{\prime \prime \prime }+\left (x^{2}-1\right ) y^{\prime \prime }-2 y^{\prime }+y&=5 \sin \left (x \right ) \\
\end{align*} |
[[_3rd_order, _linear, _nonhomogeneous]] |
✗ |
✗ |
✗ |
0.080 |
|
| \(1985\) |
\begin{align*}
x^{2} y^{\prime \prime }+2 y^{\prime }+y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
0.607 |
|
| \(1986\) |
\begin{align*}
x^{3} y^{\prime \prime }+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_Emden, _Fowler]] |
✗ |
✓ |
✗ |
0.207 |
|
| \(1987\) |
\begin{align*}
\left (x +1\right )^{3} y^{\prime \prime }+\left (x^{2}-1\right ) \left (x +1\right ) y^{\prime }+\left (x -1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
0.300 |
|
| \(1988\) |
\begin{align*}
y^{\prime \prime }+z+y&=0 \\
y^{\prime }+z^{\prime }&=0 \\
\end{align*} With initial conditions \begin{align*}
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
z \left (0\right ) &= 1 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.036 |
|
| \(1989\) |
\begin{align*}
z^{\prime \prime }+y^{\prime }&=\cos \left (t \right ) \\
y^{\prime \prime }-z&=\sin \left (t \right ) \\
\end{align*} With initial conditions \begin{align*}
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
z \left (0\right ) &= -1 \\
z^{\prime }\left (0\right ) &= -1 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.031 |
|
| \(1990\) |
\begin{align*}
w^{\prime \prime }-y+2 z&=3 \,{\mathrm e}^{-t} \\
-2 w^{\prime }+2 y^{\prime }+z&=0 \\
2 w^{\prime }-2 y+z^{\prime }+2 z^{\prime \prime }&=0 \\
\end{align*} With initial conditions \begin{align*}
y \left (0\right ) &= 2 \\
z \left (0\right ) &= 2 \\
z^{\prime }\left (0\right ) &= -2 \\
w \left (0\right ) &= 1 \\
w^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.056 |
|
| \(1991\) |
\begin{align*}
u^{\prime \prime }-2 v&=2 \\
u+v^{\prime }&=5 \,{\mathrm e}^{2 t}+1 \\
\end{align*} With initial conditions \begin{align*}
u \left (0\right ) &= 2 \\
u^{\prime }\left (0\right ) &= 2 \\
v \left (0\right ) &= 1 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.026 |
|
| \(1992\) |
\begin{align*}
w^{\prime \prime }-2 z&=0 \\
w^{\prime }+y^{\prime }-z&=2 t \\
w^{\prime }-2 y+z^{\prime \prime }&=0 \\
\end{align*} With initial conditions \begin{align*}
w \left (0\right ) &= 0 \\
w^{\prime }\left (0\right ) &= 0 \\
z \left (0\right ) &= 1 \\
z^{\prime }\left (0\right ) &= 0 \\
y \left (0\right ) &= 0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.041 |
|
| \(1993\) |
\begin{align*}
w^{\prime \prime }+y+z&=-1 \\
w+y^{\prime \prime }-z&=0 \\
-w-y^{\prime }+z^{\prime \prime }&=0 \\
\end{align*} With initial conditions \begin{align*}
w \left (0\right ) &= 0 \\
w^{\prime }\left (0\right ) &= 1 \\
z \left (0\right ) &= -1 \\
z^{\prime }\left (0\right ) &= 1 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
system_of_ODEs |
✓ |
✗ |
✗ |
0.040 |
|
| \(1994\) |
\begin{align*}
y^{\prime \prime }+y&=x \\
y \left (\frac {\pi }{2}\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
31.884 |
|
| \(1995\) |
\begin{align*}
{s^{\prime \prime \prime }}^{2}+{s^{\prime \prime }}^{3}&=s-3 t \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
0.566 |
|
| \(1996\) |
\begin{align*}
y^{\prime \prime }+y x&=\sin \left (y^{\prime \prime }\right ) \\
\end{align*} |
[NONE] |
✗ |
✗ |
✗ |
2.471 |
|
| \(1997\) |
\begin{align*}
{| y^{\prime }|}+1&=0 \\
\end{align*} |
[_sym_implicit] |
✓ |
✗ |
✗ |
0.325 |
|
| \(1998\) |
\begin{align*}
y^{\prime }&=x^{2}+y^{2} \\
y \left (0\right ) &= 2 \\
\end{align*} |
[[_Riccati, _special]] |
✓ |
✓ |
✗ |
91.779 |
|
| \(1999\) |
\begin{align*}
y^{\prime }&=y \csc \left (x \right ) \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✗ |
✗ |
✗ |
49.074 |
|
| \(2000\) |
\begin{align*}
y^{\prime }&=\frac {1}{\sqrt {x^{2}+4 y^{2}-4}} \\
y \left (3\right ) &= 2 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
24.682 |
|
| \(2001\) |
\begin{align*}
U^{\prime }&=\frac {U+1}{\sqrt {s}+\sqrt {s U}} \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✗ |
66.487 |
|
| \(2002\) |
\begin{align*}
x^{2}+y \left (x -y\right )^{2} \tan \left (\frac {y}{x}\right )-\left (x^{2}+x \left (x -y\right )^{2} \tan \left (\frac {y}{x}\right )\right ) y^{\prime }&=0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✗ |
132.289 |
|
| \(2003\) |
\begin{align*}
y^{\prime }&=\sqrt {y+\sin \left (x \right )}-\cos \left (x \right ) \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
✓ |
39.455 |
|
| \(2004\) |
\begin{align*}
\left (r^{2}+r \right ) R^{\prime \prime }+r R^{\prime }-n \left (n +1\right ) R&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
132.403 |
|
| \(2005\) |
\begin{align*}
y^{\prime \prime \prime }&=\frac {24 x +24 y}{x^{3}} \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
0.054 |
|
| \(2006\) |
\begin{align*}
