| # | 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] |
✓ |
✓ |
✗ |
4.691 |
|
| \(2\) |
\begin{align*}
y^{\prime }&=y^{2}+x^{2} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[[_Riccati, _special]] |
✓ |
✓ |
✗ |
8.184 |
|
| \(3\) |
\begin{align*}
t y^{\prime \prime \prime }+2 y^{\prime \prime }-y^{\prime }+t y&=0 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.059 |
|
| \(4\) |
\begin{align*}
\left (-t +2\right ) y^{\prime \prime \prime }+\left (2 t -3\right ) y^{\prime \prime }-t y^{\prime }+y&=0 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.061 |
|
| \(5\) |
\begin{align*}
t^{2} \left (t +3\right ) y^{\prime \prime \prime }-3 t \left (t +2\right ) y^{\prime \prime }+6 \left (t +1\right ) y^{\prime }-6 y&=0 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.064 |
|
| \(6\) |
\begin{align*}
y^{\prime }&=\tan \left (x y\right ) \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✗ |
0.891 |
|
| \(7\) |
\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]] |
✓ |
✓ |
✗ |
12.524 |
|
| \(8\) |
\begin{align*}
y^{\prime }&=t^{2}+y^{2} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[[_Riccati, _special]] |
✓ |
✓ |
✗ |
8.735 |
|
| \(9\) |
\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 |
✓ |
✓ |
✗ |
0.065 |
|
| \(10\) |
\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 |
✓ |
✓ |
✗ |
0.067 |
|
| \(11\) |
\begin{align*}
x^{\prime }&=x \,y^{2}-x \\
y^{\prime }&=x \sin \left (\pi y\right ) \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.054 |
|
| \(12\) |
\begin{align*}
x^{\prime }&=\cos \left (y\right ) \\
y^{\prime }&=\sin \left (x\right )-1 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.052 |
|
| \(13\) |
\begin{align*}
x^{\prime }&=x-y^{2} \\
y^{\prime }&=x^{2}-y \\
z^{\prime }&={\mathrm e}^{z}-x \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.065 |
|
| \(14\) |
\begin{align*}
x^{\prime }&=x^{2}+y^{2}-1 \\
y^{\prime }&=2 x y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.057 |
|
| \(15\) |
\begin{align*}
x^{\prime }&={\mathrm e}^{y}-x \\
y^{\prime }&={\mathrm e}^{x}+y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.056 |
|
| \(16\) |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime }+x y&=x \left (-x^{2}+1\right ) \sqrt {y} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✗ |
9.054 |
|
| \(17\) |
\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]] |
✓ |
✓ |
✗ |
4.548 |
|
| \(18\) |
\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]] |
✓ |
✓ |
✗ |
0.067 |
|
| \(19\) |
\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 |
✓ |
✓ |
✓ |
0.067 |
|
| \(20\) |
\begin{align*}
x_{1}^{\prime }&=\frac {x_{1}}{t} \\
x_{2}^{\prime }&=x_{2} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.054 |
|
| \(21\) |
\begin{align*}
x_{1}^{\prime }&=\frac {x_{1}}{t}+x_{2} t \\
x_{2}^{\prime }&=-\frac {x_{1}}{t} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.057 |
|
| \(22\) |
\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 |
✓ |
✓ |
✓ |
0.062 |
|
| \(23\) |
\begin{align*}
x^{\prime \prime }+x^{\prime }+y^{\prime }-2 y&=0 \\
x^{\prime }+x-y^{\prime }&=0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.065 |
|
| \(24\) |
\begin{align*}
x^{\prime \prime }-3 x-4 y&=0 \\
x+y^{\prime \prime }+y&=0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.058 |
|
| \(25\) |
\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 |
✓ |
✓ |
✓ |
0.061 |
|
| \(26\) |
\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 |
✓ |
✓ |
✓ |
0.054 |
|
| \(27\) |
\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 |
✓ |
✓ |
✓ |
0.050 |
|
| \(28\) |
\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 |
✓ |
✓ |
✗ |
0.061 |
|
| \(29\) |
\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 |
✓ |
✓ |
✓ |
0.063 |
|
| \(30\) |
\begin{align*}
y^{\prime }+\left (a x +y\right ) y^{2}&=0 \\
\end{align*} |
[_Abel] |
✓ |
✓ |
✗ |
3.471 |
|
| \(31\) |
\begin{align*}
y^{\prime }&=\left (a \,{\mathrm e}^{x}+y\right ) y^{2} \\
\end{align*} |
[_Abel] |
✓ |
✓ |
✗ |
3.970 |
|
| \(32\) |
\begin{align*}
y^{\prime }+3 a \left (2 x +y\right ) y^{2}&=0 \\
\end{align*} |
[_Abel] |
✓ |
✓ |
✗ |
3.700 |
|
| \(33\) |
\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’)‘] |
✓ |
✓ |
✓ |
7.564 |
|
| \(34\) |
\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)]‘]] |
✓ |
✓ |
✗ |
5.967 |
|
| \(35\) |
\begin{align*}
x y^{\prime }+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)]‘]] |
✓ |
✓ |
✗ |
4.730 |
|
| \(36\) |
\begin{align*}
x^{2} y^{\prime }&=a \,x^{2} y^{2}-a y^{3} \\
\end{align*} |
[_rational, _Abel] |
✓ |
✓ |
✗ |
2.392 |
|
| \(37\) |
\begin{align*}
x^{2} y^{\prime }+a y^{2}+b \,x^{2} y^{3}&=0 \\
\end{align*} |
[_rational, _Abel] |
✓ |
✓ |
✗ |
3.280 |
|
| \(38\) |
\begin{align*}
x^{2} y^{\prime }&=\sec \left (y\right )+3 x \tan \left (y\right ) \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✗ |
15.930 |
|
| \(39\) |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime }&=n \left (y^{2}-2 x y+1\right ) \\
\end{align*} |
[_rational, _Riccati] |
✓ |
✓ |
✗ |
2.269 |
|
| \(40\) |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime }&=1+y^{2}-2 x y \left (1+y^{2}\right ) \\
\end{align*} |
[_rational, _Abel] |
✓ |
✓ |
✗ |
54.878 |
|
| \(41\) |
\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’)‘] |
✓ |
✓ |
✗ |
22.958 |
|
| \(42\) |
\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] |
✓ |
✓ |
✗ |
14.895 |
|
| \(43\) |
\begin{align*}
x^{7} y^{\prime }+5 x^{3} y^{2}+2 \left (x^{2}+1\right ) y^{3}&=0 \\
\end{align*} |
[_rational, _Abel] |
✓ |
✓ |
✗ |
32.012 |
|
| \(44\) |
\begin{align*}
y^{\prime } y+x +f \left (y^{2}+x^{2}\right ) g \left (x \right )&=0 \\
\end{align*} |
[NONE] |
✓ |
✓ |
✗ |
8.921 |
|
| \(45\) |
\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‘]] |
✓ |
✓ |
✗ |
27.361 |
|
| \(46\) |
\begin{align*}
\left (1-x^{2} y\right ) y^{\prime }-1+x y^{2}&=0 \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✗ |
55.832 |
|
| \(47\) |
\begin{align*}
x^{7} y y^{\prime }&=2 x^{2}+2+5 x^{3} y \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✗ |
26.688 |
|
| \(48\) |
\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] |
✓ |
✓ |
✗ |
4.411 |
|
| \(49\) |
\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*} |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
✗ |
31.545 |
|
| \(50\) |
\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] |
✓ |
✓ |
✗ |
4.192 |
|
| \(51\) |
\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] |
✓ |
✓ |
✗ |
7.505 |
|
| \(52\) |
\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)]‘]] |
✓ |
✓ |
✗ |
22.019 |
|
| \(53\) |
\begin{align*}
x y^{2} {y^{\prime }}^{2}+\left (a -x^{3}-y^{3}\right ) y^{\prime }+x^{2} y&=0 \\
\end{align*} |
[_rational] |
✓ |
✓ |
✗ |
172.437 |
|
| \(54\) |
\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)]‘]] |
✓ |
✓ |
✓ |
10.872 |
|
| \(55\) |
\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)]‘]] |
✓ |
✓ |
✓ |
16.401 |
|
| \(56\) |
\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)]‘]] |
✓ |
✓ |
✓ |
14.062 |
|
| \(57\) |
\begin{align*}
\left (x^{2}+a \right ) y+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
1.261 |
|
| \(58\) |
\begin{align*}
\left (-x^{2}+a \right ) y+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
1.133 |
|
| \(59\) |
\begin{align*}
y^{\prime \prime }&=\left (x^{2}+a \right ) y \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
1.100 |
|
| \(60\) |
\begin{align*}
\left (b^{2} x^{2}+a \right ) y+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
1.286 |
|
| \(61\) |
\begin{align*}
\left (c \,x^{2}+b x +a \right ) y+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
1.465 |
|
| \(62\) |
\begin{align*}
\left (x^{4}+\operatorname {a1} \,x^{2}+\operatorname {a0} \right ) y+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
3.825 |
|
| \(63\) |
\begin{align*}
\left (a +b \cos \left (2 x \right )\right ) y+y^{\prime \prime }&=0 \\
\end{align*} |
[_ellipsoidal] |
✓ |
✓ |
✗ |
1.492 |
|
| \(64\) |
\begin{align*}
a \csc \left (x \right )^{2} y+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
1.457 |
|
| \(65\) |
\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]] |
✓ |
✓ |
✗ |
3.867 |
|
| \(66\) |
\begin{align*}
\left (a +b \sin \left (x \right )^{2}\right ) y+y^{\prime \prime }&=0 \\
\end{align*} |
[_ellipsoidal] |
✓ |
✓ |
✗ |
1.720 |
|
| \(67\) |
\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]] |
✓ |
✓ |
✗ |
1.340 |
|
| \(68\) |
\begin{align*}
\left (a +b \cosh \left (x \right )^{2}\right ) y+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
3.782 |
|
| \(69\) |
\begin{align*}
\left (a +b \sinh \left (x \right )^{2}\right ) y+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
4.751 |
|
| \(70\) |
\begin{align*}
\left (a +b \sin \left (x \right )^{2}\right ) y+y^{\prime \prime }&=0 \\
\end{align*} |
[_ellipsoidal] |
✓ |
✓ |
✗ |
2.222 |
|
| \(71\) |
\begin{align*}
\left (c \,x^{2}+b \right ) y+a y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
2.545 |
|
| \(72\) |
\begin{align*}
n y-x y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
[_Hermite] |
✓ |
✓ |
✗ |
2.248 |
|
| \(73\) |
\begin{align*}
-a y-x y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
[_Hermite] |
✓ |
✓ |
✗ |
1.708 |
|
| \(74\) |
\begin{align*}
2 n y-2 x y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
2.189 |
|
| \(75\) |
\begin{align*}
b y+a x y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
2.362 |
|
| \(76\) |
\begin{align*}
c y+\left (b x +a \right ) y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
2.587 |
|
| \(77\) |
\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]] |
✓ |
✓ |
✗ |
2.777 |
|
| \(78\) |
\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]] |
✓ |
✓ |
✗ |
3.888 |
|
| \(79\) |
\begin{align*}
b \,x^{-1+k} y+a \,x^{k} y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
3.035 |
|
| \(80\) |
\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]] |
✓ |
✓ |
✗ |
2.002 |
|
| \(81\) |
\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]] |
✓ |
✓ |
✗ |
3.110 |
|
| \(82\) |
\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]] |
✓ |
✓ |
✗ |
5.947 |
|
| \(83\) |
\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]] |
✓ |
✓ |
✗ |
4.275 |
|
| \(84\) |
\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]] |
✓ |
✓ |
✗ |
113.853 |
|
| \(85\) |
\begin{align*}
-a \left (a +1\right ) \csc \left (x \right )^{2} y-\tan \left (x \right ) y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
3.371 |
|
| \(86\) |
\begin{align*}
b y+a \tan \left (x \right ) y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
3.251 |
|
| \(87\) |
\begin{align*}
b y+a \tanh \left (x \right ) y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
10.362 |
|
| \(88\) |
\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]] |
✓ |
✓ |
✗ |
2.437 |
|
| \(89\) |
\begin{align*}
4 y^{\prime \prime }&=\left (x^{2}+a \right ) y \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
1.359 |
|
| \(90\) |
\begin{align*}
\left (-x^{2}+4 a +2\right ) y+4 y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
1.370 |
|
| \(91\) |
\begin{align*}
\left (x +a \right ) y+x y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
1.262 |
|
| \(92\) |
\begin{align*}
\left ({\mathrm e}^{x^{2}}-k^{2}\right ) x^{3} y-y^{\prime }+x y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
4.663 |
|
| \(93\) |
\begin{align*}
y+\left (a +1\right ) y^{\prime }+x y^{\prime \prime }&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✗ |
4.290 |
|
| \(94\) |
\begin{align*}
y+\left (1-a \right ) y^{\prime }+x y^{\prime \prime }&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✗ |
2.978 |
|
| \(95\) |
\begin{align*}
-y+\left (a +1\right ) y^{\prime }+x y^{\prime \prime }&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✗ |
2.185 |
|
| \(96\) |
\begin{align*}
\left (\operatorname {b2} x +\operatorname {b1} \right ) y+a y^{\prime }+x y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
3.413 |
|
| \(97\) |
\begin{align*}
n y+\left (1-x \right ) y^{\prime }+x y^{\prime \prime }&=0 \\
\end{align*} |
[_Laguerre] |
✓ |
✓ |
✗ |
3.020 |
|
| \(98\) |
\begin{align*}
n y+\left (1+k -x \right ) y^{\prime }+x y^{\prime \prime }&=0 \\
\end{align*} |
[_Laguerre] |
✓ |
✓ |
✗ |
3.645 |
|
| \(99\) |
\begin{align*}
b y+\left (x +a \right ) y^{\prime }+x y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
3.427 |
|
| \(100\) |
\begin{align*}
-a y+\left (c -x \right ) y^{\prime }+x y^{\prime \prime }&=0 \\
\end{align*} |
[_Laguerre] |
✓ |
✓ |
✗ |
3.390 |
|
| \(101\) |
\begin{align*}
c y+\left (b x +a \right ) y^{\prime }+x y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
3.635 |
|
| \(102\) |
\begin{align*}
\left (\operatorname {b2} x +\operatorname {a2} \right ) y+\left (\operatorname {b1} x +\operatorname {a1} \right ) y^{\prime }+x y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
4.440 |
|
| \(103\) |
\begin{align*}
\left (b x +2 a \right ) y-2 \left (b x +a \right ) y^{\prime }+x y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
4.125 |
|
| \(104\) |
\begin{align*}
\left (a b x +a n +b m \right ) y+\left (m +n +x \left (a +b \right )\right ) y^{\prime }+x y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
6.054 |
|
| \(105\) |
\begin{align*}
\left (\operatorname {b2} x +\operatorname {a2} \right ) y+\left (\operatorname {b1} x +\operatorname {a1} \right ) y^{\prime }+\left (x +a \right ) y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
13.339 |
|
| \(106\) |
\begin{align*}
\left (b x +a \right ) y+y^{\prime }+2 x y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
3.972 |
|
| \(107\) |
\begin{align*}
\left (b x +a \right ) y+8 y^{\prime }+16 x y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
2.985 |
|
| \(108\) |
\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]] |
✓ |
✓ |
✗ |
18.037 |
|
| \(109\) |
\begin{align*}
\left (c \,x^{2}+b x +a \right ) y+x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
2.096 |
|
| \(110\) |
\begin{align*}
x^{k} \left (a +b \,x^{k}\right ) y+x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
1.664 |
|
| \(111\) |
\begin{align*}
-\left (c \,x^{2}+b x +a \right ) y+x y^{\prime }+x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
27.340 |
|
| \(112\) |
\begin{align*}
-\left (-x^{4}+4 a \,x^{2}+n^{2}\right ) y+x y^{\prime }+x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
33.034 |
|
| \(113\) |
\begin{align*}
-\left (c^{2} x^{4}+b^{2} x^{2}+a^{2}\right ) y+x y^{\prime }+x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
26.754 |
|
| \(114\) |
\begin{align*}
\left (m +1\right ) x^{m} a \left (m \right ) y+x y^{\prime }+x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
25.237 |
|
| \(115\) |
\begin{align*}
a y-2 \left (1-x \right ) y^{\prime }+x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
6.401 |
|
| \(116\) |
\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]] |
✓ |
✓ |
✗ |
6.891 |
|
| \(117\) |
\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]] |
✓ |
✓ |
✗ |
7.308 |
|
| \(118\) |
\begin{align*}
c y+\left (b x +a \right ) y^{\prime }+x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
6.595 |
|
| \(119\) |
\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]] |
✓ |
✓ |
✗ |
3.353 |
|
| \(120\) |
\begin{align*}
-y+x \left (x +3\right ) y^{\prime }+x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
6.863 |
|
| \(121\) |
\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]] |
✓ |
✓ |
✗ |
11.069 |
|
| \(122\) |
\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]] |
✓ |
✓ |
✗ |
10.834 |
|
| \(123\) |
\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]] |
✓ |
✓ |
✗ |
2.625 |
|
| \(124\) |
\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]] |
✓ |
✓ |
✗ |
30.614 |
|
| \(125\) |
\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]] |
✓ |
✓ |
✗ |
2.639 |
|
| \(126\) |
\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]] |
✓ |
✓ |
✗ |
31.593 |
|
| \(127\) |
\begin{align*}
\left (b \,x^{2}+a \right ) y-x y^{\prime }+\left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
19.402 |
|
| \(128\) |
\begin{align*}
n \left (n +1\right ) y-2 x y^{\prime }+\left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
[_Gegenbauer] |
✓ |
✓ |
✗ |
72.894 |
|
| \(129\) |
\begin{align*}
n \left (n +1\right ) y-2 x y^{\prime }+\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]] |
✓ |
✓ |
✗ |
62.865 |
|
| \(130\) |
\begin{align*}
-p \left (1+p \right ) y+2 x y^{\prime }+\left (x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
16.605 |
|
| \(131\) |
\begin{align*}
p \left (1+p \right ) y-2 x y^{\prime }+\left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
[_Gegenbauer] |
✓ |
✓ |
✗ |
68.647 |
|
| \(132\) |
\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]] |
✓ |
✓ |
✗ |
104.104 |
|
| \(133\) |
\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] |
✓ |
✓ |
✗ |
39.606 |
|
| \(134\) |
\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] |
✓ |
✓ |
✗ |
43.746 |
|
| \(135\) |
\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] |
✓ |
✓ |
✗ |
36.516 |
|
| \(136\) |
\begin{align*}
b y+a x y^{\prime }+\left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
[_Gegenbauer] |
✓ |
✓ |
✗ |
80.437 |
|
| \(137\) |
\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]] |
✓ |
✓ |
✗ |
34.786 |
|
| \(138\) |
\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]] |
✓ |
✓ |
✗ |
104.832 |
|
| \(139\) |
\begin{align*}
\left (c^{2} x^{2}+b^{2}\right ) y-x y^{\prime }+\left (a^{2}-x^{2}\right ) y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
45.078 |
|
| \(140\) |
\begin{align*}
y+2 y^{\prime }+x \left (1-x \right ) y^{\prime \prime }&=0 \\
\end{align*} |
[_Jacobi] |
✓ |
✓ |
✗ |
18.041 |
|
| \(141\) |
\begin{align*}
p \left (1+p \right ) y+\left (1-2 x \right ) y^{\prime }+x \left (1-x \right ) y^{\prime \prime }&=0 \\
\end{align*} |
[_Jacobi] |
✓ |
✓ |
✗ |
32.537 |
|
| \(142\) |
\begin{align*}
2 y+\left (1-x \right ) y^{\prime }+x \left (1-x \right ) y^{\prime \prime }&=0 \\
\end{align*} |
[_Jacobi] |
✓ |
✓ |
✗ |
43.747 |
|
| \(143\) |
\begin{align*}
\left (-k +p \right ) \left (1+k +p \right ) y+\left (1+k \right ) \left (1-2 x \right ) y^{\prime }+x \left (1-x \right ) y^{\prime \prime }&=0 \\
\end{align*} |
[_Jacobi] |
✓ |
✓ |