x y^{\prime \prime \prime }+2 y^{\prime \prime } x -y^{\prime } x -2 y x&=1 \\
\end{align*} |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
0.056 |
|
| \(2007\) |
\begin{align*}
y^{\prime \prime }&=x \\
y^{\prime \prime }&=y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.037 |
|
| \(2008\) |
\begin{align*}
y^{\prime \prime }&=x-2 \\
y^{\prime \prime }&=2+y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.038 |
|
| \(2009\) |
\begin{align*}
x^{\prime \prime }+2 y^{\prime }+8 x&=32 t \\
y^{\prime \prime }+3 x^{\prime }-2 y&=60 \,{\mathrm e}^{-t} \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 6 \\
x^{\prime }\left (0\right ) &= 0 \\
y \left (0\right ) &= -24 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.035 |
|
| \(2010\) |
\begin{align*}
x^{\prime }+3 y^{\prime }&=x y \\
3 x^{\prime }-y^{\prime }&=\sin \left (t \right ) \\
\end{align*} |
system_of_ODEs |
✓ |
✗ |
✗ |
0.054 |
|
| \(2011\) |
\begin{align*}
r^{\prime \prime }\left (t \right )&=r \left (t \right )+y \\
y^{\prime \prime }&=5 r \left (t \right )-3 y+t^{2} \\
\end{align*} |
system_of_ODEs |
✗ |
✓ |
✓ |
0.039 |
|
| \(2012\) |
\begin{align*}
x y^{\prime }+y x^{\prime }&=t^{2} \\
2 x^{\prime \prime }-y^{\prime }&=5 t \\
\end{align*} |
system_of_ODEs |
✗ |
✗ |
✗ |
0.049 |
|
| \(2013\) |
\begin{align*}
x^{\prime \prime }+y^{\prime }+x&=y+\sin \left (t \right ) \\
y^{\prime \prime }+x^{\prime }-y&=2 t^{2}-x \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 2 \\
x^{\prime }\left (0\right ) &= -1 \\
y \left (0\right ) &= -{\frac {9}{2}} \\
y^{\prime }\left (0\right ) &= -{\frac {7}{2}} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.036 |
|
| \(2014\) |
\begin{align*}
x^{\prime }&=y z \\
y^{\prime }&=x z \\
z^{\prime }&=x y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.051 |
|
| \(2015\) |
\begin{align*}
x^{\prime }&=x y \\
y^{\prime }&=1+y^{2} \\
z^{\prime }&=z \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.049 |
|
| \(2016\) |
\begin{align*}
t^{2} y^{\prime \prime }+t z^{\prime }+z&=t \\
y^{\prime } t +z&=\ln \left (t \right ) \\
\end{align*} |
system_of_ODEs |
✓ |
✗ |
✗ |
0.047 |
|
| \(2017\) |
\begin{align*}
x^{\prime \prime }&=-2 y \\
y^{\prime }&=y-x^{\prime } \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 10 \\
y \left (0\right ) &= 5 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.029 |
|
| \(2018\) |
\begin{align*}
y^{\prime \prime }&=x-2 \\
x^{\prime \prime }&=2+y \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 1 \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= -3 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.027 |
|
| \(2019\) |
\begin{align*}
x^{\prime }+y^{\prime }&=\cos \left (t \right ) \\
x+y^{\prime \prime }&=2 \\
\end{align*} With initial conditions \begin{align*}
x \left (\pi \right ) &= 2 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= {\frac {1}{2}} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.028 |
|
| \(2020\) |
\begin{align*}
x^{\prime \prime }&=y+4 \,{\mathrm e}^{-2 t} \\
y^{\prime \prime }&=x-{\mathrm e}^{-2 t} \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.031 |
|
| \(2021\) |
\begin{align*}
x^{\prime \prime }&=y+4 \,{\mathrm e}^{-2 t} \\
y^{\prime \prime }&=x-{\mathrm e}^{-2 t} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.044 |
|
| \(2022\) |
\begin{align*}
x^{\prime \prime }+y^{\prime \prime }&=t \\
x^{\prime \prime }-y^{\prime \prime }&=3 t \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.038 |
|
| \(2023\) |
\begin{align*}
y^{\prime \prime }-\tan \left (x \right ) y^{\prime }-\frac {\tan \left (x \right ) y}{x}&=\frac {y^{3}}{x^{3}} \\
\end{align*} |
[NONE] |
✗ |
✗ |
✗ |
3.233 |
|
| \(2024\) |
\begin{align*}
y^{\prime } x +y&=3 \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✗ |
✗ |
✓ |
211.237 |
|
| \(2025\) |
\begin{align*}
y^{\prime }&=x^{2}+y^{2} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[[_Riccati, _special]] |
✓ |
✓ |
✗ |
93.716 |
|
| \(2026\) |
\begin{align*}
y y^{\prime }&=y+x^{2} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
✗ |
✗ |
77.502 |
|
| \(2027\) |
\begin{align*}
y^{2} y^{\prime }+\tan \left (x \right ) y&=\sin \left (x \right )^{3} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
117.594 |
|
| \(2028\) |
\begin{align*}
{\mathrm e}^{x} \cos \left (y\right )-x^{2}+\left ({\mathrm e}^{y} \sin \left (x \right )+y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[NONE] |
✗ |
✗ |
✗ |
90.727 |
|
| \(2029\) |
\begin{align*}
2 x -3 y+\left (7 y^{2}+x^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[_rational] |
✗ |
✗ |
✗ |
55.146 |
|
| \(2030\) |
\begin{align*}
y x +1+y^{2} y^{\prime }&=0 \\
\end{align*} |
[_rational] |
✗ |
✗ |
✗ |
111.970 |
|
| \(2031\) |
\begin{align*}
y^{\prime \prime \prime }+x^{2} y&={\mathrm e}^{x} \\
\end{align*} |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✗ |