✗ |
82.145 |
|
| \(144\) |
\begin{align*}
n \left (a +n \right ) y+\left (c -\left (a +1\right ) x \right ) y^{\prime }+x \left (1-x \right ) y^{\prime \prime }&=0 \\
\end{align*} |
[_Jacobi] |
✓ |
✓ |
✗ |
93.876 |
|
| \(145\) |
\begin{align*}
c y+\left (b x +a \right ) y^{\prime }+x \left (1+x \right ) y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
67.127 |
|
| \(146\) |
\begin{align*}
-a b y+\left (c -\left (a +b +1\right ) x \right ) y^{\prime }+x \left (1-x \right ) y^{\prime \prime }&=0 \\
\end{align*} |
[_Jacobi] |
✓ |
✓ |
✗ |
115.533 |
|
| \(147\) |
\begin{align*}
c y+\left (b x +a \right ) y^{\prime }+x \left (1-x \right ) y^{\prime \prime }&=0 \\
\end{align*} |
[_Jacobi] |
✓ |
✓ |
✗ |
66.749 |
|
| \(148\) |
\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]] |
✓ |
✓ |
✗ |
73.346 |
|
| \(149\) |
\begin{align*}
2 a^{2} y-x y^{\prime }+2 \left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
56.183 |
|
| \(150\) |
\begin{align*}
a y-\left (1-2 x \right ) y^{\prime }+2 x \left (1-x \right ) y^{\prime \prime }&=0 \\
\end{align*} |
[_Jacobi] |
✓ |
✓ |
✗ |
136.085 |
|
| \(151\) |
\begin{align*}
\left (b x +a \right ) y+\left (1-2 x \right ) y^{\prime }+2 x \left (1-x \right ) y^{\prime \prime }&=0 \\
\end{align*} |
[_Jacobi] |
✓ |
✓ |
✗ |
59.203 |
|
| \(152\) |
\begin{align*}
2 a \left (a +1\right ) y-\left (1+3 x \right ) y^{\prime }+2 x \left (1-x \right ) y^{\prime \prime }&=0 \\
\end{align*} |
[_Jacobi] |
✓ |
✓ |
✗ |
55.968 |
|
| \(153\) |
\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]] |
✓ |
✓ |
✗ |
2.243 |
|
| \(154\) |
\begin{align*}
-y-8 x y^{\prime }+4 \left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
30.603 |
|
| \(155\) |
\begin{align*}
-\left (4 p^{2}+1\right ) y-8 x y^{\prime }+4 \left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
49.149 |
|
| \(156\) |
\begin{align*}
y+2 \left (1-x \right ) y^{\prime }+4 x \left (1-x \right ) y^{\prime \prime }&=0 \\
\end{align*} |
[_Jacobi] |
✓ |
✓ |
✗ |
22.449 |
|
| \(157\) |
\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 x \left (1-x \right ) y^{\prime \prime }&=0 \\
\end{align*} |
[_Jacobi] |
✓ |
✓ |
✗ |
85.993 |
|
| \(158\) |
\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]] |
✓ |
✓ |
✗ |
524.683 |
|
| \(159\) |
\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]] |
✓ |
✓ |
✗ |
117.690 |
|
| \(160\) |
\begin{align*}
-y+2 x y^{\prime }+x^{3} y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
20.389 |
|
| \(161\) |
\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]] |
✓ |
✓ |
✗ |
15.275 |
|
| \(162\) |
\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]] |
✓ |
✓ |
✗ |
29.946 |
|
| \(163\) |
\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]] |
✓ |
✓ |
✗ |
30.780 |
|
| \(164\) |
\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]] |
✓ |
✓ |
✗ |
58.965 |
|
| \(165\) |
\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]] |
✓ |
✓ |
✗ |
105.527 |
|
| \(166\) |
\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]] |
✓ |
✓ |
✗ |
96.819 |
|
| \(167\) |
\begin{align*}
c x y+\left (a -\left (a +1\right ) x^{2}\right ) y^{\prime }+x \left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
96.904 |
|
| \(168\) |
\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]] |
✓ |
✓ |
✗ |
87.539 |
|
| \(169\) |
\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]] |
✓ |
✓ |
✗ |
112.964 |
|
| \(170\) |
\begin{align*}
\left (\operatorname {b2} x +\operatorname {a2} \right ) y+x \left (\operatorname {b1} x +\operatorname {a1} \right ) y^{\prime }+x^{2} \left (1-x \right ) y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
115.358 |
|
| \(171\) |
\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]] |
✓ |
✓ |
✗ |
115.207 |
|
| \(172\) |
\begin{align*}
\operatorname {a0} \operatorname {a1} \left (-k +x \right ) y+\left (1-\operatorname {a0} +\operatorname {a1} +\operatorname {a0} \operatorname {a2} -\operatorname {a3} +\left (\operatorname {a2} +\operatorname {a3} \right ) x +\left (1+\operatorname {a0} +\operatorname {a1} \right ) x^{2}\right ) y^{\prime }+\left (1-x \right ) \left (-x +a \right ) x y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
309.483 |
|
| \(173\) |
\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]] |
✓ |
✓ |
✗ |
407.785 |
|
| \(174\) |
\begin{align*}
\left (b x +a \right ) y+2 \left (1-3 x \right ) \left (1-x \right ) y^{\prime }+4 x \left (1-x \right ) y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
65.609 |
|
| \(175\) |
\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]] |
✓ |
✓ |
✗ |
2.344 |
|
| \(176\) |
\begin{align*}
y+x \left (x^{2}+1\right ) y^{\prime }+x^{4} y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
11.741 |
|
| \(177\) |
\begin{align*}
a \left (a +1\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]] |
✓ |
✓ |
✗ |
68.760 |
|
| \(178\) |
\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]] |
✓ |
✓ |
✗ |
66.297 |
|
| \(179\) |
\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]] |
✓ |
✓ |
✗ |
63.477 |
|
| \(180\) |
\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]] |
✓ |
✓ |
✗ |
51.824 |
|
| \(181\) |
\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]] |
✓ |
✓ |
✗ |
65.489 |
|
| \(182\) |
\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]] |
✓ |
✓ |
✗ |
84.436 |
|
| \(183\) |
\begin{align*}
\left (c \,x^{2}+b x +a \right ) y+x^{2} \left (1-x \right )^{2} y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
5.373 |
|
| \(184\) |
\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 }+x^{2} \left (1-x \right )^{2} y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
149.721 |
|
| \(185\) |
\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]] |
✓ |
✓ |
✗ |
53.968 |
|
| \(186\) |
\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]] |
✓ |
✓ |
✗ |
53.849 |
|
| \(187\) |
\begin{align*}
\left (\operatorname {c2} \,x^{2}+\operatorname {b2} x +\operatorname {a2} \right ) y+\left (-x +a \right ) \left (-x +b \right ) \left (c -x \right ) \left (\operatorname {c1} \,x^{2}+\operatorname {b1} x +\operatorname {a1} \right ) y^{\prime }+\left (-x +a \right )^{2} \left (-x +b \right )^{2} \left (c -x \right )^{2} y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
1379.480 |
|
| \(188\) |
\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]] |
✓ |
✓ |
✗ |
86.215 |
|
| \(189\) |
\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]] |
✓ |
✓ |
✗ |
25.181 |
|
| \(190\) |
\begin{align*}
a y+y^{\prime } y+y^{\prime \prime }&=y^{3} \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✗ |
177.938 |
|
| \(191\) |
\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]] |
✓ |
✓ |
✗ |
34.462 |
|
| \(192\) |
\begin{align*}
y^{\prime \prime }&=a +4 y b^{2}+3 b y^{2}+3 y^{\prime } y \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✗ |
31.998 |
|
| \(193\) |
\begin{align*}
y^{\prime \prime }&=a \left (1+2 y^{\prime } y\right ) \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✗ |
106.677 |
|
| \(194\) |
\begin{align*}
y^{\prime \prime }&=a \left (-y+x y^{\prime }\right )^{k} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.718 |
|
| \(195\) |
\begin{align*}
y^{\prime \prime }&=a \sqrt {b y^{2}+{y^{\prime }}^{2}} \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✗ |
560.101 |
|
| \(196\) |
\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]] |
✓ |
✓ |
✗ |
0.839 |
|
| \(197\) |
\begin{align*}
a \,{\mathrm e}^{y} x +y^{\prime }+x y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
✗ |
0.495 |
|
| \(198\) |
\begin{align*}
y^{5} x +2 y^{\prime }+x y^{\prime \prime }&=0 \\
\end{align*} |
[_Emden, [_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.386 |
|
| \(199\) |
\begin{align*}
x y^{\prime \prime }&=-y^{2}-2 y^{\prime }+{y^{\prime }}^{2} x^{2} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✗ |
0.523 |
|
| \(200\) |
\begin{align*}
x^{2} y^{\prime \prime }&=6 y-4 x^{2} y^{2}+x^{4} {y^{\prime }}^{2} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✗ |
0.838 |
|
| \(201\) |
\begin{align*}
a \left (-y+x y^{\prime }\right )^{2}+x^{2} y^{\prime \prime }&=b \,x^{2} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.632 |
|
| \(202\) |
\begin{align*}
2 y+a y^{3}+9 x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.437 |
|
| \(203\) |
\begin{align*}
x^{3} y^{\prime \prime }&=a \left (-y+x y^{\prime }\right )^{2} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✗ |
0.717 |
|
| \(204\) |
\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]] |
✓ |
✓ |
✗ |
0.860 |
|
| \(205\) |
\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]] |
✓ |
✓ |
✗ |
1.063 |
|
| \(206\) |
\begin{align*}
\left (-y+x y^{\prime }\right )^{3}+x^{4} y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
1.426 |
|
| \(207\) |
\begin{align*}
x^{{3}/{2}} y^{\prime \prime }&=f \left (\frac {y}{\sqrt {x}}\right ) \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
15.311 |
|
| \(208\) |
\begin{align*}
y y^{\prime \prime }&=-x^{2} y^{2}+\ln \left (y\right ) y^{2}+{y^{\prime }}^{2} \\
\end{align*} |
[[_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✗ |
0.417 |
|
| \(209\) |
\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]] |
✓ |
✓ |
✗ |
1.047 |
|
| \(210\) |
\begin{align*}
y y^{\prime \prime }&=\operatorname {a2} y^{2}+\operatorname {a3} y^{a +1}+\operatorname {a1} y y^{\prime }+a {y^{\prime }}^{2} \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✗ |
239.460 |
|
| \(211\) |
\begin{align*}
2 y^{\prime } \left (y^{\prime }+1\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]] |
✓ |
✓ |
✗ |
0.560 |
|
| \(212\) |
\begin{align*}
\left (x -y\right ) y^{\prime \prime }&=\left (y^{\prime }+1\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]] |
✓ |
✓ |
✗ |
0.630 |
|
| \(213\) |
\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]] |
✓ |
✓ |
✗ |
2.647 |
|
| \(214\) |
\begin{align*}
f \left (x \right )+a y y^{\prime }+{y^{\prime }}^{2} x +x y y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✗ |
1.035 |
|
| \(215\) |
\begin{align*}
x y y^{\prime \prime }&=-\left (1+y\right ) y^{\prime }+2 {y^{\prime }}^{2} x \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✗ |
0.555 |
|
| \(216\) |
\begin{align*}
\left (-y+x y^{\prime }\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]] |
✓ |
✓ |
✗ |
0.573 |
|
| \(217\) |
\begin{align*}
x^{2} y y^{\prime \prime }&=a y^{2}+a x y y^{\prime }+2 {y^{\prime }}^{2} x^{2} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✗ |
0.618 |
|
| \(218\) |
\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]] |
✓ |
✓ |
✗ |
0.623 |
|
| \(219\) |
\begin{align*}
2 \left (1-y\right )^{2} y-2 x \left (1-y\right ) y^{\prime }+2 {y^{\prime }}^{2} x^{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]] |
✓ |
✓ |
✗ |
1.755 |
|
| \(220\) |
\begin{align*}
x^{2} \left (x -y\right ) y^{\prime \prime }&=\left (-y+x y^{\prime }\right )^{2} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✗ |
0.906 |
|
| \(221\) |
\begin{align*}
\left (-y+x y^{\prime }\right )^{2}+x^{2} \left (x -y\right ) y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✗ |
0.763 |
|
| \(222\) |
\begin{align*}
x^{2} \left (x -y\right ) y^{\prime \prime }&=a \left (-y+x y^{\prime }\right )^{2} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✗ |
0.859 |
|
| \(223\) |
\begin{align*}
2 x^{2} y y^{\prime \prime }&=-y^{2}+{y^{\prime }}^{2} x^{2} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✗ |
0.513 |
|
| \(224\) |
\begin{align*}
2 x^{2} y y^{\prime \prime }&=-4 y^{2}+2 x y y^{\prime }+{y^{\prime }}^{2} x^{2} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✗ |
0.615 |
|
| \(225\) |
\begin{align*}
x \left (1+x \right )^{2} y y^{\prime \prime }&=a \left (x +2\right ) y^{2}-2 \left (x^{2}+1\right ) y y^{\prime }+x \left (1+x \right )^{2} {y^{\prime }}^{2} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✗ |
1.028 |
|
| \(226\) |
\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]] |
✓ |
✓ |
✗ |
0.953 |
|
| \(227\) |
\begin{align*}
\sqrt {a^{2}-x^{2}}\, \left (-y^{\prime } y-{y^{\prime }}^{2} x +x y y^{\prime \prime }\right )&=b x {y^{\prime }}^{2} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
1.296 |
|
| \(228\) |
\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^{\prime } y\right ) \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
✓ |
✗ |
0.931 |
|
| \(229\) |
\begin{align*}
2 \left (1-y\right ) y y^{\prime \prime }&=f \left (x \right ) \left (1-y\right ) y y^{\prime }+\left (-2 y+1\right ) {y^{\prime }}^{2} \\
\end{align*} |
[_Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✗ |
0.901 |
|
| \(230\) |
\begin{align*}
x y^{2} y^{\prime \prime }&=a \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.319 |
|
| \(231\) |
\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]] |
✓ |
✓ |
✗ |
0.535 |
|
| \(232\) |
\begin{align*}
x^{2} y^{2} y^{\prime \prime }&=\left (y^{2}+x^{2}\right ) \left (-y+x y^{\prime }\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]] |
✓ |
✓ |
✗ |
0.895 |
|
| \(233\) |
\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]] |
✓ |
✓ |
✗ |
1.990 |
|
| \(234\) |
\begin{align*}
\left (x +y\right ) \left (-y+x y^{\prime }\right )^{3}+x^{3} y^{2} y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
2.393 |
|
| \(235\) |
\begin{align*}
A y+\left (a +2 b x +c \,x^{2}+y^{2}\right )^{2} y^{\prime \prime }&=0 \\
\end{align*} |
[NONE] |
✓ |
✓ |
✗ |
0.829 |
|
| \(236\) |
\begin{align*}
\left ({y^{\prime }}^{2}+a \left (-y+x y^{\prime }\right )\right ) y^{\prime \prime }&=b \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.794 |
|
| \(237\) |
\begin{align*}
{y^{\prime \prime }}^{2}&=a +b y \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
✗ |
0.060 |
|
| \(238\) |
\begin{align*}
4 {y^{\prime }}^{2}-2 \left (3 x y^{\prime }+y\right ) y^{\prime \prime }+3 x^{2} {y^{\prime \prime }}^{2}&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
4.188 |
|
| \(239\) |
\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 {y^{\prime }}^{2} x \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
27.228 |
|
| \(240\) |
\begin{align*}
y^{\prime \prime \prime }&=x y \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.032 |
|
| \(241\) |
\begin{align*}
y+2 x y^{\prime }+y^{\prime \prime \prime }&=0 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.036 |
|
| \(242\) |
\begin{align*}
a y+2 a x y^{\prime }+y^{\prime \prime \prime }&=0 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.038 |
|
| \(243\) |
\begin{align*}
-8 a x y-2 \left (-4 x^{2}-2 a +1\right ) y^{\prime }-6 x y^{\prime \prime }+y^{\prime \prime \prime }&=0 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.047 |
|
| \(244\) |
\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]] |
✓ |
✓ |
✗ |
0.048 |
|
| \(245\) |
\begin{align*}
-2 y+2 x y^{\prime }-x^{2} y^{\prime \prime }+y^{\prime \prime \prime }&=0 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.039 |
|
| \(246\) |
\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]] |
✓ |
✓ |
✗ |
3.708 |
|
| \(247\) |
\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]] |
✓ |
✓ |
✗ |
0.042 |
|
| \(248\) |
\begin{align*}
-y+x y^{\prime }-y^{\prime \prime }+x y^{\prime \prime \prime }&=0 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.039 |
|
| \(249\) |
\begin{align*}
y-x y^{\prime }-y^{\prime \prime }+x y^{\prime \prime \prime }&=0 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.039 |
|
| \(250\) |
\begin{align*}
y-x y^{\prime }-y^{\prime \prime }+x y^{\prime \prime \prime }&=-x^{2}+1 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.041 |
|
| \(251\) |
\begin{align*}
-x^{2} y+3 y^{\prime \prime }+x y^{\prime \prime \prime }&=0 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.039 |
|
| \(252\) |
\begin{align*}
a \,x^{2} y-6 y^{\prime }+x^{2} y^{\prime \prime \prime }&=0 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.043 |
|
| \(253\) |
\begin{align*}
3 x y+y^{\prime } \left (x^{2}+2\right )+4 x y^{\prime \prime }+x^{2} y^{\prime \prime \prime }&=f \left (x \right ) \\
\end{align*} |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✗ |
0.046 |
|
| \(254\) |
\begin{align*}
a \,x^{2} y+6 y^{\prime }+6 x y^{\prime \prime }+x^{2} y^{\prime \prime \prime }&=0 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.043 |
|
| \(255\) |
\begin{align*}
-2 x y+y^{\prime } \left (x^{2}+2\right )-2 x y^{\prime \prime }+\left (x^{2}+2\right ) y^{\prime \prime \prime }&=0 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.042 |
|
| \(256\) |
\begin{align*}
-2 y+2 x y^{\prime }-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 |
|
| \(257\) |
\begin{align*}
y+x y^{\prime }+\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]] |
✓ |
✓ |
✗ |
2.600 |
|
| \(258\) |
\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]] |
✓ |
✓ |
✗ |
0.047 |
|
| \(259\) |
\begin{align*}
-y+2 x y^{\prime }+x^{2} \ln \left (x \right ) y^{\prime \prime }+x^{3} y^{\prime \prime \prime }&=2 x^{3} \\
\end{align*} |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✗ |
1.422 |
|
| \(260\) |
\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 |
|
| \(261\) |
\begin{align*}
-8 y+3 \left (1+x \right ) y^{\prime }+\left (1+x \right )^{2} y^{\prime \prime }+\left (1+x \right )^{3} y^{\prime \prime \prime }&=0 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.046 |
|
| \(262\) |
\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]] |
✓ |
✓ |
✗ |
0.041 |
|
| \(263\) |
\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 (1+x \right ) y^{\prime \prime \prime }&=0 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.052 |
|
| \(264\) |
\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]] |
✓ |
✓ |
✗ |
0.052 |
|
| \(265\) |
\begin{align*}
\left (-x +a \right )^{3} \left (-x +b \right )^{3} y^{\prime \prime \prime }&=c y \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.046 |
|
| \(266\) |
\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]] |
✓ |
✓ |
✗ |
0.058 |
|
| \(267\) |
\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]] |
✓ |
✓ |
✗ |
0.049 |
|
| \(268\) |
\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]] |
✓ |
✓ |
✗ |
0.056 |
|
| \(269\) |
\begin{align*}
-a^{4} x^{3} y-x y^{\prime \prime }+2 x^{2} y^{\prime \prime \prime }+x^{3} y^{\prime \prime \prime \prime }&=0 \\
\end{align*} |