0.053 |
|
| \(2032\) |
\begin{align*}
y^{\prime \prime }+y y^{\prime \prime \prime \prime }&=5 \\
\end{align*} |
[[_high_order, _missing_x], [_high_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
0.043 |
|
| \(2033\) |
\begin{align*}
2 y^{\prime \prime \prime }+3 y^{\prime \prime }-4 y^{\prime }+y x&=0 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
0.051 |
|
| \(2034\) |
\begin{align*}
x y^{\prime \prime \prime }+4 y^{\prime \prime } x -y x&=1 \\
\end{align*} |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✗ |
0.051 |
|
| \(2035\) |
\begin{align*}
\left (1+a \cos \left (2 x \right )\right ) y^{\prime \prime }+\lambda y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✗ |
✗ |
52.802 |
|
| \(2036\) |
\begin{align*}
y^{\prime \prime }+\cos \left (x \right ) y^{\prime }+{\mathrm e}^{x} y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
48.357 |
|
| \(2037\) |
\begin{align*}
y^{\prime \prime } x +y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✗ |
✗ |
✗ |
11.137 |
|
| \(2038\) |
\begin{align*}
\left (1-x \right ) y^{\prime \prime }-y^{\prime } x +{\mathrm e}^{x} y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 4 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
93.184 |
|
| \(2039\) |
\begin{align*}
\sin \left (x \right ) y^{\prime \prime }+y^{\prime } x +y&=2 \\
y \left (\frac {3 \pi }{4}\right ) &= 1 \\
y^{\prime }\left (\frac {3 \pi }{4}\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
69.351 |
|
| \(2040\) |
\begin{align*}
\left (x^{3}-1\right ) y^{\prime \prime \prime }-3 y^{\prime \prime }+4 y x&=0 \\
y \left (-1\right ) &= 0 \\
y^{\prime }\left (-1\right ) &= 2 \\
y^{\prime \prime }\left (-1\right ) &= 2 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
0.653 |
|
| \(2041\) |
\begin{align*}
\cos \left (x \right ) y^{\prime \prime }+3 y&=1 \\
y \left (1\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
29.102 |
|
| \(2042\) |
\begin{align*}
y^{\prime \prime }+\sin \left (x \right ) y^{\prime }+{\mathrm e}^{x} y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
41.158 |
|
| \(2043\) |
\begin{align*}
2 y^{\prime \prime } x -7 \cos \left (x \right ) y^{\prime }+y&={\mathrm e}^{-x} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
✗ |
✗ |
73.355 |
|
| \(2044\) |
\begin{align*}
y^{\prime \prime }+4 \tan \left (x \right ) y^{\prime }-y x&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
30.803 |
|
| \(2045\) |
\begin{align*}
\cos \left (x \right ) y^{\prime \prime }+y&=\sin \left (x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✗ |
✗ |
31.252 |
|
| \(2046\) |
\begin{align*}
\left (x^{2}-4\right ) y^{\prime \prime }+3 x^{3} y^{\prime }+\frac {4 y}{x -1}&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
260.213 |
|
| \(2047\) |
\begin{align*}
x^{\prime \prime }+y^{\prime }+6 x&=0 \\
y^{\prime \prime }-x^{\prime }+6 y&=0 \\
\end{align*} With initial conditions \begin{align*}
x^{\prime }\left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.058 |
|
| \(2048\) |
\begin{align*}
y^{\prime \prime \prime }-\sin \left (x \right ) y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
y^{\prime \prime }\left (0\right ) &= 0 \\
\end{align*} Series expansion around \(x=0\). |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.076 |
|
| \(2049\) |
\begin{align*}
y^{\prime \prime \prime \prime }-\ln \left (x +1\right ) y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 1 \\
y^{\prime \prime }\left (0\right ) &= 0 \\
y^{\prime \prime \prime }\left (0\right ) &= 0 \\
\end{align*} Series expansion around \(x=0\). |
[[_high_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.072 |
|
| \(2050\) |
\begin{align*}
y^{\prime \prime \prime }-3 x^{2} y^{\prime }+2 y x&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 1 \\
y^{\prime \prime }\left (0\right ) &= 0 \\
\end{align*} Series expansion around \(x=0\). |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.044 |
|
| \(2051\) |
\begin{align*}
y^{\prime \prime \prime }+4 y^{\prime \prime }+2 y^{\prime }-x^{3} y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 1 \\
y^{\prime \prime }\left (0\right ) &= 0 \\
\end{align*} Series expansion around \(x=0\). |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.047 |
|
| \(2052\) |
\begin{align*}
y^{\prime \prime \prime }+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✗ |
0.026 |
|
| \(2053\) |
\begin{align*}
y^{\prime \prime \prime }-2 y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.028 |
|
| \(2054\) |
\begin{align*}
3 x y^{\prime \prime \prime }-4 y x&=\cos \left (y\right ) \\
\end{align*} |
[NONE] |
✗ |
✗ |
✗ |
0.044 |
|
| \(2055\) |
\begin{align*}
y^{\prime \prime \prime }-3 y^{\prime \prime } x +4 y&=x^{2} \\
\end{align*} |
[[_3rd_order, _linear, _nonhomogeneous]] |
✗ |
✗ |
✗ |
0.059 |
|
| \(2056\) |
\begin{align*}
y^{\left (5\right )}-y^{\prime }-\frac {4 y}{x}&=0 \\
\end{align*} |
[[_high_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
0.060 |
|
| \(2057\) |
\begin{align*}
x_{1}^{\prime }&=2 \sin \left (t \right ) x_{1}+\ln \left (t \right ) x_{2} \\
x_{2}^{\prime }&=\frac {x_{1}}{-2+t}+\frac {{\mathrm e}^{t} x_{2}}{1+t} \\
\end{align*} With initial conditions \begin{align*}
x_{1} \left (3\right ) &= 0 \\
x_{2} \left (3\right ) &= 0 \\
\end{align*} |
system_of_ODEs |
✓ |
✗ |
✓ |
0.056 |
|
| \(2058\) |
\begin{align*}
x_{1}^{\prime }&=x_{1}+\left (1-t \right ) x_{2} \\
x_{2}^{\prime }&=\frac {x_{1}}{t}-x_{2} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.047 |
|
| \(2059\) |
\begin{align*}
t x^{\prime }&=3 x-2 y \\
y^{\prime } t&=x+y-t^{2} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.042 |
|
| \(2060\) |
\begin{align*}
t x^{\prime }&=3 x-2 y \\
y^{\prime } t&=x+y-t^{2} \\
\end{align*} With initial conditions \begin{align*}
x \left (1\right ) &= 1 \\
y \left (1\right ) &= {\frac {1}{2}} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.051 |
|
| \(2061\) |
\begin{align*}
x^{3} \left (-x^{2}+1\right ) y^{\prime \prime }+\left (2 x -3\right ) y^{\prime }+y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
0.290 |
|
| \(2062\) |
\begin{align*}
x^{2} y^{\prime \prime }+\left (1-x \right ) y^{\prime }+2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
0.512 |
|
| \(2063\) |
\begin{align*}
x^{3} y^{\prime \prime }-\left (x +1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
0.219 |
|
| \(2064\) |
\begin{align*}
y^{\prime \prime }+9 y&=0 \\
y \left (0\right ) &= 1 \\
y \left (\pi \right ) &= B \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✗ |
✗ |
✗ |
43.544 |
|
| \(2065\) |
\begin{align*}
y^{\prime \prime }+9 y&=0 \\
y \left (0\right ) &= 1 \\
y \left (\pi \right ) &= 2 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✗ |
✗ |
✗ |
43.242 |
|
| \(2066\) |
\begin{align*}
x^{\prime }&=y^{2}-x^{2} \\
y^{\prime }&=2 x y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.041 |
|
| \(2067\) |
\begin{align*}
x^{\prime }&=y \\
y^{\prime }&=-\sin \left (x\right ) \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.039 |
|
| \(2068\) |
\begin{align*}
x^{\prime }&=y \\
y^{\prime }&=-4 \sin \left (x\right ) \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.039 |
|
| \(2069\) |
\begin{align*}
x^{\prime }&=x-x y \\
y^{\prime }&=-y+x y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.042 |
|
| \(2070\) |
\begin{align*}
x_{1}^{\prime }&=x_{2} \\
x_{2}^{\prime }&=\sin \left (x_{1}\right ) \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.038 |
|
| \(2071\) |
\begin{align*}
x_{1}^{\prime }&=x_{2} \\
x_{2}^{\prime }&=x_{1}-x_{1}^{3} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.041 |
|
| \(2072\) |
\begin{align*}
x^{\prime }&=5 x-6 y+x y \\
y^{\prime }&=6 x-7 y-x y \\
\end{align*} |
system_of_ODEs |
✗ |
✗ |
✗ |
0.043 |
|
| \(2073\) |
\begin{align*}
x^{\prime }&=3 x-2 y+\left (x^{2}+y^{2}\right )^{2} \\
y^{\prime }&=4 x-y+\left (x^{2}-y^{2}\right )^{5} \\
\end{align*} |
system_of_ODEs |
✗ |
✗ |
✗ |
0.047 |
|
| \(2074\) |
\begin{align*}
x^{\prime }&=y+x^{2}-x y \\
y^{\prime }&=-2 x+3 y+y^{2} \\
\end{align*} |
system_of_ODEs |
✗ |
✗ |
✗ |
0.043 |
|
| \(2075\) |
\begin{align*}
x^{\prime }&=x-x y \\
y^{\prime }&=-y+x y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.042 |
|
| \(2076\) |
\begin{align*}
x^{\prime }&=-x-x^{2}+y^{2} \\
y^{\prime }&=-y+2 x y \\
\end{align*} |
system_of_ODEs |
✓ |
✗ |
✗ |
0.046 |
|
| \(2077\) |
\begin{align*}
x^{\prime }&=-2 x+y-x^{2}+2 y^{2} \\
y^{\prime }&=3 x+2 y+x^{2} y^{2} \\
\end{align*} |
system_of_ODEs |
✗ |
✗ |
✗ |
0.042 |
|
| \(2078\) |
\begin{align*}
x^{\prime }&=-x+x^{2} \\
y^{\prime }&=-3 y+x y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.040 |
|
| \(2079\) |
\begin{align*}
x^{\prime }&=-x+x y \\
y^{\prime }&=y+\left (x^{2}+y^{2}\right )^{2} \\
\end{align*} |
system_of_ODEs |
✗ |
✗ |
✗ |
0.042 |
|
| \(2080\) |
\begin{align*}
x^{\prime }&=2 x+y^{2} \\
y^{\prime }&=3 y-x^{2} \\
\end{align*} |
system_of_ODEs |
✗ |
✗ |
✗ |
0.041 |
|
| \(2081\) |
\begin{align*}
x^{\prime }&=x-x y \\
y^{\prime }&=-y+x y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.041 |
|
| \(2082\) |
\begin{align*}
2 x^{3} y+\left (2 y^{2} x^{2}+2 y^{4}+\ln \left (y\right )\right ) y^{\prime }&=0 \\
\end{align*} |
[‘x=_G(y,y’)‘] |
✗ |
✗ |
✗ |
117.408 |
|
| \(2083\) |
\begin{align*}
y^{\prime }&=\frac {y x +3}{5 x -y} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
✗ |
✗ |
106.313 |
|
| \(2084\) |
\begin{align*}
y^{\prime }&=\frac {2 y x +3 y}{x^{2}+2 y^{2}} \\
\end{align*} |
[_rational] |
✗ |
✗ |
✗ |
41.565 |
|
| \(2085\) |
\begin{align*}
\frac {8 x^{4} y+12 x^{3} y^{2}+2}{2 x +3 y}+\frac {\left (2 x^{5}+3 x^{4} y+3\right ) y^{\prime }}{1+x^{2} y^{4}}&=0 \\