[[_high_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.053 |
|
| \(270\) |
\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]] |
✓ |
✓ |
✗ |
0.068 |
|
| \(271\) |
\begin{align*}
-b^{4} x^{\frac {2}{a}} y+16 \left (1-2 a \right ) \left (1-a \right ) a^{2} x^{2} y^{\prime \prime }-32 \left (1-2 a \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]] |
✓ |
✓ |
✗ |
0.092 |
|
| \(272\) |
\begin{align*}
\left (1-y\right ) y^{\prime }+{y^{\prime }}^{2} x -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]] |
✓ |
✓ |
✗ |
0.048 |
|
| \(273\) |
\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]] |
✓ |
✓ |
✗ |
0.043 |
|
| \(274\) |
\begin{align*}
3 y^{\prime } y^{\prime \prime }+\left (y+a \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]] |
✓ |
✓ |
✗ |
0.041 |
|
| \(275\) |
\begin{align*}
3 y^{2}+18 x y y^{\prime }+9 {y^{\prime }}^{2} x^{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]] |
✓ |
✓ |
✗ |
0.058 |
|
| \(276\) |
\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]] |
✓ |
✓ |
✗ |
0.051 |
|
| \(277\) |
\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]] |
✓ |
✓ |
✗ |
0.045 |
|
| \(278\) |
\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]] |
✓ |
✓ |
✗ |
0.045 |
|
| \(279\) |
\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]] |
✓ |
✓ |
✗ |
0.152 |
|
| \(280\) |
\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] |
✓ |
✓ |
✗ |
31.998 |
|
| \(281\) |
\begin{align*}
x y y^{\prime \prime }-2 {y^{\prime }}^{2} x +\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]] |
✓ |
✓ |
✗ |
0.334 |
|
| \(282\) |
\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] |
✓ |
✓ |
✗ |
10.603 |
|
| \(283\) |
\begin{align*}
x^{2} y^{\prime }+x y^{3}+a y^{2}&=0 \\
\end{align*} |
[_rational, _Abel] |
✓ |
✓ |
✗ |
11.670 |
|
| \(284\) |
\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] |
✓ |
✓ |
✗ |
17.043 |
|
| \(285\) |
\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‘]] |
✓ |
✓ |
✗ |
24.019 |
|
| \(286\) |
\begin{align*}
2 x +2 y+2 x^{3} y+4 x^{2} y^{2}+\left (2 x +x^{4}+2 x^{3} y\right ) y^{\prime }&=0 \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✗ |
18.353 |
|
| \(287\) |
\begin{align*}
x y^{\prime \prime }+\left (1-x \right ) y^{\prime }+m y&=0 \\
\end{align*} |
[_Laguerre] |
✓ |
✓ |
✗ |
4.144 |
|
| \(288\) |
\begin{align*}
\left (2 x -3\right ) y^{\prime \prime \prime }-\left (6 x -7\right ) y^{\prime \prime }+4 x y^{\prime }-4 y&=8 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.048 |
|
| \(289\) |
\begin{align*}
x^{3} \left (1+x \right ) y^{\prime \prime \prime }-\left (4 x +2\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]] |
✓ |
✓ |
✗ |
0.036 |
|
| \(290\) |
\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]] |
✓ |
✓ |
✗ |
0.038 |
|
| \(291\) |
\begin{align*}
\left (1-x \right ) y^{\prime \prime }-4 x y^{\prime }+5 y&=\cos \left (x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✗ |
8.536 |
|
| \(292\) |
\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 |
|
| \(293\) |
\begin{align*}
y^{\prime }&=y^{2}+x^{2} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[[_Riccati, _special]] |
✓ |
✓ |
✗ |
14.722 |
|
| \(294\) |
\begin{align*}
y^{\prime }&=x^{2}-y^{2} \\
y \left (0\right ) &= 2 \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✗ |
10.366 |
|
| \(295\) |
\begin{align*}
x^{2} \left (1+x \right ) y^{\prime \prime }+x \left (3+4 x \right ) y^{\prime }-y&=x +\frac {1}{x} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✗ |
80.773 |
|
| \(296\) |
\begin{align*}
\left (\cos \left (x \right )-\sin \left (x \right )\right ) y^{\prime \prime }-2 \sin \left (x \right ) y^{\prime }+y \left (\cos \left (x \right )+\sin \left (x \right )\right )&=\left (\cos \left (x \right )-\sin \left (x \right )\right )^{2} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✗ |
9.030 |
|
| \(297\) |
\begin{align*}
x^{2} y y^{\prime \prime }&=-y^{2}+{y^{\prime }}^{2} x^{2} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✗ |
0.479 |
|
| \(298\) |
\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]] |
✓ |
✓ |
✗ |
80.714 |
|
| \(299\) |
\begin{align*}
\left (-x^{2}+1\right ) \eta ^{\prime \prime }-\left (1+x \right ) \eta ^{\prime }+\left (1+k \right ) \eta &=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
78.669 |
|
| \(300\) |
\begin{align*}
y^{\prime \prime \prime }-x y&=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]] |
✓ |
✓ |
✗ |
0.067 |
|
| \(301\) |
\begin{align*}
y^{\prime \prime }-2 x y^{\prime }+2 \alpha y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
3.288 |
|
| \(302\) |
\begin{align*}
x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }+\left (x^{2}+x \right ) y^{\prime }+x y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.034 |
|
| \(303\) |
\begin{align*}
x^{3} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }-3 x y^{\prime }+\left (-1+x \right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.034 |
|
| \(304\) |
\begin{align*}
x^{3} y^{\prime \prime \prime }-2 x^{2} y^{\prime \prime }+\left (x^{2}+2 x \right ) y^{\prime }-x y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.034 |
|
| \(305\) |
\begin{align*}
x^{3} y^{\prime \prime \prime }+\left (2 x^{3}-x^{2}\right ) y^{\prime \prime }-x y^{\prime }+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.033 |
|
| \(306\) |
\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]] |
✓ |
✓ |
✗ |
14.729 |
|
| \(307\) |
\begin{align*}
y^{\prime \prime }-y^{\prime } y&=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]] |
✓ |
✓ |
✗ |
125.466 |
|
| \(308\) |
\begin{align*}
y^{\prime \prime }-a x y^{\prime }-b x y-c x&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
4.482 |
|
| \(309\) |
\begin{align*}
y^{\prime \prime }-a x y^{\prime }-b x y-c \,x^{2}&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
2.554 |
|
| \(310\) |
\begin{align*}
y^{\prime \prime }-a x y^{\prime }-b x y-x^{3} c&=0 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✗ |
2.668 |
|
| \(311\) |
\begin{align*}
y^{\prime \prime }-x^{2} y^{\prime }-x y-x^{2}&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
6.408 |
|
| \(312\) |
\begin{align*}
y^{\prime \prime }-\frac {y^{\prime }}{x}-x y-x^{2}-\frac {1}{x}&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
33.119 |
|
| \(313\) |
\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]] |
✓ |
✓ |
✗ |
183.062 |
|
| \(314\) |
\begin{align*}
y^{\prime \prime }-x^{3} y^{\prime }-x^{2} y-x^{3}&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
4.586 |
|
| \(315\) |
\begin{align*}
y^{\prime \prime \prime }-x^{3} y^{\prime }-x^{2} y-x^{3}&=0 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.046 |
|
| \(316\) |
\begin{align*}
\frac {x y^{\prime \prime }}{1-x}+y&=\frac {1}{1-x} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✗ |
2.323 |
|
| \(317\) |
\begin{align*}
\frac {x y^{\prime \prime }}{1-x}+y&=\cos \left (x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✗ |
2.066 |
|
| \(318\) |
\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]] |
✓ |
✓ |
✗ |
0.525 |
|
| \(319\) |
\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]] |
✓ |
✓ |
✗ |
2.033 |
|
| \(320\) |
\begin{align*}
y^{\prime \prime }+\left (x +3\right ) y^{\prime }+\left (y^{2}+3\right ) {y^{\prime }}^{2}&=0 \\
\end{align*} |
[_Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✗ |
0.559 |
|
| \(321\) |
\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]] |
✓ |
✓ |
✗ |
2.278 |
|
| \(322\) |
\begin{align*}
y^{\prime \prime \prime }-x y&=0 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.038 |
|
| \(323\) |
\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] |
✓ |
✓ |
✗ |
6.645 |
|
| \(324\) |
\begin{align*}
y^{\prime }+y^{3}+a x y^{2}&=0 \\
\end{align*} |
[_Abel] |
✓ |
✓ |
✗ |
7.977 |
|
| \(325\) |
\begin{align*}
y^{\prime }-y^{3}-a \,{\mathrm e}^{x} y^{2}&=0 \\
\end{align*} |
[_Abel] |
✓ |
✓ |
✗ |
5.476 |
|
| \(326\) |
\begin{align*}
y^{\prime }+3 a y^{3}+6 a x y^{2}&=0 \\
\end{align*} |
[_Abel] |
✓ |
✓ |
✗ |
7.868 |
|
| \(327\) |
\begin{align*}
y^{\prime }-x \left (x +2\right ) y^{3}-y^{2} \left (x +3\right )&=0 \\
\end{align*} |
[_Abel] |
✓ |
✓ |
✗ |
8.047 |
|
| \(328\) |
\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] |
✓ |
✓ |
✗ |
15.330 |
|
| \(329\) |
\begin{align*}
y^{\prime }+2 \left (a^{2} x^{3}-b^{2} x \right ) y^{3}+3 b y^{2}&=0 \\
\end{align*} |
[_Abel] |
✓ |
✓ |
✗ |
10.658 |
|
| \(330\) |
\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] |
✓ |
✓ |
✗ |
11.127 |
|
| \(331\) |
\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] |
✓ |
✓ |
✗ |
32.516 |
|
| \(332\) |
\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’)‘] |
✓ |
✓ |
✗ |
3.117 |
|
| \(333\) |
\begin{align*}
y^{\prime }+2 \tan \left (y\right ) \tan \left (x \right )-1&=0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✗ |
3.469 |
|
| \(334\) |
\begin{align*}
y^{\prime }-x^{a -1} 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)]‘]] |
✓ |
✓ |
✗ |
11.213 |
|
| \(335\) |
\begin{align*}
2 y^{\prime }-3 y^{2}-4 a y-b -c \,{\mathrm e}^{-2 a x}&=0 \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✗ |
36.308 |
|
| \(336\) |
\begin{align*}
x y^{\prime }+y^{3}+3 x y^{2}&=0 \\
\end{align*} |
[_rational, _Abel] |
✓ |
✓ |
✗ |
11.253 |
|
| \(337\) |
\begin{align*}
x y^{\prime }+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)]‘]] |
✓ |
✓ |
✗ |
6.262 |
|
| \(338\) |
\begin{align*}
x^{2} y^{\prime }+a y^{3}-a \,x^{2} y^{2}&=0 \\
\end{align*} |
[_rational, _Abel] |
✓ |
✓ |
✗ |
5.470 |
|
| \(339\) |
\begin{align*}
x^{2} y^{\prime }+x y^{3}+a y^{2}&=0 \\
\end{align*} |
[_rational, _Abel] |
✓ |
✓ |
✗ |
9.884 |
|
| \(340\) |
\begin{align*}
x^{2} y^{\prime }+y^{3} a \,x^{2}+b y^{2}&=0 \\
\end{align*} |
[_rational, _Abel] |
✓ |
✓ |
✗ |
8.028 |
|
| \(341\) |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime }+\left (1+y^{2}\right ) \left (2 x y-1\right )&=0 \\
\end{align*} |
[_rational, _Abel] |
✓ |
✓ |
✗ |
58.483 |
|
| \(342\) |
\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’)‘] |
✓ |
✓ |
✗ |
17.802 |
|
| \(343\) |
\begin{align*}
\left (x^{2}-1\right ) y^{\prime }+a \left (y^{2}-2 x y+1\right )&=0 \\
\end{align*} |
[_rational, _Riccati] |
✓ |
✓ |
✗ |
5.705 |
|
| \(344\) |
\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] |
✓ |
✓ |
✗ |
11.745 |
|
| \(345\) |
\begin{align*}
x^{7} y^{\prime }+5 x^{3} y^{2}+2 \left (x^{2}+1\right ) y^{3}&=0 \\
\end{align*} |
[_rational, _Abel] |
✓ |
✓ |
✗ |
26.684 |
|
| \(346\) |
\begin{align*}
y^{\prime } y+x +f \left (y^{2}+x^{2}\right ) g \left (x \right )&=0 \\
\end{align*} |
[NONE] |
✓ |
✓ |
✗ |
11.035 |
|
| \(347\) |
\begin{align*}
\left (x^{2} y-1\right ) y^{\prime }-x y^{2}+1&=0 \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✗ |
64.987 |
|
| \(348\) |
\begin{align*}
x \left (x y+x^{4}-1\right ) y^{\prime }-y \left (x y-x^{4}-1\right )&=0 \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✗ |
28.517 |
|
| \(349\) |
\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] |
✓ |
✓ |
✗ |
4.879 |
|
| \(350\) |
\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] |
✓ |
✓ |
✗ |
8.601 |
|
| \(351\) |
\begin{align*}
\cos \left (y\right ) y^{\prime }-\cos \left (x \right ) \sin \left (y\right )^{2}-\sin \left (y\right )&=0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✓ |
34.771 |
|
| \(352\) |
\begin{align*}
\cos \left (y\right ) y^{\prime }+x \sin \left (y\right ) \cos \left (y\right )^{2}-\sin \left (y\right )^{3}&=0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✓ |
55.100 |
|
| \(353\) |
\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’)‘] |
✓ |
✓ |
✓ |
39.910 |
|
| \(354\) |
\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)]‘]] |
✓ |
✓ |
✗ |
38.771 |
|
| \(355\) |
\begin{align*}
x y^{2} {y^{\prime }}^{2}-\left (y^{3}+x^{3}-a \right ) y^{\prime }+x^{2} y&=0 \\
\end{align*} |
[_rational] |
✓ |
✓ |
✗ |
199.212 |
|
| \(356\) |
\begin{align*}
\left (a^{2} \sqrt {y^{2}+x^{2}}-x^{2}\right ) {y^{\prime }}^{2}+2 x y y^{\prime }+a^{2} \sqrt {y^{2}+x^{2}}-y^{2}&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
101.197 |
|
| \(357\) |
\begin{align*}
\left (a \left (y^{2}+x^{2}\right )^{{3}/{2}}-x^{2}\right ) {y^{\prime }}^{2}+2 x y y^{\prime }+a \left (y^{2}+x^{2}\right )^{{3}/{2}}-y^{2}&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
141.386 |
|
| \(358\) |
\begin{align*}
f \left (y^{2}+x^{2}\right ) \left (1+{y^{\prime }}^{2}\right )-\left (-y+x y^{\prime }\right )^{2}&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
40.511 |
|
| \(359\) |
\begin{align*}
x^{n -1} {y^{\prime }}^{n}-n x y^{\prime }+y&=0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✗ |
9.614 |
|
| \(360\) |
\begin{align*}
y \sqrt {1+{y^{\prime }}^{2}}-a y y^{\prime }-a x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✗ |
0.225 |
|
| \(361\) |
\begin{align*}
f \left (y^{2}+x^{2}\right ) \sqrt {1+{y^{\prime }}^{2}}-x y^{\prime }+y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
51.729 |
|
| \(362\) |
\begin{align*}
a \,x^{n} f \left (y^{\prime }\right )+x y^{\prime }-y&=0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✗ |
3.437 |
|
| \(363\) |
\begin{align*}
f \left ({y^{\prime }}^{2} x \right )+2 x y^{\prime }-y&=0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✗ |
1.227 |
|
| \(364\) |
\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)]‘]] |
✓ |
✓ |
✗ |
4.955 |
|
| \(365\) |
\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)]‘]] |
✓ |
✓ |
✗ |
5.065 |
|
| \(366\) |
\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)]‘]] |
✓ |
✓ |
✗ |
5.155 |
|
| \(367\) |
\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)]‘]] |
✓ |
✓ |
✗ |
9.100 |
|
| \(368\) |
\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)]‘]] |
✓ |
✓ |
✗ |
6.719 |
|
| \(369\) |
\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)]‘]] |
✓ |
✓ |
✗ |
7.433 |
|
| \(370\) |
\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)]‘]] |
✓ |
✓ |
✗ |
7.411 |
|
| \(371\) |
\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)]‘]] |
✓ |
✓ |
✗ |
18.187 |
|
| \(372\) |
\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] |
✓ |
✓ |
✗ |
5.956 |
|
| \(373\) |
\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)]‘]] |
✓ |
✓ |
✗ |
5.509 |
|
| \(374\) |
\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’)‘] |
✓ |
✓ |
✗ |
5.090 |
|
| \(375\) |
\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)]‘]] |
✓ |
✓ |
✗ |
10.970 |
|
| \(376\) |
\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)]‘]] |
✓ |
✓ |
✗ |
16.266 |
|
| \(377\) |
\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’)‘] |
✓ |
✓ |
✓ |
45.155 |
|
| \(378\) |
\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’)‘] |
✓ |
✓ |
✗ |
5.996 |
|
| \(379\) |
\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)]‘]] |
✓ |
✓ |
✗ |
1.701 |
|
| \(380\) |
\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)]‘]] |
✓ |
✓ |
✗ |
12.784 |
|
| \(381\) |
\begin{align*}
y^{\prime }&=-\left (-\ln \left (\ln \left (y\right )\right )+\ln \left (x \right )\right ) y \\
\end{align*} |
[‘x=_G(y,y’)‘] |
✓ |
✓ |
✗ |
7.346 |
|
| \(382\) |
\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’)‘] |
✓ |
✓ |
✗ |
9.155 |
|
| \(383\) |
\begin{align*}
y^{\prime }&=\frac {y}{\ln \left (\ln \left (y\right )\right )-\ln \left (x \right )+1} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✗ |
11.419 |
|
| \(384\) |
\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)]‘]] |
✓ |
✓ |
✗ |
12.399 |
|
| \(385\) |
\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 (1+x \right )} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
✓ |
✗ |
26.300 |
|
| \(386\) |
\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 (1+x \right )} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
✓ |
✓ |
2.004 |
|
| \(387\) |
\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)]‘]] |
✓ |
✓ |
✗ |
9.894 |
|
| \(388\) |
\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’)‘] |
✓ |
✓ |
✗ |
205.534 |
|
| \(389\) |
\begin{align*}
y^{\prime }&=\frac {x +1+2 x^{6} \sqrt {4 x^{2} y+1}}{2 x^{3} \left (1+x \right )} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✗ |
12.211 |
|
| \(390\) |
\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)]‘]] |
✓ |
✓ |
✗ |
23.738 |
|
| \(391\) |
\begin{align*}
y^{\prime }&=\frac {-x^{2}+1+4 x^{3} \sqrt {x^{2}-2 x +1+8 y}}{4+4 x} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
✓ |
✗ |
13.929 |
|
| \(392\) |
\begin{align*}
y^{\prime }&=\frac {x +1+2 \sqrt {4 x^{2} y+1}\, x^{3}}{2 x^{3} \left (1+x \right )} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✗ |
12.176 |
|
| \(393\) |
\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)]‘]] |
✓ |
✓ |
✗ |
21.216 |
|
| \(394\) |
\begin{align*}
y^{\prime }&=-\frac {\left (-\ln \left (y-1\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’)‘] |
✓ |
✓ |
✗ |
48.864 |
|
| \(395\) |
\begin{align*}
y^{\prime }&=\frac {\left (-\ln \left (y-1\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’)‘] |
✓ |
✓ |
✗ |
57.543 |
|
| \(396\) |
\begin{align*}
y^{\prime }&=\frac {2 a x +2 a +x^{3} \sqrt {-y^{2}+4 a x}}{\left (1+x \right ) y} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✗ |
53.760 |
|
| \(397\) |
\begin{align*}
y^{\prime }&=-\frac {\left (x \ln \left (y\right )+\ln \left (y\right )-1\right ) y}{1+x} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
18.617 |
|
| \(398\) |
\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)]‘]] |
✓ |
✓ |
✗ |
14.441 |
|
| \(399\) |
\begin{align*}
y^{\prime }&=\frac {-x^{2}+x +2+2 x^{3} \sqrt {x^{2}+4 y-4 x}}{2 x +2} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
✓ |
✗ |
15.227 |
|
| \(400\) |
\begin{align*}
y^{\prime }&=\frac {3 x^{4}+3 x^{3}+\sqrt {9 x^{4}-4 y^{3}}}{\left (1+x \right ) y^{2}} \\
\end{align*} |
[_rational] |
✓ |
✓ |
✗ |
108.700 |
|
| \(401\) |
\begin{align*}
y^{\prime }&=\frac {x^{3} \left (3 x +3+\sqrt {9 x^{4}-4 y^{3}}\right )}{\left (1+x \right ) y^{2}} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✗ |
201.241 |
|
| \(402\) |
\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)]‘]] |
✓ |
✓ |
✗ |
15.384 |
|
| \(403\) |
\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)]‘]] |
✓ |
✓ |
✗ |
16.314 |
|
| \(404\) |
\begin{align*}
y^{\prime }&=\frac {\left (-x \ln \left (y\right )-\ln \left (y\right )+x^{3}\right ) y}{1+x} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