\end{align*} |
[_rational] |
✗ |
✗ |
✗ |
68.326 |
|
| \(2086\) |
\begin{align*}
x^{2} y+\left (x^{2}-y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[_rational] |
✗ |
✗ |
✗ |
40.078 |
|
| \(2087\) |
\begin{align*}
x^{3}+y^{2}+\left (y x -3 x^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
67.807 |
|
| \(2088\) |
\begin{align*}
y^{\prime }&=-2 \\
z^{\prime }&=x \,{\mathrm e}^{2 x +y} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.041 |
|
| \(2089\) |
\begin{align*}
y y^{\prime }&=-x \\
y z^{\prime }&=2 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.040 |
|
| \(2090\) |
\begin{align*}
y^{\prime } x&=y \\
z^{\prime }&=3 y-x \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.040 |
|
| \(2091\) |
\begin{align*}
y^{\prime \prime }+p \left (x \right ) y^{\prime }+q \left (x \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
41.287 |
|
| \(2092\) |
\begin{align*}
y^{\prime \prime \prime }-x^{2} y^{\prime \prime }-2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.032 |
|
| \(2093\) |
\begin{align*}
\left (-x^{4}+1\right ) y^{\prime \prime \prime }-24 y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_3rd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✗ |
0.031 |
|
| \(2094\) |
\begin{align*}
x^{2} y^{\prime \prime \prime }-y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.031 |
|
| \(2095\) |
\begin{align*}
x^{4} y^{\prime \prime \prime }+\frac {x^{2} y^{\prime \prime }}{x +1}-\left (x +1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
0.038 |
|
| \(2096\) |
\begin{align*}
x^{4} y^{\prime \prime \prime }-\frac {x^{2} y^{\prime }}{x +1}+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
0.034 |
|
| \(2097\) |
\begin{align*}
x^{2} y^{\prime }-y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[_separable] |
✗ |
✓ |
✗ |
0.302 |
|
| \(2098\) |
\begin{align*}
x +\sin \left (y\right )-\cos \left (y\right )-x \cos \left (y\right ) \left (2 x \sin \left (y\right )+1\right ) y^{\prime }&=0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
183.086 |
|
| \(2099\) |
\begin{align*}
y^{2} \left (-x^{2}+1\right )+x \left (y^{2} x^{2}+2 x +y\right ) y^{\prime }&=0 \\
\end{align*} |
[_rational] |
✗ |
✗ |
✗ |
19.808 |
|
| \(2100\) |
\begin{align*}
y \left (y^{2} x^{2}-1\right )+x \left (x^{2} y+2 x +y\right ) y^{\prime }&=0 \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class C‘]] |
✗ |
✗ |
✗ |
109.472 |
|
| \(2101\) |
\begin{align*}
y \left (x \tan \left (x \right )+\ln \left (y\right )\right )+\tan \left (x \right ) y^{\prime }&=0 \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
57.309 |
|
| \(2102\) |
\begin{align*}
y^{\prime }&=\tan \left (y\right ) \cot \left (x \right )-\sec \left (y\right ) \cos \left (x \right ) \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✓ |
22.465 |
|
| \(2103\) |
\begin{align*}
y^{\prime \prime \prime }+y^{\prime \prime }-y^{\prime }-y&=0 \\
y \left (0\right ) &= 1 \\
y \left (2\right ) &= 0 \\
y \left (\infty \right ) &= 0 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
0.674 |
|
| \(2104\) |
\begin{align*}
y^{\prime \prime \prime }+5 y^{\prime \prime }+3 y^{\prime }-9 y&=0 \\
y \left (0\right ) &= -1 \\
y \left (1\right ) &= 0 \\
y \left (\infty \right ) &= 0 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
0.567 |
|
| \(2105\) |
\begin{align*}
y^{\prime \prime }+y&=x^{3} \\
y \left (0\right ) &= 0 \\
y \left (\pi \right ) &= 0 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
✗ |
✗ |
36.736 |
|
| \(2106\) |
\begin{align*}
{y^{\prime }}^{2}+4 x^{4} y^{\prime }-12 x^{4} y&=0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
293.428 |
|
| \(2107\) |
\begin{align*}
y+2 t +2 t y y^{\prime }&=0 \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
181.960 |
|
| \(2108\) |
\begin{align*}
2 t^{2}-y+\left (t +y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[_rational] |
✗ |
✗ |
✗ |
16.439 |
|
| \(2109\) |
\begin{align*}
y^{\prime \prime }-y y^{\prime }&=6 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✗ |
353.107 |
|
| \(2110\) |
\begin{align*}
y^{\prime \prime \prime \prime }+y^{4}&=0 \\
\end{align*} |
[[_high_order, _missing_x], [_high_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
0.044 |
|
| \(2111\) |
\begin{align*}
y^{\left (5\right )}+t y^{\prime \prime }-3 y&=0 \\
\end{align*} |
[[_high_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
0.071 |
|
| \(2112\) |
\begin{align*}
y_{1}^{\prime }-2 y_{1}&=2 y_{2} \\
y_{2}^{\prime \prime }+2 y_{2}^{\prime }+y_{2}&=-2 y_{1} \\
\end{align*} With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 3 \\
y_{2} \left (0\right ) &= 0 \\
y_{2}^{\prime }\left (0\right ) &= 3 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.025 |
|
| \(2113\) |
\begin{align*}
y_{1}^{\prime }+4 y_{1}&=10 y_{2} \\
y_{2}^{\prime \prime }-6 y_{2}^{\prime }+23 y_{2}&=9 y_{1} \\
\end{align*} With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 0 \\
y_{2} \left (0\right ) &= 2 \\
y_{2}^{\prime }\left (0\right ) &= 2 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.028 |
|
| \(2114\) |
\begin{align*}
y_{1}^{\prime }-2 y_{1}&=-2 y_{2} \\
y_{2}^{\prime \prime }+y_{2}^{\prime }+6 y_{2}&=4 y_{1} \\
\end{align*} With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 1 \\
y_{2} \left (0\right ) &= 5 \\
y_{2}^{\prime }\left (0\right ) &= 4 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.028 |
|
| \(2115\) |
\begin{align*}
y_{1}^{\prime \prime }+2 y_{1}^{\prime }+6 y_{1}&=5 y_{2} \\
y_{2}^{\prime \prime }-2 y_{2}^{\prime }+6 y_{2}&=9 y_{1} \\
\end{align*} With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 0 \\
y_{1}^{\prime }\left (0\right ) &= 0 \\
y_{2} \left (0\right ) &= 6 \\
y_{2}^{\prime }\left (0\right ) &= 6 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.031 |
|
| \(2116\) |
\begin{align*}
y_{1}^{\prime \prime }+2 y_{1}&=-3 y_{2} \\
y_{2}^{\prime \prime }+2 y_{2}^{\prime }-9 y_{2}&=6 y_{1} \\
\end{align*} With initial conditions \begin{align*}
y_{1} \left (0\right ) &= -1 \\
y_{1}^{\prime }\left (0\right ) &= -4 \\
y_{2} \left (0\right ) &= 1 \\
y_{2}^{\prime }\left (0\right ) &= 2 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.032 |
|
| \(2117\) |
\begin{align*}
y_{1}^{\prime }-2 y_{1}&=-y_{2} \\
y_{2}^{\prime \prime }-y_{2}^{\prime }+y_{2}&=y_{1} \\
\end{align*} With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 0 \\
y_{2} \left (0\right ) &= -1 \\
y_{2}^{\prime }\left (0\right ) &= 2 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.027 |
|
| \(2118\) |
\begin{align*}
y_{1}^{\prime }+2 y_{1}&=5 y_{2} \\
y_{2}^{\prime \prime }-2 y_{2}^{\prime }+5 y_{2}&=2 y_{1} \\
\end{align*} With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 1 \\
y_{2} \left (0\right ) &= 0 \\
y_{2}^{\prime }\left (0\right ) &= 3 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.027 |
|
| \(2119\) |
\begin{align*}
y_{1}^{\prime \prime }+2 y_{1}&=-3 y_{2} \\
y_{2}^{\prime \prime }+2 y_{2}^{\prime }-9 y_{2}&=6 y_{1} \\
\end{align*} With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 10 \\
y_{1}^{\prime }\left (0\right ) &= 0 \\
y_{2} \left (0\right ) &= 10 \\
y_{2}^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.031 |
|
| \(2120\) |
\begin{align*}
y^{\prime \prime }+y^{\prime } t +\left (t^{2}+1\right )^{2} y^{2}&=0 \\
\end{align*} |
[NONE] |
✗ |
✗ |
✗ |
2.553 |
|
| \(2121\) |
\begin{align*}
y^{\prime \prime }+\sqrt {y^{\prime }}+y&=t \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
1.456 |
|
| \(2122\) |
\begin{align*}
y^{\prime \prime }+\sqrt {t}\, y^{\prime }+y&=\sqrt {t} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
✗ |
✗ |
61.001 |
|
| \(2123\) |
\begin{align*}
y^{\prime \prime }+2 y+t \sin \left (y\right )&=0 \\
\end{align*} |
[NONE] |
✗ |
✗ |
✗ |
2.363 |
|
| \(2124\) |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }+\sin \left (t \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
23.202 |
|
| \(2125\) |
\begin{align*}
\sin \left (t \right ) y^{\prime \prime }+y&=\cos \left (t \right ) \\
y \left (\frac {\pi }{2}\right ) &= y_{1} \\
y^{\prime }\left (\frac {\pi }{2}\right ) &= y_{1} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
✗ |
✗ |
20.525 |
|
| \(2126\) |
\begin{align*}
\left (t^{2}+1\right ) y^{\prime \prime }-y^{\prime } t +t^{2} y&=\cos \left (t \right ) \\
y \left (0\right ) &= y_{1} \\
y^{\prime }\left (0\right ) &= y_{1} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✗ |
✗ |
93.398 |
|
| \(2127\) |
\begin{align*}
y^{\prime \prime }+\sqrt {t}\, y^{\prime }-\sqrt {t -3}\, y&=0 \\
y \left (10\right ) &= y_{1} \\
y^{\prime }\left (10\right ) &= y_{1} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
60.806 |
|
| \(2128\) |
\begin{align*}
t \left (t^{2}-4\right ) y^{\prime \prime }+y&={\mathrm e}^{t} \\
y \left (1\right ) &= y_{1} \\
y^{\prime }\left (1\right ) &= y_{1} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
✗ |
✗ |
64.867 |
|
| \(2129\) |
\begin{align*}
y^{\prime \prime }+a_{1} \left (t \right ) y^{\prime }+a_{0} \left (t \right ) y&=f \left (t \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
✗ |
✗ |
69.872 |
|
| \(2130\) |
\begin{align*}
t^{2} y^{\prime \prime }-4 y^{\prime } t +6 y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= -1 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✗ |
✗ |
✗ |
43.649 |
|
| \(2131\) |
\begin{align*}
t y^{\prime \prime \prime }+3 y^{\prime \prime }+y^{\prime } t +y&=0 \\
\end{align*} Using Laplace transform method. |
[[_3rd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✗ |
0.037 |
|
| \(2132\) |
\begin{align*}