8.374 |
|
| \(405\) |
\begin{align*}
y^{\prime }&=-\frac {\cos \left (y\right ) \left (x -\cos \left (y\right )+1\right )}{\left (\sin \left (y\right ) x -1\right ) \left (1+x \right )} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✗ |
69.358 |
|
| \(406\) |
\begin{align*}
y^{\prime }&=\frac {\cos \left (y\right ) \left (\cos \left (y\right ) x^{3}-x -1\right )}{\left (\sin \left (y\right ) x -1\right ) \left (1+x \right )} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✗ |
40.633 |
|
| \(407\) |
\begin{align*}
y^{\prime }&=\frac {\left (x +1+x^{4} \ln \left (y\right )\right ) y \ln \left (y\right )}{x \left (1+x \right )} \\
\end{align*} |
[‘x=_G(y,y’)‘] |
✓ |
✓ |
✓ |
9.173 |
|
| \(408\) |
\begin{align*}
y^{\prime }&=\frac {\left (2 x +2+x^{3} y\right ) y}{\left (-1+2 x +\ln \left (y\right )\right ) \left (1+x \right )} \\
\end{align*} |
[‘x=_G(y,y’)‘] |
✓ |
✓ |
✗ |
8.939 |
|
| \(409\) |
\begin{align*}
y^{\prime }&=-\frac {\left (x \ln \left (y\right )+\ln \left (y\right )-x \right ) y}{x \left (1+x \right )} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
29.979 |
|
| \(410\) |
\begin{align*}
y^{\prime }&=\frac {\left (-x \ln \left (y\right )-\ln \left (y\right )+x^{4}\right ) y}{x \left (1+x \right )} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
9.084 |
|
| \(411\) |
\begin{align*}
y^{\prime }&=\frac {\left (x +1+x \ln \left (y\right )\right ) \ln \left (y\right ) y}{x \left (1+x \right )} \\
\end{align*} |
[‘x=_G(y,y’)‘] |
✓ |
✓ |
✓ |
27.480 |
|
| \(412\) |
\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)]‘]] |
✓ |
✓ |
✗ |
5.248 |
|
| \(413\) |
\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)]‘]] |
✓ |
✓ |
✗ |
9.735 |
|
| \(414\) |
\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 (1+x \right )} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✗ |
11.933 |
|
| \(415\) |
\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 (1+x \right )} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✗ |
72.722 |
|
| \(416\) |
\begin{align*}
y^{\prime }&=-\frac {1}{-x -\textit {\_F1} \left (y-\ln \left (x \right )\right ) y \,{\mathrm e}^{y}} \\
\end{align*} |
[NONE] |
✓ |
✓ |
✗ |
6.263 |
|
| \(417\) |
\begin{align*}
y^{\prime }&=\frac {x^{3} {\mathrm e}^{y}+x^{4}+y \,{\mathrm e}^{y}-{\mathrm e}^{y} \ln \left ({\mathrm e}^{y}+x \right )+x y-\ln \left ({\mathrm e}^{y}+x \right ) x +x}{x^{2}} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✗ |
33.670 |
|
| \(418\) |
\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)]‘]] |
✓ |
✓ |
✗ |
21.117 |
|
| \(419\) |
\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)]‘]] |
✓ |
✓ |
✗ |
18.908 |
|
| \(420\) |
\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’)‘] |
✓ |
✓ |
✓ |
11.025 |
|
| \(421\) |
\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)]‘]] |
✓ |
✓ |
✗ |
14.375 |
|
| \(422\) |
\begin{align*}
y^{\prime }&=\frac {-2 \cos \left (y\right )+x^{2} \cos \left (2 y\right ) \ln \left (x \right )+x^{2} \ln \left (x \right )}{2 \sin \left (y\right ) \ln \left (x \right ) x} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✓ |
10.973 |
|
| \(423\) |
\begin{align*}
y^{\prime }&=\frac {\left (3 x y^{2}+x +3 y^{2}\right ) y}{\left (x +6 y^{2}\right ) x \left (1+x \right )} \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✗ |
17.595 |
|
| \(424\) |
\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)]‘]] |
✓ |
✓ |
✗ |
13.617 |
|
| \(425\) |
\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’)‘] |
✓ |
✓ |
✗ |
38.025 |
|
| \(426\) |
\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 (1+x \right )} \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✗ |
7.476 |
|
| \(427\) |
\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] |
✓ |
✓ |
✗ |
46.744 |
|
| \(428\) |
\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*} |
[NONE] |
✓ |
✓ |
✗ |
5.873 |
|
| \(429\) |
\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)]‘]] |
✓ |
✓ |
✗ |
14.630 |
|
| \(430\) |
\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)]‘]] |
✓ |
✓ |
✗ |
8.234 |
|
| \(431\) |
\begin{align*}
y^{\prime }&=-\frac {x}{2}+1+\sqrt {x^{2}+4 y-4 x}+x^{2} \sqrt {x^{2}+4 y-4 x}+x^{3} \sqrt {x^{2}+4 y-4 x} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
✓ |
✗ |
16.194 |
|
| \(432\) |
\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)]‘]] |
✓ |
✓ |
✗ |
11.066 |
|
| \(433\) |
\begin{align*}
y^{\prime }&=\frac {y \left (\ln \left (x \right )+\ln \left (y\right )-1+x^{2} \ln \left (x \right )^{2}+2 x^{2} \ln \left (y\right ) \ln \left (x \right )+x^{2} \ln \left (y\right )^{2}\right )}{x} \\
\end{align*} |
[NONE] |
✓ |
✓ |
✗ |
11.990 |
|
| \(434\) |
\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] |
✓ |
✓ |
✗ |
10.889 |
|
| \(435\) |
\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] |
✓ |
✓ |
✗ |
7.528 |
|
| \(436\) |
\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)]‘]] |
✓ |
✓ |
✗ |
14.558 |
|
| \(437\) |
\begin{align*}
y^{\prime }&=-\frac {-x -\textit {\_F1} \left (y^{2}-2 x \right )}{\sqrt {y^{2}}\, x} \\
\end{align*} |
[NONE] |
✓ |
✓ |
✗ |
7.535 |
|
| \(438\) |
\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)]‘]] |
✓ |
✓ |
✗ |
6.522 |
|
| \(439\) |
\begin{align*}
y^{\prime }&=\left (\frac {\ln \left (y-1\right ) y}{\left (1-y\right ) \ln \left (x \right ) x}-\frac {\ln \left (y-1\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)]‘]] |
✓ |
✓ |
✗ |
10.357 |
|
| \(440\) |
\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)]‘]] |
✓ |
✓ |
✗ |
18.315 |
|
| \(441\) |
\begin{align*}
y^{\prime }&=\frac {\left ({\mathrm e}^{-\frac {y}{x}} y+x \,{\mathrm e}^{-\frac {y}{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)]‘]] |
✓ |
✓ |
✗ |
8.493 |
|
| \(442\) |
\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 y^{3} {\mathrm e}^{x}-54 y^{{3}/{2}} {\mathrm e}^{2 x}+27 \,{\mathrm e}^{3 x}\right ) {\mathrm e}^{x}}{8 \sqrt {y}} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
✗ |
37.335 |
|
| \(443\) |
\begin{align*}
y^{\prime }&=\frac {y \left (x \ln \left (y\right )+\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 (1+x \right )} \\
\end{align*} |
[NONE] |
✓ |
✓ |
✗ |
12.510 |
|
| \(444\) |
\begin{align*}
y^{\prime }&=\frac {y \left (x \ln \left (x \right )+\ln \left (x \right )+x \ln \left (y\right )+\ln \left (y\right )-x -1+x \ln \left (x \right )^{2}+2 x \ln \left (y\right ) \ln \left (x \right )+x \ln \left (y\right )^{2}\right )}{x \left (1+x \right )} \\
\end{align*} |
[NONE] |
✓ |
✓ |
✗ |
13.934 |
|
| \(445\) |
\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}+x \,{\mathrm e}^{-\frac {y}{x}}+x \right ) {\mathrm e}^{\frac {y}{x}}}{x \left (1+x \right )} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✗ |
10.092 |
|
| \(446\) |
\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}+x \,{\mathrm e}^{-\frac {y}{x}}+x^{4}\right ) {\mathrm e}^{\frac {y}{x}}}{x \left (1+x \right )} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✗ |
8.689 |
|
| \(447\) |
\begin{align*}
y^{\prime }&=\frac {y \left (\ln \left (x \right )+\ln \left (y\right )-1+x \ln \left (x \right )^{2}+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] |
✓ |
✓ |
✗ |
12.086 |
|
| \(448\) |
\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] |
✓ |
✓ |
✓ |
24.256 |
|
| \(449\) |
\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] |
✓ |
✓ |
✓ |
22.499 |
|
| \(450\) |
\begin{align*}
y^{\prime }&=\frac {y \left (x^{2} y^{2}+y x \,{\mathrm e}^{x}+{\mathrm e}^{2 x}\right ) {\mathrm e}^{-2 x} \left (-1+x \right )}{x} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘], _Abel] |
✓ |
✓ |
✗ |
19.623 |
|
| \(451\) |
\begin{align*}
y^{\prime \prime }-\left (x^{2}+a \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
2.649 |
|
| \(452\) |
\begin{align*}
y^{\prime \prime }+\left (a \,x^{2 c}+b \,x^{c -1}\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
2.662 |
|
| \(453\) |
\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]] |
✓ |
✓ |
✗ |
2.232 |
|
| \(454\) |
\begin{align*}
y^{\prime \prime }+\left (a \cosh \left (x \right )^{2}+b \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
6.262 |
|
| \(455\) |
\begin{align*}
y^{\prime \prime }+\left (a \cos \left (2 x \right )+b \right ) y&=0 \\
\end{align*} |
[_ellipsoidal] |
✓ |
✓ |
✗ |
3.129 |
|
| \(456\) |
\begin{align*}
y^{\prime \prime }+\left (\cos \left (x \right )^{2} a +b \right ) y&=0 \\
\end{align*} |
[_ellipsoidal] |
✓ |
✓ |
✗ |
3.317 |
|
| \(457\) |
\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]] |
✓ |
✓ |
✗ |
7.996 |
|
| \(458\) |
\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]] |
✓ |
✓ |
✗ |
2.031 |
|
| \(459\) |
\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]] |
✓ |
✓ |
✗ |
2.907 |
|
| \(460\) |
\begin{align*}
y^{\prime \prime }+a y^{\prime }-\left (b^{2} x^{2}+c \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
4.773 |
|
| \(461\) |
\begin{align*}
y^{\prime \prime }+x y^{\prime }+\left (n +1\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
5.467 |
|
| \(462\) |
\begin{align*}
y^{\prime \prime }+x y^{\prime }-n y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
3.662 |
|
| \(463\) |
\begin{align*}
-a y-x y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
[_Hermite] |
✓ |
✓ |
✗ |
3.656 |
|
| \(464\) |
\begin{align*}
y^{\prime \prime }-2 x y^{\prime }+a y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
3.852 |
|
| \(465\) |
\begin{align*}
y^{\prime \prime }-4 x y^{\prime }+\left (3 x^{2}+2 n -1\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
5.600 |
|
| \(466\) |
\begin{align*}
b y+a x y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
4.052 |
|
| \(467\) |
\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]] |
✓ |
✓ |
✗ |
6.216 |
|
| \(468\) |
\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]] |
✓ |
✓ |
✗ |
6.561 |
|
| \(469\) |
\begin{align*}
y^{\prime \prime }+a \,x^{-1+q} y^{\prime }+b \,x^{q -2} y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
6.296 |
|
| \(470\) |
\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]] |
✓ |
✓ |
✗ |
6.444 |
|
| \(471\) |
\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]] |
✓ |
✓ |
✗ |
4.872 |
|
| \(472\) |
\begin{align*}
b y+a \tan \left (x \right ) y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
4.503 |
|
| \(473\) |
\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]] |
✓ |
✓ |
✗ |
8.649 |
|
| \(474\) |
\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]] |
✓ |
✓ |
✗ |
5.531 |
|
| \(475\) |
\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]] |
✓ |
✓ |
✗ |
5.561 |
|
| \(476\) |
\begin{align*}
4 y^{\prime \prime }-\left (x^{2}+a \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
2.616 |
|
| \(477\) |
\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]] |
✓ |
✓ |
✗ |
7.803 |
|
| \(478\) |
\begin{align*}
\left (x +a \right ) y+x y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
2.363 |
|
| \(479\) |
\begin{align*}
x y^{\prime \prime }+y^{\prime }+\left (x +a \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
5.296 |
|
| \(480\) |
\begin{align*}
x y^{\prime \prime }-y^{\prime }+x^{3} \left ({\mathrm e}^{x^{2}}-v^{2}\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
6.463 |
|
| \(481\) |
\begin{align*}
x y^{\prime \prime }+\left (x +b \right ) y^{\prime }+a y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
6.598 |
|
| \(482\) |
\begin{align*}
x y^{\prime \prime }+\left (x +a +b \right ) y^{\prime }+a y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
6.469 |
|
| \(483\) |
\begin{align*}
x y^{\prime \prime }-x y^{\prime }-a y&=0 \\
\end{align*} |
[_Laguerre] |
✓ |
✓ |
✗ |
4.347 |
|
| \(484\) |
\begin{align*}
x y^{\prime \prime }+\left (-x +b \right ) y^{\prime }-a y&=0 \\
\end{align*} |
[_Laguerre] |
✓ |
✓ |
✗ |
5.968 |
|
| \(485\) |
\begin{align*}
x y^{\prime \prime }-2 \left (-1+x \right ) y^{\prime }-y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
5.623 |
|
| \(486\) |
\begin{align*}
x y^{\prime \prime }-\left (3 x -2\right ) y^{\prime }-\left (2 x -3\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
6.067 |
|
| \(487\) |
\begin{align*}
x y^{\prime \prime }+\left (a x +b +n \right ) y^{\prime }+n a y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
7.186 |
|
| \(488\) |
\begin{align*}
x y^{\prime \prime }-\left (a +b \right ) \left (1+x \right ) y^{\prime }+a b x y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
7.974 |
|
| \(489\) |
\begin{align*}
\left (a b x +a n +b m \right ) y+\left (m +n +x \left (a +b \right )\right ) y^{\prime }+x y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
8.051 |
|
| \(490\) |
\begin{align*}
x y^{\prime \prime }+\left (a x +b \right ) y^{\prime }+\left (c x +d \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
7.543 |
|
| \(491\) |
\begin{align*}
x y^{\prime \prime }-2 \left (x^{2}-a \right ) y^{\prime }+2 n x y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
14.974 |
|
| \(492\) |
\begin{align*}
2 x y^{\prime \prime }-\left (-1+x \right ) y^{\prime }+a y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
5.777 |
|
| \(493\) |
\begin{align*}
2 x y^{\prime \prime }-\left (2 x -1\right ) y^{\prime }+a y&=0 \\
\end{align*} |
[_Laguerre] |
✓ |
✓ |
✗ |
5.512 |
|
| \(494\) |
\begin{align*}
4 x y^{\prime \prime }-\left (x +a \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
2.511 |
|
| \(495\) |
\begin{align*}
4 x y^{\prime \prime }+4 y-\left (x +2\right ) y+l y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
22.582 |
|
| \(496\) |
\begin{align*}
4 x y^{\prime \prime }+4 m y^{\prime }-\left (x -2 m -4 n \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
6.867 |
|
| \(497\) |
\begin{align*}
16 x y^{\prime \prime }+8 y^{\prime }-\left (x +a \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
5.102 |
|
| \(498\) |
\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]] |
✓ |
✓ |
✗ |
23.292 |
|
| \(499\) |
\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]] |
✓ |
✓ |
✗ |
28.993 |
|
| \(500\) |
\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]] |
✓ |
✓ |
✗ |
29.396 |
|
| \(501\) |
\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]] |
✓ |
✓ |
✗ |
22.843 |
|
| \(502\) |
\begin{align*}
x^{2} y^{\prime \prime }+\left (a \,x^{2}+b x +c \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
3.633 |
|
| \(503\) |
\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]] |
✓ |
✓ |
✗ |
2.851 |
|
| \(504\) |
\begin{align*}
x^{2} y^{\prime \prime }+2 x y^{\prime }+\left (l \,x^{2}+a x -n \left (n +1\right )\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
32.773 |
|
| \(505\) |
\begin{align*}
x^{2} y^{\prime \prime }+2 \left (-1+x \right ) y^{\prime }+a y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
5.667 |
|
| \(506\) |
\begin{align*}
x^{2} y^{\prime \prime }+2 \left (x +a \right ) y^{\prime }-b \left (b -1\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
13.778 |
|
| \(507\) |
\begin{align*}
x^{2} y^{\prime \prime }+\left (a x +b \right ) y^{\prime }+c y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
13.864 |
|
| \(508\) |
\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]] |
✓ |
✓ |
✗ |
5.126 |
|
| \(509\) |
\begin{align*}
-y+x \left (x +3\right ) y^{\prime }+x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
6.617 |
|
| \(510\) |
\begin{align*}
x^{2} y^{\prime \prime }-\left (x^{2}-2 x \right ) y^{\prime }-\left (x +a \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
15.609 |
|
| \(511\) |
\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]] |
✓ |
✓ |
✗ |
5.831 |
|
| \(512\) |
\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]] |
✓ |
✓ |
✗ |
18.306 |
|
| \(513\) |
\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]] |
✓ |
✓ |
✗ |
18.124 |
|
| \(514\) |
\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]] |
✓ |
✓ |
✗ |
19.811 |
|
| \(515\) |
\begin{align*}
x^{2} y^{\prime \prime }+\left (x^{3}+1\right ) x y^{\prime }-y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
19.970 |
|
| \(516\) |
\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]] |
✓ |
✓ |
✗ |
5.019 |
|
| \(517\) |
\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]] |
✓ |
✓ |
✗ |
16.703 |
|
| \(518\) |
\begin{align*}
x^{2} y^{\prime \prime }-\left (2 \tan \left (x \right ) x^{2}-x \right ) y^{\prime }-\left (a +x \tan \left (x \right )\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
9.525 |
|
| \(519\) |
\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]] |
✓ |
✓ |
✗ |
8.904 |
|
| \(520\) |
\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]] |
✓ |
✓ |
✗ |
16.146 |
|
| \(521\) |
\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]] |
✓ |
✓ |
✗ |
12.914 |
|
| \(522\) |
\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]] |
✓ |
✓ |
✗ |
19.763 |
|
| \(523\) |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime \prime }+2 x y^{\prime }-v \left (v -1\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
12.727 |
|
| \(524\) |
\begin{align*}
\left (x^{2}-1\right ) y^{\prime \prime }-v \left (v +1\right ) y&=0 \\
\end{align*} |
[_Gegenbauer] |
✓ |
✓ |
✓ |
4.404 |
|
| \(525\) |
\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]] |
✓ |
✓ |
✗ |
5.457 |
|
| \(526\) |
\begin{align*}
\left (x^{2}-1\right ) y^{\prime \prime }+2 x y^{\prime }-l y&=0 \\
\end{align*} |
[_Gegenbauer] |
✓ |
✓ |
✗ |
54.529 |
|
| \(527\) |
\begin{align*}
\left (x^{2}-1\right ) y^{\prime \prime }+2 x y^{\prime }-v \left (v +1\right ) y&=0 \\
\end{align*} |
[_Gegenbauer] |
✓ |
✓ |
✗ |
74.668 |
|
| \(528\) |
\begin{align*}
\left (x^{2}-1\right ) y^{\prime \prime }-2 x y^{\prime }-\left (v +2\right ) \left (v -1\right ) y&=0 \\
\end{align*} |
[_Gegenbauer] |
✓ |
✓ |
✗ |
734.075 |
|
| \(529\) |
\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] |
✓ |
✓ |
✗ |
61.408 |
|
| \(530\) |
\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] |
✓ |
✓ |
✗ |
59.783 |
|
| \(531\) |
\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]] |
✓ |
✓ |
✗ |
0.067 |
|
| \(532\) |
\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]] |
✓ |
✓ |
✗ |
49.334 |
|
| \(533\) |
\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]] |
✓ |
✓ |
✗ |
126.520 |
|
| \(534\) |
\begin{align*}
x \left (1+x \right ) y^{\prime \prime }+\left (a x +b \right ) y^{\prime }+c y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