\left (\cos \left (2 t \right )+1\right ) y^{\prime \prime }-4 y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
32.066 |
|
| \(2133\) |
\begin{align*}
y^{\prime \prime }+\frac {y^{\prime }}{t}+\frac {\left (1-t \right ) y}{t^{3}}&=0 \\
\end{align*} Series expansion around \(t=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
0.690 |
|
| \(2134\) |
\begin{align*}
y_{1}^{\prime }&=y_{2} \\
y_{2}^{\prime }&=y_{1} y_{2} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.039 |
|
| \(2135\) |
\begin{align*}
y_{1}^{\prime }&=\sin \left (t \right ) y_{1} \\
y_{2}^{\prime }&=y_{1}+\cos \left (t \right ) y_{2} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.048 |
|
| \(2136\) |
\begin{align*}
y_{1}^{\prime }&=t \sin \left (y_{1}\right )-y_{2} \\
y_{2}^{\prime }&=y_{1}+t \cos \left (y_{2}\right ) \\
\end{align*} |
system_of_ODEs |
✓ |
✗ |
✗ |
0.051 |
|
| \(2137\) |
\begin{align*}
y_{1}^{\prime }&=y_{2} t \\
y_{2}^{\prime }&=-y_{1} t \\
\end{align*} With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 1 \\
y_{2} \left (0\right ) &= 0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.050 |
|
| \(2138\) |
\begin{align*}
y_{1}^{\prime }&=y_{1} t +y_{2} t \\
y_{2}^{\prime }&=-y_{1} t -y_{2} t \\
\end{align*} With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 4 \\
y_{2} \left (0\right ) &= 0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.057 |
|
| \(2139\) |
\begin{align*}
y_{1}^{\prime }&=\frac {y_{1}}{t}+y_{2} \\
y_{2}^{\prime }&=-y_{1}+\frac {y_{2}}{t} \\
\end{align*} With initial conditions \begin{align*}
y_{1} \left (\pi \right ) &= 1 \\
y_{2} \left (\pi \right ) &= -1 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.055 |
|
| \(2140\) |
\begin{align*}
y_{1}^{\prime }&=\left (2 t +1\right ) y_{1}+2 y_{2} t \\
y_{2}^{\prime }&=-2 y_{1} t +\left (1-2 t \right ) y_{2} \\
\end{align*} With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 1 \\
y_{2} \left (0\right ) &= 0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.057 |
|
| \(2141\) |
\begin{align*}
y_{1}^{\prime }&=y_{1}+y_{2} \\
y_{2}^{\prime }&=\frac {y_{1}}{t}+\frac {y_{2}}{t} \\
\end{align*} With initial conditions \begin{align*}
y_{1} \left (1\right ) &= -3 \\
y_{2} \left (1\right ) &= 4 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.054 |
|
| \(2142\) |
\begin{align*}
y_{1}^{\prime }&=\frac {y_{1}}{t}+1 \\
y_{2}^{\prime }&=\frac {y_{2}}{t}+t \\
\end{align*} With initial conditions \begin{align*}
y_{1} \left (1\right ) &= 1 \\
y_{2} \left (1\right ) &= 2 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.051 |
|
| \(2143\) |
\begin{align*}
y_{1}^{\prime }&=-\frac {y_{2}}{t}+1 \\
y_{2}^{\prime }&=\frac {y_{1}}{t}+\frac {2 y_{2}}{t}-1 \\
\end{align*} With initial conditions \begin{align*}
y_{1} \left (1\right ) &= 2 \\
y_{2} \left (1\right ) &= 0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.056 |
|
| \(2144\) |
\begin{align*}
y_{1}^{\prime }&=\frac {4 t y_{1}}{t^{2}+1}+\frac {6 y_{2} t}{t^{2}+1}-3 t \\
y_{2}^{\prime }&=-\frac {2 t y_{1}}{t^{2}+1}-\frac {4 y_{2} t}{t^{2}+1}+t \\
\end{align*} With initial conditions \begin{align*}
y_{1} \left (1\right ) &= 1 \\
y_{2} \left (1\right ) &= -1 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.058 |
|
| \(2145\) |
\begin{align*}
y_{1}^{\prime }&=3 \sec \left (t \right ) y_{1}+5 \sec \left (t \right ) y_{2} \\
y_{2}^{\prime }&=-\sec \left (t \right ) y_{1}-3 \sec \left (t \right ) y_{2} \\
\end{align*} With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 2 \\
y_{2} \left (0\right ) &= 1 \\
\end{align*} |
system_of_ODEs |
✓ |
✗ |
✓ |
0.057 |
|
| \(2146\) |
\begin{align*}
y_{1}^{\prime }&=y_{1} t +y_{2} t +4 t \\
y_{2}^{\prime }&=-y_{1} t -y_{2} t +4 t \\
\end{align*} With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 4 \\
y_{2} \left (0\right ) &= 0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.067 |
|
| \(2147\) |
\begin{align*}
\left (1-x \right ) y^{\prime \prime }-4 y^{\prime } x +5 y&=\cos \left (x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✗ |
63.310 |
|
| \(2148\) |
\begin{align*}
x y^{\prime \prime \prime }-{y^{\prime }}^{4}+y&=0 \\
\end{align*} |
[NONE] |
✗ |
✗ |
✗ |
0.048 |
|
| \(2149\) |
\begin{align*}
t^{5} y^{\prime \prime \prime \prime }-t^{3} y^{\prime \prime }+6 y&=0 \\
\end{align*} |
[[_high_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
0.067 |
|
| \(2150\) |
\begin{align*}
u^{\prime \prime }+u^{\prime }+u&=\cos \left (r +u\right ) \\
\end{align*} |
[NONE] |
✗ |
✗ |
✗ |
4.523 |
|
| \(2151\) |
\begin{align*}
\sin \left (t \right ) y^{\prime \prime \prime }-\cos \left (t \right ) y^{\prime }&=2 \\
\end{align*} |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
✗ |
3.788 |
|
| \(2152\) |
\begin{align*}
x^{\prime \prime }-\left (1-\frac {{x^{\prime }}^{2}}{3}\right ) x^{\prime }+x&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✗ |