82.253 |
|
| \(535\) |
\begin{align*}
x \left (-1+x \right ) y^{\prime \prime }+\left (2 x -1\right ) y^{\prime }-v \left (v +1\right ) y&=0 \\
\end{align*} |
[_Jacobi] |
✓ |
✓ |
✗ |
59.821 |
|
| \(536\) |
\begin{align*}
x \left (-1+x \right ) y^{\prime \prime }+\left (a x +b \right ) y^{\prime }+c y&=0 \\
\end{align*} |
[_Jacobi] |
✓ |
✓ |
✗ |
81.841 |
|
| \(537\) |
\begin{align*}
x \left (-1+x \right ) y^{\prime \prime }+\left (\left (a +1\right ) x +b \right ) y^{\prime }-l y&=0 \\
\end{align*} |
[_Jacobi] |
✓ |
✓ |
✗ |
97.644 |
|
| \(538\) |
\begin{align*}
x \left (x +2\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]] |
✓ |
✓ |
✗ |
141.239 |
|
| \(539\) |
\begin{align*}
\left (-1+x \right ) \left (x -2\right ) y^{\prime \prime }-\left (2 x -3\right ) y^{\prime }+y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
338.676 |
|
| \(540\) |
\begin{align*}
2 x \left (-1+x \right ) y^{\prime \prime }+\left (2 x -1\right ) y^{\prime }+\left (a x +b \right ) y&=0 \\
\end{align*} |
[_Jacobi] |
✓ |
✓ |
✗ |
29.731 |
|
| \(541\) |
\begin{align*}
2 x \left (-1+x \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] |
✓ |
✓ |
✗ |
72.467 |
|
| \(542\) |
\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]] |
✓ |
✓ |
✗ |
3.973 |
|
| \(543\) |
\begin{align*}
4 x^{2} y^{\prime \prime }+4 x y^{\prime }+\left (-x^{2}+2 \left (1-m +2 l \right ) x -m^{2}+1\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
31.246 |
|
| \(544\) |
\begin{align*}
x \left (4 x -1\right ) y^{\prime \prime }+\left (\left (4 a +2\right ) x -a \right ) y^{\prime }+a \left (a -1\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
67.752 |
|
| \(545\) |
\begin{align*}
48 x \left (-1+x \right ) y^{\prime \prime }+\left (152 x -40\right ) y^{\prime }+53 y&=0 \\
\end{align*} |
[_Jacobi] |
✓ |
✓ |
✗ |
59.324 |
|
| \(546\) |
\begin{align*}
144 x \left (-1+x \right ) y^{\prime \prime }+\left (120 x -48\right ) y^{\prime }+y&=0 \\
\end{align*} |
[_Jacobi] |
✓ |
✓ |
✗ |
59.616 |
|
| \(547\) |
\begin{align*}
144 x \left (-1+x \right ) y^{\prime \prime }+\left (168 x -96\right ) y^{\prime }+y&=0 \\
\end{align*} |
[_Jacobi] |
✓ |
✓ |
✗ |
59.544 |
|
| \(548\) |
\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]] |
✓ |
✓ |
✗ |
17.158 |
|
| \(549\) |
\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]] |
✓ |
✓ |
✗ |
22.350 |
|
| \(550\) |
\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]] |
✓ |
✓ |
✗ |
91.611 |
|
| \(551\) |
\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]] |
✓ |
✓ |
✗ |
140.289 |
|
| \(552\) |
\begin{align*}
-y+2 x y^{\prime }+x^{3} y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
9.620 |
|
| \(553\) |
\begin{align*}
x^{3} y^{\prime \prime }-\left (x^{2}-1\right ) y^{\prime }+x y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
42.607 |
|
| \(554\) |
\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]] |
✓ |
✓ |
✗ |
122.951 |
|
| \(555\) |
\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]] |
✓ |
✓ |
✗ |
149.907 |
|
| \(556\) |
\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]] |
✓ |
✓ |
✗ |
144.719 |
|
| \(557\) |
\begin{align*}
x \left (x^{2}-1\right ) y^{\prime \prime }+\left (x^{2}-1\right ) y^{\prime }-x y&=0 \\
\end{align*} |
[[_elliptic, _class_II]] |
✓ |
✓ |
✗ |
207.442 |
|
| \(558\) |
\begin{align*}
x \left (x^{2}-1\right ) y^{\prime \prime }+\left (3 x^{2}-1\right ) y^{\prime }+x y&=0 \\
\end{align*} |
[[_elliptic, _class_I]] |
✓ |
✓ |
✗ |
81.352 |
|
| \(559\) |
\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]] |
✓ |
✓ |
✗ |
128.825 |
|
| \(560\) |
\begin{align*}
y^{\prime \prime }&=-\frac {\left (\left (a +b +1\right ) x +\alpha +\beta -1\right ) y^{\prime }}{x \left (-1+x \right )}-\frac {\left (a b x -\alpha \beta \right ) y}{x^{2} \left (-1+x \right )} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
137.424 |
|
| \(561\) |
\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]] |
✓ |
✓ |
✗ |
98.834 |
|
| \(562\) |
\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 (-1+x \right ) \left (x -a \right )}-\frac {\left (\alpha \beta x -q \right ) y}{x \left (-1+x \right ) \left (x -a \right )} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
352.750 |
|
| \(563\) |
\begin{align*}
y^{\prime \prime }&=-\frac {\left (A \,x^{2}+B x +C \right ) y^{\prime }}{\left (x -a \right ) \left (x -b \right ) \left (x -c \right )}-\frac {\left (\operatorname {DD} x +E \right ) y}{\left (x -a \right ) \left (x -b \right ) \left (x -c \right )} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
359.887 |
|
| \(564\) |
\begin{align*}
y^{\prime \prime }&=-\frac {\left (3 x -1\right ) y^{\prime }}{2 x \left (-1+x \right )}+\frac {v \left (v +1\right ) y}{4 x^{2}} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
23.710 |
|
| \(565\) |
\begin{align*}
y^{\prime \prime }&=-\frac {\left (\left (a +1\right ) x -1\right ) y^{\prime }}{x \left (-1+x \right )}-\frac {\left (\left (a^{2}-b^{2}\right ) x +c^{2}\right ) y}{4 x^{2} \left (-1+x \right )} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
74.473 |
|
| \(566\) |
\begin{align*}
y^{\prime \prime }&=-\frac {\left (3 x -1\right ) y^{\prime }}{2 x \left (-1+x \right )}-\frac {\left (a x +b \right ) y}{4 x \left (-1+x \right )^{2}} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
11.742 |
|
| \(567\) |
\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]] |
✓ |
✓ |
✗ |
179.930 |
|
| \(568\) |
\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]] |
✓ |
✓ |
✗ |
140.984 |
|
| \(569\) |
\begin{align*}
y^{\prime \prime }&=-\frac {\left (a \left (1-a \right ) x^{2}-b \left (x +b \right )\right ) y}{x^{4}} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
5.195 |
|
| \(570\) |
\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]] |
✓ |
✓ |
✗ |
3.304 |
|
| \(571\) |
\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]] |
✓ |
✓ |
✗ |
8.345 |
|
| \(572\) |
\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]] |
✓ |
✓ |
✗ |
20.886 |
|
| \(573\) |
\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]] |
✓ |
✓ |
✗ |
91.457 |
|
| \(574\) |
\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]] |
✓ |
✓ |
✗ |
135.832 |
|
| \(575\) |
\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]] |
✓ |
✓ |
✗ |
34.245 |
|
| \(576\) |
\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]] |
✓ |
✓ |
✗ |
35.693 |
|
| \(577\) |
\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]] |
✓ |
✓ |
✗ |
136.730 |
|
| \(578\) |
\begin{align*}
y^{\prime \prime }&=\frac {\left (2 b c \,x^{c} \left (x^{2}-1\right )+2 \left (a -1\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 (\left (a -1\right ) a -v \left (v +1\right )\right )-a \left (a +1\right )\right ) y}{x^{2} \left (x^{2}-1\right )} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
419.687 |
|
| \(579\) |
\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]] |
✓ |
✓ |
✗ |
114.426 |
|
| \(580\) |
\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]] |
✓ |
✓ |
✗ |
89.500 |
|
| \(581\) |
\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]] |
✓ |
✓ |
✗ |
69.870 |
|
| \(582\) |
\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]] |
✓ |
✓ |
✗ |
100.973 |
|
| \(583\) |
\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]] |
✓ |
✓ |
✗ |
95.356 |
|
| \(584\) |
\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]] |
✓ |
✓ |
✗ |
160.310 |
|
| \(585\) |
\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]] |
✓ |
✓ |
✗ |
199.847 |
|
| \(586\) |
\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]] |
✓ |
✓ |
✗ |
4.702 |
|
| \(587\) |
\begin{align*}
y^{\prime \prime }&=-\frac {\left (3 x -1\right ) y^{\prime }}{2 x \left (-1+x \right )}-\frac {\left (v \left (v +1\right ) \left (-1+x \right )-a^{2} x \right ) y}{4 x^{2} \left (-1+x \right )^{2}} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
37.179 |
|
| \(588\) |
\begin{align*}
y^{\prime \prime }&=-\frac {\left (3 x -1\right ) y^{\prime }}{2 x \left (-1+x \right )}-\frac {\left (-v \left (v +1\right ) \left (-1+x \right )^{2}-4 n^{2} x \right ) y}{4 x^{2} \left (-1+x \right )^{2}} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
39.595 |
|
| \(589\) |
\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]] |
✓ |
✓ |
✗ |
127.838 |
|
| \(590\) |
\begin{align*}
y^{\prime \prime }&=-\frac {\left (b \,x^{2}+c x +d \right ) y}{a \,x^{2} \left (-1+x \right )^{2}} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
7.470 |
|
| \(591\) |
\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]] |
✓ |
✓ |
✗ |
145.472 |
|
| \(592\) |
\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]] |
✓ |
✓ |
✗ |
1117.693 |
|
| \(593\) |
\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]] |
✓ |
✓ |
✗ |
1248.425 |
|
| \(594\) |
\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]] |
✓ |
✓ |
✗ |
34.775 |
|
| \(595\) |
\begin{align*}
y^{\prime \prime }&=\frac {y}{1+{\mathrm e}^{x}} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✗ |
2.707 |
|
| \(596\) |
\begin{align*}
y^{\prime \prime }&=-\frac {\left (-a^{2} \sinh \left (x \right )^{2}-\left (n -1\right ) n \right ) y}{\sinh \left (x \right )^{2}} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
10.857 |
|
| \(597\) |
\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]] |
✓ |
✓ |
✗ |
22.718 |
|
| \(598\) |
\begin{align*}
y^{\prime \prime }&=-\frac {\left (1+2 n \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]] |
✓ |
✓ |
✗ |
8.441 |
|
| \(599\) |
\begin{align*}
\cos \left (x \right )^{2} y^{\prime \prime }-\left (\cos \left (x \right )^{2} a +\left (n -1\right ) n \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
5.461 |
|
| \(600\) |
\begin{align*}
y^{\prime \prime }&=-\frac {a y}{\sin \left (x \right )^{2}} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
4.227 |
|
| \(601\) |
\begin{align*}
\sin \left (x \right )^{2} y^{\prime \prime }-\left (a \sin \left (x \right )^{2}+\left (n -1\right ) n \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
5.257 |
|
| \(602\) |
\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]] |
✓ |
✓ |
✗ |
7.433 |
|
| \(603\) |
\begin{align*}
\sin \left (x \right )^{2} y^{\prime \prime }-\left (a^{2} \cos \left (x \right )^{2}+\cos \left (x \right ) b +\frac {b^{2}}{\left (2 a -3\right )^{2}}+3 a +2\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
14.956 |
|
| \(604\) |
\begin{align*}
y^{\prime \prime }&=-\frac {\left (-\left (a^{2} b^{2}-\left (a +1\right )^{2}\right ) \sin \left (x \right )^{2}-a \left (a +1\right ) b \sin \left (2 x \right )-\left (a -1\right ) a \right ) y}{\sin \left (x \right )^{2}} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
12.297 |
|
| \(605\) |
\begin{align*}
y^{\prime \prime }&=-\frac {\left (\cos \left (x \right )^{2} a +b \sin \left (x \right )^{2}+c \right ) y}{\sin \left (x \right )^{2}} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
7.009 |
|
| \(606\) |
\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]] |
✓ |
✓ |
✗ |
9.011 |
|
| \(607\) |
\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]] |
✓ |
✓ |
✗ |
18.519 |
|
| \(608\) |
\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]] |
✓ |
✓ |
✗ |
12.597 |
|
| \(609\) |
\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]] |
✓ |
✓ |
✗ |
6.034 |
|
| \(610\) |
\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]] |
✓ |
✓ |
✗ |
7.679 |
|
| \(611\) |
\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]] |
✓ |
✓ |
✗ |
6.631 |
|
| \(612\) |
\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]] |
✓ |
✓ |
✗ |
7.139 |
|
| \(613\) |
\begin{align*}
y^{\prime \prime \prime }+a \,x^{3} y-b x&=0 \\
\end{align*} |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✗ |
0.110 |
|
| \(614\) |
\begin{align*}
y^{\prime \prime \prime }-a \,x^{b} y&=0 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.133 |
|
| \(615\) |
\begin{align*}
a y+2 a x y^{\prime }+y^{\prime \prime \prime }&=0 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.133 |
|
| \(616\) |
\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]] |
✓ |
✓ |
✗ |
0.121 |
|
| \(617\) |
\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]] |
✓ |
✓ |
✗ |
0.171 |
|
| \(618\) |
\begin{align*}
y^{\prime \prime \prime }-6 x y^{\prime \prime }+2 \left (4 x^{2}+2 a -1\right ) y^{\prime }-8 a x y&=0 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.101 |
|
| \(619\) |
\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]] |
✓ |
✓ |
✗ |
0.131 |
|
| \(620\) |
\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]] |
✓ |
✓ |
✗ |
0.094 |
|
| \(621\) |
\begin{align*}
y^{\prime \prime \prime }+f \left (x \right ) \left (x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y\right )&=0 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.120 |
|
| \(622\) |
\begin{align*}
x y^{\prime \prime \prime }+3 y^{\prime \prime }+x y&=0 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.132 |
|
| \(623\) |
\begin{align*}
x y^{\prime \prime \prime }+3 y^{\prime \prime }-a \,x^{2} y&=0 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.134 |
|
| \(624\) |
\begin{align*}
x y^{\prime \prime \prime }+\left (a +b \right ) y^{\prime \prime }-x y^{\prime }-a y&=0 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.108 |
|
| \(625\) |
\begin{align*}
x y^{\prime \prime \prime }-\left (x +2 v \right ) y^{\prime \prime }-\left (x -2 v -1\right ) y^{\prime }+\left (-1+x \right ) y&=0 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.113 |
|
| \(626\) |
\begin{align*}
2 x y^{\prime \prime \prime }+3 y^{\prime \prime }+a x y-b&=0 \\
\end{align*} |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✗ |
0.090 |
|
| \(627\) |
\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]] |
✓ |
✓ |
✗ |
0.123 |
|
| \(628\) |
\begin{align*}
\left (2 x -1\right ) y^{\prime \prime \prime }-8 x y^{\prime }+8 y&=0 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.107 |
|
| \(629\) |
\begin{align*}
a \,x^{2} y-6 y^{\prime }+x^{2} y^{\prime \prime \prime }&=0 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.138 |
|
| \(630\) |
\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]] |
✓ |
✓ |
✗ |
0.142 |
|
| \(631\) |
\begin{align*}
x^{2} y^{\prime \prime \prime }+4 x y^{\prime \prime }+y^{\prime } \left (x^{2}+2\right )+3 x y-f \left (x \right )&=0 \\
\end{align*} |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✗ |
0.140 |
|
| \(632\) |
\begin{align*}
a \,x^{2} y+6 y^{\prime }+6 x y^{\prime \prime }+x^{2} y^{\prime \prime \prime }&=0 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.097 |
|
| \(633\) |
\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]] |
✓ |
✓ |
✗ |
0.115 |
|
| \(634\) |
\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]] |
✓ |
✓ |
✗ |
0.103 |
|
| \(635\) |
\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]] |
✓ |
✓ |
✗ |
0.127 |
|
| \(636\) |
\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]] |
✓ |
✓ |
✗ |
0.100 |
|
| \(637\) |
\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]] |
✓ |
✓ |
✗ |
0.142 |
|
| \(638\) |
\begin{align*}
-2 x y+y^{\prime } \left (x^{2}+2\right )-2 x y^{\prime \prime }+\left (x^{2}+2\right ) y^{\prime \prime \prime }&=0 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.095 |
|
| \(639\) |
\begin{align*}
2 x \left (-1+x \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]] |
✓ |
✓ |
✗ |
0.120 |
|
| \(640\) |
\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]] |
✓ |
✓ |
✗ |
0.096 |
|
| \(641\) |
\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]] |
✓ |
✓ |
✗ |
0.102 |
|
| \(642\) |
\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]] |
✓ |
✓ |
✗ |
0.152 |
|
| \(643\) |
\begin{align*}
x^{3} y^{\prime \prime \prime }+x^{2} \left (x +3\right ) y^{\prime \prime }+5 \left (-6+x \right ) x y^{\prime }+\left (4 x +30\right ) y&=0 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.098 |
|
| \(644\) |
\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]] |
✓ |
✓ |
✗ |
0.092 |
|
| \(645\) |
\begin{align*}
\left (x +3\right ) x^{2} y^{\prime \prime \prime }-3 x \left (x +2\right ) y^{\prime \prime }+6 \left (1+x \right ) y^{\prime }-6 y&=0 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.119 |
|
| \(646\) |
\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]] |
✓ |
✓ |
✗ |
0.160 |
|
| \(647\) |
\begin{align*}
x^{3} \left (1+x \right ) y^{\prime \prime \prime }-\left (4 x +2\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]] |
✓ |
✓ |
✗ |
0.123 |
|
| \(648\) |
\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]] |
✓ |
✓ |
✗ |
0.109 |
|
| \(649\) |
\begin{align*}
x^{6} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }-2 y&=0 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.120 |
|
| \(650\) |
\begin{align*}
x^{6} y^{\prime \prime \prime }+6 x^{5} y^{\prime \prime }+a y&=0 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.090 |
|
| \(651\) |
\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]] |
✓ |
✓ |
✗ |
0.134 |
|
| \(652\) |
\begin{align*}
\left (x -a \right )^{3} \left (x -b \right )^{3} y^{\prime \prime \prime }-c y&=0 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.147 |
|
| \(653\) |
\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]] |
✓ |
✓ |
✗ |
0.169 |
|
| \(654\) |
\begin{align*}
y^{\prime \prime \prime }+x y^{\prime }+n y&=0 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.106 |
|
| \(655\) |
\begin{align*}
y^{\prime \prime \prime }-x y^{\prime }-n y&=0 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.089 |
|
| \(656\) |
\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]] |
✓ |
✓ |
✗ |
0.146 |
|
| \(657\) |
\begin{align*}
y^{\prime \prime \prime \prime } x -\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]] |
✓ |
✓ |
✗ |
0.146 |
|
| \(658\) |
\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]] |
✓ |
✓ |
✗ |
0.149 |
|
| \(659\) |
\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]] |
✓ |
✓ |
✗ |
0.123 |
|
| \(660\) |
\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]] |
✓ |
✓ |
✗ |
0.123 |
|
| \(661\) |
\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]] |
✓ |
✓ |
✗ |
0.121 |
|
| \(662\) |
\begin{align*}
x^{3} y^{\prime \prime \prime \prime }+2 x^{2} y^{\prime \prime \prime }-x y^{\prime \prime }+y^{\prime }-a^{4} x^{3} y&=0 \\
\end{align*} |
[[_high_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.125 |
|
| \(663\) |
\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]] |
✓ |
✓ |
✗ |
0.117 |
|
| \(664\) |
\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]] |
✓ |
✓ |
✗ |
0.211 |
|
| \(665\) |
\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]] |
✓ |
✓ |
✗ |
0.140 |
|
| \(666\) |
\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]] |
✓ |
✓ |
✗ |
0.163 |
|
| \(667\) |
\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]] |
✓ |
✓ |
✗ |
0.166 |
|
| \(668\) |
\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]] |
✓ |
✓ |
✗ |
0.141 |
|
| \(669\) |
\begin{align*}
x^{4} y^{\prime \prime \prime \prime }+\left (6-4 a \right ) x^{3} y^{\prime \prime \prime }+\left (4 c^{2} x^{2 c} b^{2}+6 \left (a -1\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 \left (a -1\right ) a -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]] |
✓ |
✓ |
✗ |
0.175 |
|
| \(670\) |
\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 (a -1\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]] |
✓ |
✓ |
✗ |
0.179 |
|
| \(671\) |
\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]] |
✓ |
✓ |
✗ |
0.137 |
|
| \(672\) |
\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]] |
✓ |
✓ |
✗ |
0.148 |
|
| \(673\) |
\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]] |
✓ |
✓ |
✗ |
0.156 |
|
| \(674\) |
\begin{align*}
y^{\prime \prime \prime \prime }-2 a^{2} y^{\prime \prime }+a^{4} y-\lambda \left (a x -b \right ) \left (-a^{2} y+y^{\prime \prime }\right )&=0 \\
\end{align*} |
[[_high_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.141 |
|
| \(675\) |
\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]] |
✓ |
✓ |
✗ |
0.108 |
|
| \(676\) |
\begin{align*}
x^{2} y^{\prime \prime \prime \prime }-a y&=0 \\
\end{align*} |
[[_high_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.138 |
|
| \(677\) |
\begin{align*}
x^{10} y^{\left (5\right )}-a y&=0 \\
\end{align*} |
[[_high_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.154 |
|
| \(678\) |
\begin{align*}
x^{{5}/{2}} y^{\left (5\right )}-a y&=0 \\
\end{align*} |
[[_high_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.134 |
|
| \(679\) |
\begin{align*}
y^{\prime \prime }&=\frac {f \left (\frac {y}{\sqrt {x}}\right )}{x^{{3}/{2}}} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
17.530 |
|
| \(680\) |
\begin{align*}
y^{\prime \prime }+5 a y^{\prime }-6 y^{2}+6 a^{2} y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✗ |
119.184 |
|
| \(681\) |
\begin{align*}
y^{\prime \prime }+3 a y^{\prime }-2 y^{3}+2 a^{2} y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✗ |
40.818 |
|
| \(682\) |
\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]] |
✓ |
✓ |
✗ |
45.430 |
|
| \(683\) |
\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]] |
✓ |
✓ |
✗ |
1.721 |
|
| \(684\) |
\begin{align*}
y^{\prime \prime }-3 y^{\prime } y-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]] |
✓ |
✓ |
✗ |
51.902 |
|
| \(685\) |
\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]] |
✓ |
✓ |
✗ |
1.735 |
|
| \(686\) |
\begin{align*}
y^{\prime \prime }-a \left (-y+x y^{\prime }\right )^{v}&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.877 |
|
| \(687\) |
\begin{align*}
y^{\prime \prime }&=a \sqrt {b y^{2}+{y^{\prime }}^{2}} \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✗ |
835.448 |
|
| \(688\) |
\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]] |
✓ |
✓ |
✗ |
1.112 |
|
| \(689\) |
\begin{align*}
x y^{\prime \prime }-{y^{\prime }}^{2} x^{2}+2 y^{\prime }+y^{2}&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✗ |
0.423 |
|
| \(690\) |
\begin{align*}
x y^{\prime \prime }+a \left (-y+x y^{\prime }\right )^{2}-b&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.792 |
|
| \(691\) |
\begin{align*}
x^{2} y^{\prime \prime }+a \left (-y+x y^{\prime }\right )^{2}-b \,x^{2}&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.614 |
|
| \(692\) |
\begin{align*}
2 y+a y^{3}+9 x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.485 |
|
| \(693\) |
\begin{align*}
x^{3} y^{\prime \prime }-a \left (-y+x y^{\prime }\right )^{2}&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✗ |
0.781 |
|
| \(694\) |
\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]] |
✓ |
✓ |
✗ |
0.589 |
|
| \(695\) |
\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]] |
✓ |
✓ |
✗ |
0.732 |
|
| \(696\) |
\begin{align*}
\left (-y+x y^{\prime }\right )^{3}+x^{4} y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
1.004 |
|
| \(697\) |
\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] |
✓ |
✓ |
✗ |
95.096 |
|
| \(698\) |
\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]] |
✓ |
✓ |
✗ |
6.622 |
|
| \(699\) |
\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]] |
✓ |
✓ |
✗ |
0.480 |
|
| \(700\) |
\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]] |
✓ |
✓ |
✗ |
390.931 |
|
| \(701\) |
\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]] |
✓ |
✓ |
✗ |
244.749 |
|
| \(702\) |
\begin{align*}
2 y^{\prime } \left (y^{\prime }+1\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]] |
✓ |
✓ |
✗ |
0.547 |
|
| \(703\) |
\begin{align*}
\left (x -y\right ) y^{\prime \prime }-\left (y^{\prime }+1\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]] |
✓ |
✓ |
✗ |
0.510 |
|
| \(704\) |
\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]] |
✓ |
✓ |
✗ |
4.250 |
|
| \(705\) |
\begin{align*}
3 y y^{\prime \prime }-2 {y^{\prime }}^{2}-a \,x^{2}-b x -c&=0 \\
\end{align*} |
[NONE] |
✓ |
✓ |
✗ |
0.586 |
|
| \(706\) |
\begin{align*}
f \left (x \right )+a y y^{\prime }+{y^{\prime }}^{2} x +x y y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✗ |
0.549 |
|
| \(707\) |
\begin{align*}
x y y^{\prime \prime }-2 {y^{\prime }}^{2} x +\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]] |
✓ |
✓ |
✗ |
0.463 |
|
| \(708\) |
\begin{align*}
x y y^{\prime \prime }+\left (\frac {a x}{\sqrt {b^{2}-x^{2}}}-x \right ) {y^{\prime }}^{2}-y^{\prime } y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
4.283 |
|
| \(709\) |
\begin{align*}
x^{2} \left (x +y\right ) y^{\prime \prime }-\left (-y+x y^{\prime }\right )^{2}&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✗ |
1.119 |
|
| \(710\) |
\begin{align*}
x^{2} \left (x -y\right ) y^{\prime \prime }+a \left (-y+x y^{\prime }\right )^{2}&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✗ |
1.025 |
|
| \(711\) |
\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]] |
✓ |
✓ |
✗ |
0.619 |
|
| \(712\) |
\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]] |
✓ |
✓ |
✗ |
1.041 |
|
| \(713\) |
\begin{align*}
x \left (1+x \right )^{2} y y^{\prime \prime }-x \left (1+x \right )^{2} {y^{\prime }}^{2}+2 \left (1+x \right )^{2} y y^{\prime }-a \left (x +2\right ) y^{2}&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✗ |
2.057 |
|
| \(714\) |
\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]] |
✓ |
✓ |
✗ |
1.341 |
|
| \(715\) |
\begin{align*}
\left (y^{2}+x^{2}\right ) y^{\prime \prime }-\left (1+{y^{\prime }}^{2}\right ) \left (-y+x y^{\prime }\right )&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
✓ |
✗ |
1.147 |
|
| \(716\) |
\begin{align*}
\left (y^{2}+x^{2}\right ) y^{\prime \prime }-2 \left (1+{y^{\prime }}^{2}\right ) \left (-y+x y^{\prime }\right )&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
✓ |
✗ |
1.088 |
|
| \(717\) |
\begin{align*}
2 \left (1-y\right ) y y^{\prime \prime }-\left (-2 y+1\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]] |
✓ |
✓ |
✗ |
2.641 |
|
| \(718\) |
\begin{align*}
x y^{2} y^{\prime \prime }-a&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.344 |
|
| \(719\) |
\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]] |
✓ |
✓ |
✗ |
0.691 |
|
| \(720\) |
\begin{align*}
\left (x +y\right ) \left (-y+x y^{\prime }\right )^{3}+x^{3} y^{2} y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
1.128 |
|
| \(721\) |
\begin{align*}
\left (c +2 b x +a \,x^{2}+y^{2}\right )^{2} y^{\prime \prime }+d y&=0 \\
\end{align*} |
[NONE] |
✓ |
✓ |
✗ |
0.967 |
|
| \(722\) |
\begin{align*}
\left (-y+x y^{\prime }\right ) y^{\prime \prime }+4 {y^{\prime }}^{2}&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
1.203 |
|
| \(723\) |
\begin{align*}
\left ({y^{\prime }}^{2}+a \left (-y+x y^{\prime }\right )\right ) y^{\prime \prime }-b&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.691 |
|
| \(724\) |
\begin{align*}
\left (a \sqrt {1+{y^{\prime }}^{2}}-x y^{\prime }\right ) y^{\prime \prime }-{y^{\prime }}^{2}-1&=0 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✗ |
158.024 |
|
| \(725\) |
\begin{align*}
{y^{\prime \prime }}^{2}-a y-b&=0 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
✗ |
0.182 |
|
| \(726\) |
\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] |
✓ |
✓ |
✗ |
0.115 |
|
| \(727\) |
\begin{align*}
4 {y^{\prime }}^{2}-2 \left (3 x y^{\prime }+y\right ) y^{\prime \prime }+3 x^{2} {y^{\prime \prime }}^{2}&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
3.315 |
|
| \(728\) |
\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 {y^{\prime }}^{2} x&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
14.276 |
|
| \(729\) |
\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]] |
✓ |
✓ |
✗ |
0.098 |
|
| \(730\) |
\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]] |
✓ |
✓ |
✗ |
0.097 |
|
| \(731\) |
\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]] |
✓ |
✓ |
✗ |
0.269 |
|
| \(732\) |
\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 |
✓ |
✓ |
✓ |
0.106 |
|
| \(733\) |
\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 |
✓ |
✓ |
✓ |
0.097 |
|
| \(734\) |
\begin{align*}
x^{\prime }&=x \cos \left (t \right ) \\
y^{\prime }&=x \,{\mathrm e}^{-\sin \left (t \right )} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.083 |
|
| \(735\) |
\begin{align*}
x^{\prime } t +y&=0 \\
t y^{\prime }+x&=0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.099 |
|
| \(736\) |
\begin{align*}
x^{\prime } t +2 x&=t \\
t y^{\prime }-\left (t +2\right ) x-t y&=-t \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.122 |
|
| \(737\) |
\begin{align*}
x^{\prime } t +2 x-2 y&=t \\
t y^{\prime }+x+5 y&=t^{2} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.128 |
|
| \(738\) |
\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 (\cos \left (t \right ) t -\sin \left (t \right )\right ) x+t \left (1-\cos \left (t \right ) t \right ) y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.108 |
|
| \(739\) |
\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 |
✓ |
✓ |
✗ |
0.143 |
|
| \(740\) |
\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 |
✓ |
✓ |
✓ |
0.154 |
|
| \(741\) |
\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 |
✓ |
✓ |
✓ |
0.110 |
|
| \(742\) |
\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 |
✓ |
✓ |
✗ |
0.103 |
|
| \(743\) |
\begin{align*}
x^{\prime } t -t y^{\prime }-2 y&=0 \\
t x^{\prime \prime }+2 x^{\prime }+t x&=0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.103 |
|
| \(744\) |
\begin{align*}
x^{\prime \prime }+a y&=0 \\
y^{\prime \prime }-a^{2} y&=0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.107 |
|
| \(745\) |
\begin{align*}
x^{\prime \prime }&=a x+b y \\
y^{\prime \prime }&=c x+d y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.125 |
|
| \(746\) |
\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 |
✓ |
✓ |
✗ |
0.116 |
|
| \(747\) |
\begin{align*}
x^{\prime \prime }+x+y&=-5 \\
y^{\prime \prime }-4 x-3 y&=-3 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.103 |
|
| \(748\) |
\begin{align*}
x^{\prime \prime }+6 x+7 y&=0 \\
y^{\prime \prime }+3 x+2 y&=2 t \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.108 |
|
| \(749\) |
\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 |
✓ |
✓ |
✓ |
0.132 |
|
| \(750\) |
\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 |
✓ |
✓ |
✗ |
0.181 |
|
| \(751\) |
\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 |
✓ |
✓ |
✗ |
0.125 |
|
| \(752\) |
\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 |
✓ |
✓ |
✗ |
0.145 |
|
| \(753\) |
\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 |
✓ |
✓ |
✓ |
0.124 |
|
| \(754\) |
\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 |
✓ |
✓ |
✓ |
0.128 |
|
| \(755\) |
\begin{align*}
x^{\prime \prime }-x^{\prime }+y^{\prime }&=0 \\
x^{\prime \prime }+y^{\prime \prime }-x&=0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.124 |
|
| \(756\) |
\begin{align*}
x^{\prime } t&=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 |
✓ |
✓ |
✗ |
0.126 |
|
| \(757\) |
\begin{align*}
a t x^{\prime }&=b c \left (y-z\right ) \\
b t y^{\prime }&=c a \left (-x+z\right ) \\
c t z^{\prime }&=a b \left (x-y\right ) \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.113 |
|
| \(758\) |
\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 |
✓ |
✓ |
✗ |
0.190 |
|
| \(759\) |
\begin{align*}
x^{\prime }&=-x \left (x+y\right ) \\
y^{\prime }&=y \left (x+y\right ) \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.109 |
|
| \(760\) |
\begin{align*}
x^{\prime }&=\left (a y+b \right ) x \\
y^{\prime }&=\left (c x+d \right ) y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.104 |
|
| \(761\) |
\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 |
✓ |
✓ |
✗ |
0.104 |
|
| \(762\) |
\begin{align*}
x^{\prime }&=y^{2}-\cos \left (x\right ) \\
y^{\prime }&=-y \sin \left (x\right ) \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.096 |
|
| \(763\) |
\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 |
✓ |
✓ |
✓ |
0.095 |
|
| \(764\) |
\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 |
✓ |
✓ |
✗ |
0.153 |
|
| \(765\) |
\begin{align*}
{x^{\prime }}^{2}+x^{\prime } t +a y^{\prime }-x&=0 \\
x^{\prime } y^{\prime }+t y^{\prime }-y&=0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.153 |
|
| \(766\) |
\begin{align*}
x&=x^{\prime } t +f \left (x^{\prime }, y^{\prime }\right ) \\
y&=t y^{\prime }+g \left (x^{\prime }, y^{\prime }\right ) \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.148 |
|
| \(767\) |
\begin{align*}
x^{\prime }&=y-z \\
y^{\prime }&=x^{2}+y \\
z^{\prime }&=x^{2}+z \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.132 |
|
| \(768\) |
\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 |
✓ |
✓ |
✗ |
0.170 |
|
| \(769\) |
\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 (-x+z\right ) \left (-y+z\right ) z^{\prime }&=f \left (t \right ) \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.143 |
|
| \(770\) |
\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] |
✓ |
✓ |
✗ |
142.235 |
|
| \(771\) |
\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] |
✓ |
✓ |
✗ |
136.812 |
|
| \(772\) |
\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] |
✓ |
✓ |
✗ |
151.726 |
|
| \(773\) |
\begin{align*}
\left (x^{2}-1\right ) y^{\prime }+\lambda \left (y^{2}-2 x y+1\right )&=0 \\
\end{align*} |
[_rational, _Riccati] |
✓ |
✓ |
✗ |
10.065 |
|
| \(774\) |
\begin{align*}
\left (a \,x^{2}+b \right ) y^{\prime }+\alpha y^{2}+\beta x y+\gamma &=0 \\
\end{align*} |
[_rational, _Riccati] |
✓ |
✓ |
✗ |
552.357 |
|
| \(775\) |
\begin{align*}
x^{3} y^{\prime }&=x^{3} a y^{2}+x \left (b x +c \right ) y+\alpha x +\beta \\
\end{align*} |
[_rational, _Riccati] |
✓ |
✓ |
✗ |
129.691 |
|
| \(776\) |
\begin{align*}
y^{\prime }&=\sigma y^{2}+a +b \,{\mathrm e}^{\lambda x}+c \,{\mathrm e}^{2 \lambda x} \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✗ |
47.694 |
|
| \(777\) |
\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] |
✓ |
✓ |
✗ |
133.017 |
|
| \(778\) |
\begin{align*}
y^{\prime }&=\cosh \left (\lambda x \right ) a y^{2}+b \cosh \left (\lambda x \right ) \sinh \left (\lambda x \right )^{n} \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✗ |
147.332 |
|
| \(779\) |
\begin{align*}
y^{\prime }&=y^{2}+a \lambda -a \left (a +\lambda \right ) \tanh \left (\lambda x \right )^{2} \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✗ |
36.894 |
|
| \(780\) |
\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] |
✓ |
✓ |
✗ |
131.520 |
|
| \(781\) |
\begin{align*}
y^{\prime }&=y^{2}+a \lambda -a \left (a +\lambda \right ) \coth \left (\lambda x \right )^{2} \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✗ |
37.337 |
|
| \(782\) |
\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] |
✓ |
✓ |
✗ |
68.757 |
|
| \(783\) |
\begin{align*}
y^{\prime }&=y^{2}+a \lambda +a \left (\lambda -a \right ) \tan \left (\lambda x \right )^{2} \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✗ |
19.966 |
|
| \(784\) |
\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] |
✓ |
✓ |
✗ |
136.383 |
|
| \(785\) |
\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] |
✓ |
✓ |
✗ |
90.375 |
|
| \(786\) |
\begin{align*}
y^{\prime }&=\cos \left (\lambda x \right ) a y^{2}+b \cos \left (\lambda x \right ) \sin \left (\lambda x \right )^{n} \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✗ |
157.518 |
|
| \(787\) |
\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] |
✓ |
✓ |
✗ |
50.322 |
|
| \(788\) |
\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] |
✓ |
✓ |
✗ |
64.366 |
|
| \(789\) |
\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] |
✓ |
✓ |
✗ |
54.357 |
|
| \(790\) |
\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] |
✓ |
✓ |
✗ |
84.839 |
|
| \(791\) |
\begin{align*}
x y^{\prime }&=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] |
✓ |
✓ |
✗ |
20.965 |
|
| \(792\) |
\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] |
✓ |
✓ |
✗ |
12.161 |
|
| \(793\) |
\begin{align*}
y^{\prime } y-y&=-\frac {2 x}{9}+A +\frac {B}{\sqrt {x}} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✗ |
195.842 |
|
| \(794\) |
\begin{align*}
y^{\prime } y-y&=\frac {A}{x}-\frac {A^{2}}{x^{3}} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✗ |
52.861 |
|
| \(795\) |
\begin{align*}
y^{\prime } y-y&=-\frac {2 x}{9}+6 A^{2} \left (1+\frac {2 A}{\sqrt {x}}\right ) \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✗ |
142.803 |
|
| \(796\) |
\begin{align*}
y^{\prime } y-y&=\frac {4}{9} x +2 A \,x^{2}+2 A^{2} x^{3} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✗ |
90.083 |
|
| \(797\) |
\begin{align*}
y^{\prime } y-y&=\frac {A}{x} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✗ |
129.450 |
|