✗ |
✗ |
236.425 |
|
| \(2153\) |
\begin{align*}
x^{\prime \prime }&=4 y+{\mathrm e}^{t} \\
y^{\prime \prime }&=4 x-{\mathrm e}^{t} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.041 |
|
| \(2154\) |
\begin{align*}
y^{\prime \prime }+9 y&=0 \\
y \left (0\right ) &= 0 \\
y \left (\pi \right ) &= 4 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✗ |
✗ |
✗ |
42.109 |
|
| \(2155\) |
\begin{align*}
y^{\prime \prime }+9 y&=0 \\
y^{\prime }\left (\frac {\pi }{3}\right ) &= 1 \\
y^{\prime }\left (\pi \right ) &= 0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✗ |
✗ |
✗ |
46.186 |
|
| \(2156\) |
\begin{align*}
y^{\prime }&=6 \sqrt {y}+5 x^{3} \\
y \left (-1\right ) &= 4 \\
\end{align*} |
[_Chini] |
✗ |
✗ |
✗ |
27.074 |
|
| \(2157\) |
\begin{align*}
y^{\prime \prime }+y \sec \left (x \right )&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✗ |
✗ |
26.952 |
|
| \(2158\) |
\begin{align*}
y^{\prime }&=x^{2}-y^{2} \\
y \left (0\right ) &= 2 \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✗ |
86.093 |
|
| \(2159\) |
\begin{align*}
y^{\prime }&={\mathrm e}^{-\frac {x y^{2}}{100}} \\
y \left (-6\right ) &= 0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
6.242 |
|
| \(2160\) |
\begin{align*}
y^{\prime }&={\mathrm e}^{-\frac {x y^{2}}{100}} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
5.797 |
|
| \(2161\) |
\begin{align*}
y^{\prime }&={\mathrm e}^{-\frac {x y^{2}}{100}} \\
y \left (0\right ) &= -4 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
5.846 |
|
| \(2162\) |
\begin{align*}
y^{\prime }&={\mathrm e}^{-\frac {x y^{2}}{100}} \\
y \left (8\right ) &= -4 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
5.863 |
|
| \(2163\) |
\begin{align*}
y^{\prime }&=x^{2}+y^{2} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[[_Riccati, _special]] |
✓ |
✓ |
✗ |
93.786 |
|
| \(2164\) |
\begin{align*}
y^{\prime }-2 y x&=6 y \,{\mathrm e}^{y^{2}} \\
\end{align*} |
[‘x=_G(y,y’)‘] |
✗ |
✗ |
✗ |
44.191 |
|
| \(2165\) |
\begin{align*}
y^{\prime \prime }-y+5 y^{\prime }&=t \\
2 y^{\prime }-x^{\prime \prime }+4 x&=2 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.050 |
|
| \(2166\) |
\begin{align*}
x^{\prime \prime }+y^{\prime }&=2 \\
x^{\prime \prime }-y^{\prime \prime }&=0 \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 2 \\
y \left (0\right ) &= -2 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.035 |
|
| \(2167\) |
\begin{align*}
x^{\prime \prime }&=y \\
y^{\prime \prime }&=x \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.016 |
|
| \(2168\) |
\begin{align*}
x^{\prime }&=\frac {1}{y} \\
y^{\prime }&=\frac {1}{x} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.023 |
|
| \(2169\) |
\begin{align*}
x^{\prime }&=-2 x+y+x \,y^{2} \\
y^{\prime }&=-7 x-2 y-7 y \,x^{2} \\
\end{align*} |
system_of_ODEs |
✗ |
✗ |
✗ |
0.043 |
|
| \(2170\) |
\begin{align*}
x^{\prime }&=-y+x^{2} y^{3} \\
y^{\prime }&=x-x^{3} y^{2} \\
\end{align*} |
system_of_ODEs |
✗ |
✗ |
✗ |
0.027 |
|
| \(2171\) |
\begin{align*}
x^{\prime }&=y+x^{3} \\
y^{\prime }&=x-y^{3} \\
\end{align*} |
system_of_ODEs |
✗ |
✗ |
✗ |
0.036 |
|
| \(2172\) |
\begin{align*}
x^{\prime }&=-2 x+\sin \left (y\right ) \\
y^{\prime }&=5 \,{\mathrm e}^{x}-5-y \\
\end{align*} |
system_of_ODEs |
✗ |
✗ |
✗ |
0.040 |
|
| \(2173\) |
\begin{align*}
x^{\prime }&=2 x-y \cos \left (y\right ) \\
y^{\prime }&=3 x-2 y-x \,y^{2} \\
\end{align*} |
system_of_ODEs |
✗ |
✗ |
✗ |
0.038 |
|
| \(2174\) |
\begin{align*}
y^{\prime \prime }+\left (1+\frac {1}{x^{2}+1}\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✗ |
✗ |
2.360 |
|
| \(2175\) |
\begin{align*}
y^{\prime \prime }+y&=0 \\
y \left (0\right ) &= 0 \\
y \left (2 \pi \right ) &= 1 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✗ |
✗ |
✗ |
2.710 |
|
| \(2176\) |
\begin{align*}
y^{\prime }&=\sin \left (y\right )-\cos \left (x \right ) \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
2.682 |
|
| \(2177\) |
\begin{align*}
y^{\prime }&=y \ln \left (y\right )^{a} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✗ |
✗ |
✗ |
16.808 |
|
| \(2178\) |
\begin{align*}
x^{2} y^{\prime }+\cos \left (2 y\right )&=1 \\
y \left (\infty \right ) &= \frac {5 \pi }{4} \\
\end{align*} |
[_separable] |
✓ |
✗ |
✗ |
9.183 |
|
| \(2179\) |
\begin{align*}
\left (x +1\right ) y^{\prime }&=-1+y \\
y \left (\infty \right ) &= y_{0} \\
\end{align*} |
[_separable] |
✓ |
✗ |
✓ |
6.156 |
|
| \(2180\) |
\begin{align*}
y^{\prime }&=2 x \left (\pi +y\right ) \\
y \left (\infty \right ) &= y_{0} \\
\end{align*} |
[_separable] |
✓ |
✗ |
✓ |
7.970 |
|
| \(2181\) |
\begin{align*}
x^{2} y^{\prime }+\sin \left (2 y\right )&=1 \\
y \left (\infty \right ) &= \frac {11 \pi }{4} \\
\end{align*} |
[_separable] |
✓ |
✗ |
✓ |
20.300 |
|