| \(798\) |
\begin{align*}
y^{\prime } y-y&=-\frac {9 x}{100}+\frac {A}{x^{{5}/{3}}} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✗ |
136.084 |
|
| \(799\) |
\begin{align*}
y^{\prime } y-y&=-\frac {2 x}{9}+\frac {A}{\sqrt {x}} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✗ |
112.157 |
|
| \(800\) |
\begin{align*}
y^{\prime } y-y&=\frac {A}{\sqrt {x}} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✗ |
119.490 |
|
| \(801\) |
\begin{align*}
y^{\prime } y-y&=A \,x^{2}-\frac {9}{625 A} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✗ |
88.698 |
|
| \(802\) |
\begin{align*}
y^{\prime } y-y&=-\frac {6}{25} x -A \,x^{2} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✗ |
95.212 |
|
| \(803\) |
\begin{align*}
y^{\prime } y-y&=\frac {6}{25} x -A \,x^{2} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✗ |
95.165 |
|
| \(804\) |
\begin{align*}
y^{\prime } y&=\left (a x +b \right ) y+1 \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✗ |
130.379 |
|
| \(805\) |
\begin{align*}
y^{\prime } y&=\frac {y}{\left (a x +b \right )^{2}}+1 \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✗ |
96.091 |
|
| \(806\) |
\begin{align*}
y^{\prime } y&=\left (a -\frac {1}{a x}\right ) y+1 \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✗ |
154.925 |
|
| \(807\) |
\begin{align*}
y^{\prime } y&=a \,{\mathrm e}^{\lambda x} y+1 \\
\end{align*} |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✗ |
63.072 |
|
| \(808\) |
\begin{align*}
y^{\prime } y+x \left (a \,x^{2}+b \right ) y+x&=0 \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✗ |
228.819 |
|
| \(809\) |
\begin{align*}
y^{\prime } y+a \left (1-\frac {1}{x}\right ) y&=a^{2} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✗ |
177.737 |
|
| \(810\) |
\begin{align*}
y^{\prime } y-a \left (1-\frac {b}{x}\right ) y&=a^{2} b \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✗ |
185.558 |
|
| \(811\) |
\begin{align*}
y^{\prime } y&=a \left (-n b +x \right ) x^{n -1} y+c \left (x^{2}-\left (1+2 n \right ) b x +n \left (n +1\right ) b^{2}\right ) x^{2 n -1} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✗ |
384.433 |
|
| \(812\) |
\begin{align*}
y^{\prime } y-a \left (1-\frac {b}{\sqrt {x}}\right ) y&=\frac {a^{2} b}{\sqrt {x}} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✗ |
219.747 |
|
| \(813\) |
\begin{align*}
y^{\prime } y&=\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‘]] |
✓ |
✓ |
✗ |
271.728 |
|
| \(814\) |
\begin{align*}
y^{\prime } y+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‘]] |
✓ |
✓ |
✗ |
168.952 |
|
| \(815\) |
\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‘]] |
✓ |
✓ |
✗ |
968.244 |
|
| \(816\) |
\begin{align*}
\left (x y+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‘]] |
✓ |
✓ |
✗ |
498.445 |
|
| \(817\) |
\begin{align*}
y^{\prime }&=-y^{3}+3 a^{2} x^{2} y-2 a^{3} x^{3}+a \\
\end{align*} |
[_Abel] |
✓ |
✓ |
✗ |
47.571 |
|
| \(818\) |
\begin{align*}
y^{\prime }&=-y^{3}+\left (a x +b \right ) y^{2} \\
\end{align*} |
[_Abel] |
✓ |
✓ |
✗ |
100.781 |
|
| \(819\) |
\begin{align*}
y^{\prime }&=-y^{3}+\frac {y^{2}}{\left (a x +b \right )^{2}} \\
\end{align*} |
[_rational, _Abel] |
✓ |
✓ |
✗ |
64.329 |
|
| \(820\) |
\begin{align*}
x^{2} y^{\prime }&=y^{3}-3 y a^{2} x^{4}+2 a^{3} x^{6}+2 a \,x^{3} \\
\end{align*} |
[_rational, _Abel] |
✓ |
✓ |
✗ |
21.972 |
|
| \(821\) |
\begin{align*}
y^{\prime }&=-y^{3}+a \,{\mathrm e}^{\lambda x} y^{2} \\
\end{align*} |
[_Abel] |
✓ |
✓ |
✗ |
54.804 |
|
| \(822\) |
\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] |
✓ |
✓ |
✗ |
26.172 |
|
| \(823\) |
\begin{align*}
y^{\prime \prime }-\left (a \,x^{2}+b \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
12.537 |
|
| \(824\) |
\begin{align*}
y^{\prime \prime }-\left (a \,x^{2}+b c x \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
9.876 |
|
| \(825\) |
\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]] |
✓ |
✓ |
✗ |
10.545 |
|
| \(826\) |
\begin{align*}
y^{\prime \prime }+\left (a \,x^{2 n}+b \,x^{n -1}\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
9.343 |
|
| \(827\) |
\begin{align*}
y^{\prime \prime }+a y^{\prime }-\left (b \,x^{2}+c \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
21.259 |
|
| \(828\) |
\begin{align*}
y^{\prime \prime }+x y^{\prime }+\left (n -1\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
20.625 |
|
| \(829\) |
\begin{align*}
2 n y-2 x y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
17.754 |
|
| \(830\) |
\begin{align*}
b y+a x y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
18.812 |
|
| \(831\) |
\begin{align*}
y^{\prime \prime }+a x y^{\prime }+b x y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
15.999 |
|
| \(832\) |
\begin{align*}
y^{\prime \prime }+a x y^{\prime }+\left (b x +c \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
16.698 |
|
| \(833\) |
\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]] |
✓ |
✓ |
✗ |
32.225 |
|
| \(834\) |
\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]] |
✓ |
✓ |
✗ |
19.086 |
|
| \(835\) |
\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]] |
✓ |
✓ |
✗ |
24.356 |
|
| \(836\) |
\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]] |
✓ |
✓ |
✗ |
23.429 |
|
| \(837\) |
\begin{align*}
y^{\prime \prime }+a \,x^{n} y^{\prime }+b \,x^{n -1} y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
25.756 |
|
| \(838\) |
\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]] |
✓ |
✓ |
✗ |
20.087 |
|
| \(839\) |
\begin{align*}
y^{\prime \prime }+2 a \,x^{n} y^{\prime }+\left (a^{2} x^{2 n}+b \,x^{2 m}+a n \,x^{n -1}+c \,x^{m -1}\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
28.461 |
|
| \(840\) |
\begin{align*}
x y^{\prime \prime }+a y^{\prime }+\left (b x +c \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
25.345 |
|
| \(841\) |
\begin{align*}
x y^{\prime \prime }+\left (1-3 n \right ) y^{\prime }-a^{2} n^{2} x^{2 n -1} y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✗ |
48.763 |
|
| \(842\) |
\begin{align*}
x y^{\prime \prime }+\left (-x +b \right ) y^{\prime }-a y&=0 \\
\end{align*} |
[_Laguerre] |
✓ |
✓ |
✗ |
21.290 |
|
| \(843\) |
\begin{align*}
x y^{\prime \prime }+\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]] |
✓ |
✓ |
✗ |
40.333 |
|
| \(844\) |
\begin{align*}
\left (a b x +a n +b m \right ) y+\left (m +n +x \left (a +b \right )\right ) y^{\prime }+x y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
27.638 |
|
| \(845\) |
\begin{align*}
x y^{\prime \prime }+\left (a x +b \right ) y^{\prime }+\left (c x +d \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
36.851 |
|
| \(846\) |
\begin{align*}
x y^{\prime \prime }+\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]] |
✓ |
✓ |
✗ |
99.802 |
|
| \(847\) |
\begin{align*}
x y^{\prime \prime }+\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]] |
✓ |
✓ |
✗ |
99.035 |
|
| \(848\) |
\begin{align*}
x y^{\prime \prime }+\left (x^{n}+1-n \right ) y^{\prime }+b \,x^{2 n -1} y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
55.185 |
|
| \(849\) |
\begin{align*}
x y^{\prime \prime }+\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]] |
✓ |
✓ |
✗ |
27.630 |
|
| \(850\) |
\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]] |
✓ |
✓ |
✗ |
75.557 |
|
| \(851\) |
\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]] |
✓ |
✓ |
✗ |
79.864 |
|
| \(852\) |
\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]] |
✓ |
✓ |
✗ |
94.395 |
|
| \(853\) |
\begin{align*}
x^{2} y^{\prime \prime }+\left (a \,x^{2}+b x +c \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
14.129 |
|
| \(854\) |
\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]] |
✓ |
✓ |
✗ |
13.954 |
|
| \(855\) |
\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]] |
✓ |
✓ |
✗ |
84.519 |
|
| \(856\) |
\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]] |
✓ |
✓ |
✗ |
22.911 |
|
| \(857\) |
\begin{align*}
x^{2} y^{\prime \prime }+\left (a x +b \right ) y^{\prime }+c y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
28.383 |
|
| \(858\) |
\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]] |
✓ |
✓ |
✗ |
22.009 |
|
| \(859\) |
\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]] |
✓ |
✓ |
✗ |
98.886 |
|
| \(860\) |
\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]] |
✓ |
✓ |
✗ |
36.588 |
|
| \(861\) |
\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]] |
✓ |
✓ |
✗ |
102.091 |
|
| \(862\) |
\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]] |
✓ |
✓ |
✗ |
47.090 |
|
| \(863\) |
\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]] |
✓ |
✓ |
✗ |
24.048 |
|
| \(864\) |
\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]] |
✓ |
✓ |
✗ |
92.239 |
|
| \(865\) |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }+n \left (n -1\right ) y&=0 \\
\end{align*} |
[_Gegenbauer] |
✓ |
✓ |
✓ |
20.255 |
|
| \(866\) |
\begin{align*}
\left (-a^{2}+x^{2}\right ) y^{\prime \prime }+b y^{\prime }-6 y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
67.998 |
|
| \(867\) |
\begin{align*}
n \left (n +1\right ) y-2 x y^{\prime }+\left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
[_Gegenbauer] |
✓ |
✓ |
✗ |
109.110 |
|
| \(868\) |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+\nu \left (\nu +1\right ) y&=0 \\
\end{align*} |
[_Gegenbauer] |
✓ |
✓ |
✗ |
103.031 |
|
| \(869\) |
\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] |
✓ |
✓ |
✗ |
68.237 |
|
| \(870\) |
\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] |
✓ |
✓ |
✗ |
67.632 |
|
| \(871\) |
\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]] |
✓ |
✓ |
✗ |
161.178 |
|
| \(872\) |
\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] |
✓ |
✓ |
✗ |
142.534 |
|
| \(873\) |
\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]] |
✓ |
✓ |
✗ |
199.740 |
|
| \(874\) |
\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]] |
✓ |
✓ |
✗ |
211.809 |
|
| \(875\) |
\begin{align*}
\left (a \,x^{2}+b \right ) y^{\prime \prime }+\left (1+2 n \right ) a x y^{\prime }+c y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
586.213 |
|
| \(876\) |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }+\left (2 a \,x^{2}+b \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
35.435 |
|
| \(877\) |
\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]] |
✓ |
✓ |
✗ |
180.990 |
|
| \(878\) |
\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 -\lambda b \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
65.554 |
|
| \(879\) |
\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 \lambda b \right ) y^{\prime }+\lambda ^{2} \left (c \,x^{2}+b \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
233.707 |
|
| \(880\) |
\begin{align*}
x \left (-1+x \right ) y^{\prime \prime }+\left (\left (\alpha +\beta +1\right ) x -\gamma \right ) y^{\prime }+\alpha \beta y&=0 \\
\end{align*} |
[_Jacobi] |
✓ |
✓ |
✗ |
236.538 |
|
| \(881\) |
\begin{align*}
x \left (x +a \right ) y^{\prime \prime }+\left (b x +c \right ) y^{\prime }+d y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
182.941 |
|
| \(882\) |
\begin{align*}
2 x \left (-1+x \right ) y^{\prime \prime }+\left (2 x -1\right ) y^{\prime }+\left (a x +b \right ) y&=0 \\
\end{align*} |
[_Jacobi] |
✓ |
✓ |
✗ |
53.193 |
|
| \(883\) |
\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]] |
✓ |
✓ |
✗ |
227.713 |
|
| \(884\) |
\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]] |
✓ |
✓ |
✗ |
253.360 |
|
| \(885\) |
\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]] |
✓ |
✓ |
✗ |
226.983 |
|
| \(886\) |
\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]] |
✓ |
✓ |
✗ |
148.695 |
|
| \(887\) |
\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]] |
✓ |
✓ |
✗ |
127.147 |
|
| \(888\) |
\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]] |
✓ |
✓ |
✗ |
74.742 |
|
| \(889\) |
\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]] |
✓ |
✓ |
✗ |
85.230 |
|
| \(890\) |
\begin{align*}
x^{3} y^{\prime \prime }+\left (a \,x^{3}+a b x -x^{2}+b \right ) y^{\prime }+y a^{2} b x&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
164.501 |
|
| \(891\) |
\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]] |
✓ |
✓ |
✗ |
227.711 |
|
| \(892\) |
\begin{align*}
x^{2} \left (a x +b \right ) y^{\prime \prime }+\left (c \,x^{2}+\left (a \lambda +2 b \right ) x +\lambda b \right ) y^{\prime }+\lambda \left (c -2 a \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
251.337 |
|
| \(893\) |
\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]] |
✓ |
✓ |
✗ |
211.621 |
|
| \(894\) |
\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]] |
✓ |
✓ |
✗ |
322.503 |
|
| \(895\) |
\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 (\alpha x +2 b -\beta \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
261.685 |
|
| \(896\) |
\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]] |
✓ |
✓ |
✗ |
306.194 |
|
| \(897\) |
\begin{align*}
x \left (-1+x \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]] |
✓ |
✓ |
✗ |
430.402 |
|
| \(898\) |
\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]] |
✓ |
✓ |
✗ |
1014.590 |
|
| \(899\) |
\begin{align*}
a \,x^{2} \left (-1+x \right )^{2} y^{\prime \prime }+\left (b \,x^{2}+c x +d \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
22.196 |
|
| \(900\) |
\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]] |
✓ |
✓ |
✗ |
202.945 |
|
| \(901\) |
\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]] |
✓ |
✓ |
✗ |
111.180 |
|
| \(902\) |
\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]] |
✓ |
✓ |
✗ |
107.061 |
|
| \(903\) |
\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]] |
✓ |
✓ |
✗ |
123.331 |
|
| \(904\) |
\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]] |
✓ |
✓ |
✗ |
111.373 |
|
| \(905\) |
\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]] |
✓ |
✓ |
✗ |
97.426 |
|
| \(906\) |
\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]] |
✓ |
✓ |
✗ |
102.291 |
|
| \(907\) |
\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)]‘]] |
✓ |
✓ |
✗ |
233.941 |
|
| \(908\) |
\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]] |
✓ |
✓ |
✗ |
152.894 |
|
| \(909\) |
\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]] |
✓ |
✓ |
✗ |
56.779 |
|
| \(910\) |
\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]] |
✓ |
✓ |
✗ |
239.073 |
|
| \(911\) |
\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]] |
✓ |
✓ |
✗ |
18.507 |
|
| \(912\) |
\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]] |
✓ |
✓ |
✗ |
8.837 |
|
| \(913\) |
\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]] |
✓ |
✓ |
✗ |
8.374 |
|
| \(914\) |
\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]] |
✓ |
✓ |
✗ |
8.634 |
|
| \(915\) |
\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]] |
✓ |
✓ |
✗ |
18.850 |
|
| \(916\) |
\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]] |
✓ |
✓ |
✗ |
28.249 |
|
| \(917\) |
\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]] |
✓ |
✓ |
✗ |
28.733 |
|
| \(918\) |
\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]] |
✓ |
✓ |
✗ |
30.552 |
|
| \(919\) |
\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]] |
✓ |
✓ |
✗ |
32.253 |
|
| \(920\) |
\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 \,{\mathrm e}^{\lambda x} b +b^{2}-\lambda b \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
45.439 |
|
| \(921\) |
\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]] |
✓ |
✓ |
✗ |
48.794 |
|
| \(922\) |
\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]] |
✓ |
✓ |
✗ |
19.632 |
|
| \(923\) |
\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]] |
✓ |
✓ |
✗ |
49.046 |
|
| \(924\) |
\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]] |
✓ |
✓ |
✗ |
19.210 |
|
| \(925\) |
\begin{align*}
\left (y^{2}+x^{2}\right ) \left (y^{\prime } y+x \right )&=\left (x^{2}+y^{2}+x \right ) \left (-y+x y^{\prime }\right ) \\
\end{align*} |
[_rational] |
✓ |
✓ |
✗ |
34.281 |
|
| \(926\) |
\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]] |
✓ |
✓ |
✗ |
89.591 |
|
| \(927\) |
\begin{align*}
-2 y+2 x y^{\prime }-x^{2} y^{\prime \prime }+\left (x^{2}-2 x +2\right ) y^{\prime \prime \prime }&=0 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.136 |
|
| \(928\) |
\begin{align*}
y-x y^{\prime }-y^{\prime \prime }+x y^{\prime \prime \prime }&=-x^{2}+1 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.135 |
|
| \(929\) |
\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 {y^{\prime }}^{2} x^{2}+36 x y y^{\prime }+6 y^{2}&=0 \\
\end{align*} |
[[_3rd_order, _exact, _nonlinear], [_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.154 |
|
| \(930\) |
\begin{align*}
x^{2} y^{\prime \prime \prime }-5 x y^{\prime \prime }+\left (4 x^{4}+5\right ) y^{\prime }-8 x^{3} y&=0 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.151 |
|
| \(931\) |
\begin{align*}
\left (-y+x y^{\prime }\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]] |
✓ |
✓ |
✗ |
0.835 |
|
| \(932\) |
\begin{align*}
x^{3} y^{\prime \prime }-\left (-y+x y^{\prime }\right )^{2}&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✗ |
2.904 |
|
| \(933\) |
\begin{align*}
y y^{\prime \prime }-{y^{\prime }}^{2}&=\ln \left (y\right ) y^{2}-x^{2} y^{2} \\
\end{align*} |
[[_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✗ |
0.722 |
|
| \(934\) |
\begin{align*}
x x^{\prime }&=1-t x \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✗ |
215.102 |
|
| \(935\) |
\begin{align*}
y^{\prime \prime }+x y^{\prime }+x^{2} y&=0 \\
y \left (1\right ) &= 0 \\
y^{\prime }\left (1\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
22.126 |
|
| \(936\) |
\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]] |
✓ |
✓ |
✗ |
0.144 |
|
| \(937\) |
\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]] |
✓ |
✓ |
✗ |
134.351 |
|
| \(938\) |
\begin{align*}
x^{\prime \prime }-\tan \left (t \right ) x^{\prime }+x&=0 \\
\end{align*} |
[_Lienard] |
✓ |
✓ |
✗ |
21.165 |
|
| \(939\) |
\begin{align*}
x^{\prime }&=x-x^{2} \\
y^{\prime }&=2 y-y^{2} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.077 |
|
| \(940\) |
\begin{align*}
x^{\prime }&=y \\
y^{\prime }&=\frac {y^{2}}{x} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.077 |
|
| \(941\) |
\begin{align*}
y^{\prime \prime \prime }+x y&=\sin \left (x \right ) \\
\end{align*} |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✗ |
0.127 |
|
| \(942\) |
\begin{align*}
y^{\prime \prime }+y^{\prime } y&=1 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✗ |
519.237 |
|
| \(943\) |
\begin{align*}
y^{\prime \prime \prime }+x y&=\cosh \left (x \right ) \\
\end{align*} |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✗ |
0.141 |
|
| \(944\) |
\begin{align*}
y^{\prime \prime \prime }+x y&=\cosh \left (x \right ) \\
\end{align*} |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✗ |
0.137 |
|
| \(945\) |
\begin{align*}
2 y^{\prime \prime }+3 y^{\prime }+4 x^{2} y&=1 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✗ |
26.210 |
|
| \(946\) |
\begin{align*}
y^{\prime \prime }-\left (-1+x \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]] |
✓ |
✓ |
✗ |
44.778 |
|
| \(947\) |
\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]] |
✓ |
✓ |
✗ |
28.412 |
|
| \(948\) |
\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]] |
✓ |
✓ |
✗ |
21.147 |
|
| \(949\) |
\begin{align*}
y^{\prime \prime }+3 y^{\prime }+\frac {y}{t}&=t \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✗ |
37.461 |
|
| \(950\) |
\begin{align*}
t^{3} y^{\prime \prime }-2 t y^{\prime }+y&=t^{4} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✗ |
74.017 |
|
| \(951\) |
\begin{align*}
n \left (n +1\right ) y-2 x y^{\prime }+\left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
[_Gegenbauer] |
✓ |
✓ |
✗ |
103.379 |
|
| \(952\) |
\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 |
✓ |
✓ |
✗ |
0.123 |
|
| \(953\) |
\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 |
✓ |
✓ |
✓ |
0.123 |
|
| \(954\) |
\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 |
✓ |
✓ |
✓ |
0.112 |
|
| \(955\) |
\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 |
✓ |
✓ |
✓ |
0.120 |
|
| \(956\) |
\begin{align*}
y^{\prime \prime }+x^{2} y^{\prime }-4 y&=x^{3} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✗ |
47.990 |
|
| \(957\) |
\begin{align*}
y^{\prime \prime }+x^{2} y^{\prime }-4 y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
19.656 |
|
| \(958\) |
\begin{align*}
y^{\prime \prime }+x^{2} y^{\prime }&=4 y \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
19.470 |
|
| \(959\) |
\begin{align*}
x^{\prime } t +2 x&=15 y \\
t y^{\prime }&=x \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.111 |
|
| \(960\) |
\begin{align*}
x^{\prime }&=x^{2} \\
y^{\prime }&={\mathrm e}^{t} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.106 |
|
| \(961\) |
\begin{align*}
y^{\prime }&=\sin \left (x y\right ) \\
y \left (0\right ) &= 0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✗ |
5.167 |
|
| \(962\) |
\begin{align*}
y^{\prime }-2 y \,{\mathrm e}^{x}&=2 \sqrt {y \,{\mathrm e}^{x}} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✗ |
92.092 |
|
| \(963\) |
\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)]‘]] |
✓ |
✓ |
✓ |
47.537 |
|
| \(964\) |
\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’)‘] |
✓ |
✓ |
✗ |
77.393 |
|
| \(965\) |
\begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&=4 \,{\mathrm e}^{-x} \\
y \left (\infty \right ) &= 0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
104.067 |
|
| \(966\) |
\begin{align*}
x_{1}^{\prime }&=-2 t x_{1}^{2} \\
x_{2}^{\prime }&=\frac {x_{2}+t}{t} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.099 |
|
| \(967\) |
\begin{align*}
x_{1}^{\prime }&={\mathrm e}^{t -x_{1}} \\
x_{2}^{\prime }&=2 \,{\mathrm e}^{x_{1}} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.098 |
|
| \(968\) |
\begin{align*}
x^{\prime }&=y \\
y^{\prime }&=\frac {y^{2}}{x} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.102 |
|
| \(969\) |
\begin{align*}
x_{1}^{\prime }&=\frac {x_{1}^{2}}{x_{2}} \\
x_{2}^{\prime }&=-x_{1}+x_{2} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.109 |
|
| \(970\) |
\begin{align*}
x^{\prime }&=\frac {{\mathrm e}^{-x}}{t} \\
y^{\prime }&=\frac {x \,{\mathrm e}^{-y}}{t} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.090 |
|
| \(971\) |
\begin{align*}
x^{\prime }&=\frac {t -y}{-x+y} \\
y^{\prime }&=\frac {x-t}{-x+y} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.112 |
|
| \(972\) |
\begin{align*}
x^{\prime \prime }&=y \\
y^{\prime \prime }&=x \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.127 |
|
| \(973\) |
\begin{align*}
x^{\prime \prime }+y^{\prime }+x&=0 \\
x^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.188 |
|
| \(974\) |
\begin{align*}
x^{\prime \prime }&=3 x+y \\
y^{\prime }&=-2 x \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.116 |
|
| \(975\) |
\begin{align*}
x^{\prime }&=x^{2}+y^{2} \\
y^{\prime }&=2 x y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.112 |
|
| \(976\) |
\begin{align*}
x^{\prime }&=-\frac {1}{y} \\
y^{\prime }&=\frac {1}{x} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.088 |
|
| \(977\) |
\begin{align*}
x^{\prime }&=\frac {x}{y} \\
y^{\prime }&=\frac {y}{x} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.096 |
|
| \(978\) |
\begin{align*}
x^{\prime }&=\frac {y}{x-y} \\
y^{\prime }&=\frac {x}{x-y} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.102 |
|
| \(979\) |
\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 |
✓ |
✓ |
✗ |
0.105 |
|
| \(980\) |
\begin{align*}
{\mathrm e}^{t} x^{\prime }&=\frac {1}{y} \\
{\mathrm e}^{t} y^{\prime }&=\frac {1}{x} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.106 |
|
| \(981\) |
\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 |
✓ |
✓ |
✓ |
0.111 |
|
| \(982\) |
\begin{align*}
x^{\prime }&=-2 t x+y \\
y^{\prime }&=3 x-y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.095 |
|
| \(983\) |
\begin{align*}
x^{\prime }&=-x+t y \\
y^{\prime }&=t x-y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.090 |
|
| \(984\) |
\begin{align*}
x^{\prime }&=-x+y+x^{2} \\
y^{\prime }&=y-2 x y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.109 |
|
| \(985\) |
\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 |
✓ |
✓ |
✗ |
0.092 |
|
| \(986\) |
\begin{align*}
x^{\prime }&=3 x-x^{2} \\
y^{\prime }&=2 x y-3 y+2 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.112 |
|
| \(987\) |
\begin{align*}
x^{\prime }&=x-x y \\
y^{\prime }&=y+2 x y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.087 |
|
| \(988\) |
\begin{align*}
x^{\prime }&=-x+2 x y \\
y^{\prime }&=y-x^{2}-y^{2} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.108 |
|
| \(989\) |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+\alpha \left (\alpha +1\right ) y&=0 \\
\end{align*} |
[_Gegenbauer] |
✓ |
✓ |
✗ |
114.069 |
|
| \(990\) |
\begin{align*}
\left (t -1\right ) y^{\prime \prime }-3 t y^{\prime }+4 y&=\sin \left (t \right ) \\
y \left (-2\right ) &= 2 \\
y^{\prime }\left (-2\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✗ |
64.313 |
|
| \(991\) |
\begin{align*}
t \left (t -4\right ) y^{\prime \prime }+3 t y^{\prime }+4 y&=2 \\
y \left (3\right ) &= 0 \\
y^{\prime }\left (3\right ) &= -1 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
138.981 |
|
| \(992\) |
\begin{align*}
x^{\prime }&=-2 y+x y \\
y^{\prime }&=x+4 x y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.127 |
|
| \(993\) |
\begin{align*}
x^{\prime }&=1+5 y \\
y^{\prime }&=1-6 x^{2} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.090 |
|
| \(994\) |
\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] |
✓ |
✓ |
✗ |
50.277 |
|
| \(995\) |
\begin{align*}
n \,x^{3} y^{\prime \prime }&=\left (y-x y^{\prime }\right )^{2} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✗ |
4.960 |
|
| \(996\) |
\begin{align*}
y^{2} \left (x^{2} y^{\prime \prime }-x y^{\prime }+y\right )&=x^{3} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
2.562 |
|
| \(997\) |
\begin{align*}
x^{2} y^{2} y^{\prime \prime }-3 x y^{2} y^{\prime }+4 y^{3}+x^{6}&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
1.900 |
|
| \(998\) |
\begin{align*}
x^{2} y y^{\prime \prime }+{y^{\prime }}^{2} x^{2}-5 x y y^{\prime }&=4 y^{2} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✗ |
1.856 |
|
| \(999\) |
\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]] |
✓ |
✓ |
✗ |
0.794 |
|
| \(1000\) |
\begin{align*}
n \left (n +1\right ) y-2 x y^{\prime }+\left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
[_Gegenbauer] |
✓ |
✓ |
✗ |
102.416 |
|
| \(1001\) |
\begin{align*}
-y+x y^{\prime }-y^{\prime \prime }+x y^{\prime \prime \prime }&=0 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.144 |
|
| \(1002\) |
\begin{align*}
-2 x y+y^{\prime } \left (x^{2}+2\right )-2 x y^{\prime \prime }+\left (x^{2}+2\right ) y^{\prime \prime \prime }&=x^{4}+12 \\
\end{align*} |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✗ |
0.161 |
|
| \(1003\) |
\begin{align*}
y^{\prime \prime }+\frac {y}{x^{2} \ln \left (x \right )}&={\mathrm e}^{x} \left (\frac {2}{x}+\ln \left (x \right )\right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✗ |
13.708 |
|
| \(1004\) |
\begin{align*}
y^{\prime }&=\frac {y^{2}}{z} \\
z^{\prime }&=\frac {y}{2} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.081 |
|
| \(1005\) |
\begin{align*}
y^{\prime }&=1-\frac {1}{z} \\
z^{\prime }&=\frac {1}{-x +y} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.092 |
|
| \(1006\) |
\begin{align*}
y^{\prime }&=\frac {z^{2}}{y} \\
z^{\prime }&=\frac {y^{2}}{z} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.078 |
|
| \(1007\) |
\begin{align*}
y^{\prime }&=\frac {y^{2}}{z} \\
z^{\prime }&=\frac {z^{2}}{y} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.078 |
|
| \(1008\) |
\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 |
✓ |
✓ |
✓ |
0.161 |
|
| \(1009\) |
\begin{align*}
y^{\prime }+\frac {2 z}{x^{2}}&=1 \\
z^{\prime }+y&=x \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.076 |
|
| \(1010\) |
\begin{align*}
x^{\prime } t -x-3 y&=t \\
t y^{\prime }-x+y&=0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.081 |
|
| \(1011\) |
\begin{align*}
x^{\prime } t +6 x-y-3 z&=0 \\
t y^{\prime }+23 x-6 y-9 z&=0 \\
z^{\prime } t +x+y-2 z&=0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.117 |
|
| \(1012\) |
\begin{align*}
y^{\prime \prime }+3 x y^{\prime }+x^{2} y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
47.856 |
|
| \(1013\) |
\begin{align*}
x^{2} y^{\prime \prime }-\frac {x^{2} {y^{\prime }}^{2}}{2 y}+4 x y^{\prime }+4 y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✗ |
3.383 |
|
| \(1014\) |
\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]] |
✓ |
✓ |
✗ |
30.323 |
|
| \(1015\) |
\begin{align*}
\left (-y+x y^{\prime }\right )^{2}&=a \left (1+{y^{\prime }}^{2}\right ) \left (y^{2}+x^{2}\right )^{{3}/{2}} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
684.507 |
|
| \(1016\) |
\begin{align*}
\left (-y+x y^{\prime }\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)]‘]] |
✓ |
✓ |
✗ |
509.422 |
|
| \(1017\) |
\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]] |
✓ |
✓ |
✗ |
115.020 |
|
| \(1018\) |
\begin{align*}
16 \left (1+x \right )^{4} y^{\prime \prime \prime \prime }+96 \left (1+x \right )^{3} y^{\prime \prime \prime }+104 \left (1+x \right )^{2} y^{\prime \prime }+8 \left (1+x \right ) y^{\prime }+y&=x^{2}+4 x +3 \\
\end{align*} |
[[_high_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.240 |
|
| \(1019\) |
\begin{align*}
\sqrt {x}\, y^{\prime \prime }+2 x y^{\prime }+3 y&=x \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
58.093 |
|
| \(1020\) |
\begin{align*}
y^{\prime \prime }-2 b y^{\prime }+b^{2} x^{2} y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
45.703 |
|
| \(1021\) |
\begin{align*}
x^{2} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y&=0 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.185 |
|
| \(1022\) |
\begin{align*}
\left (-y+x y^{\prime }\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]] |
✓ |
✓ |
✗ |
0.687 |
|
| \(1023\) |
\begin{align*}
x^{\prime \prime }-3 x-4 y&=0 \\
x+y^{\prime \prime }+y&=0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.147 |
|
| \(1024\) |
\begin{align*}
y^{\prime }-\frac {\tan \left (y\right )}{1+x}&=\left (1+x \right ) {\mathrm e}^{x} \sec \left (y\right ) \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✓ |
71.453 |
|
| \(1025\) |
\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)]‘]] |
✓ |
✓ |
✓ |
31.893 |
|
| \(1026\) |
\begin{align*}
\left (-y+x y^{\prime }\right )^{2}&=a \left (1+{y^{\prime }}^{2}\right ) \left (y^{2}+x^{2}\right )^{{3}/{2}} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
682.009 |
|
| \(1027\) |
\begin{align*}
\left (-y+x y^{\prime }\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)]‘]] |
✓ |
✓ |
✗ |
521.882 |
|
| \(1028\) |
\begin{align*}
3 x y+y^{\prime } \left (x^{2}+2\right )+4 x y^{\prime \prime }+x^{2} y^{\prime \prime \prime }&=2 \\
\end{align*} |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✗ |
0.158 |
|
| \(1029\) |
\begin{align*}
2 x^{2} y y^{\prime \prime }+y^{2}&={y^{\prime }}^{2} x^{2} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✗ |
1.342 |
|
| \(1030\) |
\begin{align*}
x^{4} y^{\prime \prime }&=\left (x^{3}+2 x y\right ) y^{\prime }-4 y^{2} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✗ |
0.954 |
|
| \(1031\) |
\begin{align*}
x^{4} y^{\prime \prime }-x^{3} y^{\prime }&={y^{\prime }}^{2} x^{2}-4 y^{2} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✗ |
0.990 |
|
| \(1032\) |
\begin{align*}
y^{\prime \prime \prime }-x y^{\prime \prime }-y^{\prime }+x y&=0 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.148 |
|
| \(1033\) |
\begin{align*}
\left (-y+x y^{\prime }\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]] |
✓ |
✓ |
✗ |
0.657 |
|
| \(1034\) |
\begin{align*}
x^{\prime } t +y&=0 \\
t y^{\prime }+x&=0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.084 |
|
| \(1035\) |
\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]] |
✓ |
✓ |
✗ |
0.183 |
|
| \(1036\) |
\begin{align*}
16 \left (1+x \right )^{4} y^{\prime \prime \prime \prime }+96 \left (1+x \right )^{3} y^{\prime \prime \prime }+104 \left (1+x \right )^{2} y^{\prime \prime }+8 \left (1+x \right ) y^{\prime }+y&=x^{2}+4 x +3 \\
\end{align*} |
[[_high_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.243 |
|
| \(1037\) |
\begin{align*}
2 x^{2} y y^{\prime \prime }+4 y^{2}&={y^{\prime }}^{2} x^{2}+2 x y y^{\prime } \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✗ |
1.584 |
|
| \(1038\) |
\begin{align*}
\sqrt {x}\, y^{\prime \prime }+2 x y^{\prime }+3 y&=x \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
26.205 |
|
| \(1039\) |
\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]] |
✓ |
✓ |
✗ |
20.146 |
|
| \(1040\) |
\begin{align*}
x^{4} y^{\prime \prime }&=\left (y-x y^{\prime }\right )^{3} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
1.880 |
|
| \(1041\) |
\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]] |
✓ |
✓ |
✗ |
23.698 |
|
| \(1042\) |
\begin{align*}
y^{\prime \prime }+\left (1-\cot \left (x \right )\right ) y^{\prime }-y \cot \left (x \right )&=\sin \left (x \right )^{2} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✗ |
26.684 |
|
| \(1043\) |
\begin{align*}
x^{\prime } t&=t -2 x \\
t y^{\prime }&=t x+t y+2 x-t \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.089 |
|
| \(1044\) |
\begin{align*}
x y^{\prime \prime }-x y^{\prime }+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]] |
✓ |
✓ |
✗ |
34.425 |
|
| \(1045\) |
\begin{align*}
x^{\prime }&=x \cos \left (t \right )-\sin \left (t \right ) y \\
y^{\prime }&=\sin \left (t \right ) x+\cos \left (t \right ) y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.085 |
|
| \(1046\) |
\begin{align*}
x^{\prime }&=\left (3 t -1\right ) x-\left (-t +1\right ) y+t \,{\mathrm e}^{t^{2}} \\
y^{\prime }&=-\left (t +2\right ) x+\left (t -2\right ) y-{\mathrm e}^{t^{2}} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.092 |
|
| \(1047\) |
\begin{align*}
w_{1}^{\prime }&=w_{2} \\
w_{2}^{\prime }&=\frac {a w_{1}}{z^{2}} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.085 |
|
| \(1048\) |
\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]] |
✓ |
✓ |
✗ |
1.607 |
|
| \(1049\) |
\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]] |
✓ |
✓ |
✗ |
0.551 |
|
| \(1050\) |
\begin{align*}
x^{\prime }+t y&=-1 \\
x^{\prime }+y^{\prime }&=2 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.108 |
|
| \(1051\) |
\begin{align*}
x^{\prime }+y&=3 t \\
y^{\prime }-x^{\prime } t&=0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.121 |
|
| \(1052\) |
\begin{align*}
x^{\prime }-t y&=1 \\
y^{\prime }-x^{\prime } t&=3 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.115 |
|
| \(1053\) |
\begin{align*}
t^{2} x^{\prime }-y&=1 \\
y^{\prime }-2 x&=0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.085 |
|
| \(1054\) |
\begin{align*}
x^{\prime } t +y^{\prime }&=1 \\
y^{\prime }+x+{\mathrm e}^{x^{\prime }}&=1 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.456 |
|
| \(1055\) |
\begin{align*}
x x^{\prime }+y&=2 t \\
y^{\prime }+2 x^{2}&=1 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.089 |
|
| \(1056\) |
\begin{align*}
x^{\prime }&=x-x y \\
y^{\prime }&=-y+x y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.097 |
|
| \(1057\) |
\begin{align*}
x^{\prime }&=2 x-2 x y \\
y^{\prime }&=-y+x y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.099 |
|
| \(1058\) |
\begin{align*}
x^{\prime }&=x-4 x y \\
y^{\prime }&=-2 y+x y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.086 |
|
| \(1059\) |
\begin{align*}
x^{\prime }&=x \left (3-y\right ) \\
y^{\prime }&=y \left (x-5\right ) \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.095 |
|
| \(1060\) |
\begin{align*}
t^{2} x^{\prime \prime }+x^{\prime } t +\left (t^{2}-1\right ) x&=0 \\
x^{\prime }\left (0\right ) &= a \\
\end{align*} |
[_Bessel] |
✓ |
✓ |
✗ |
46.872 |
|
| \(1061\) |
\begin{align*}
x^{\prime }&=-x^{3} \\
y^{\prime }&=-y^{3} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.076 |
|
| \(1062\) |
\begin{align*}
n \left (n +1\right ) y-2 x y^{\prime }+\left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
[_Gegenbauer] |
✓ |
✓ |
✗ |
121.962 |
|
| \(1063\) |
\begin{align*}
y^{\prime }&=-\sqrt {1-y^{2}} \\
x^{\prime }&=x+2 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.083 |
|
| \(1064\) |
\begin{align*}
x^{\prime }&=-x^{2}-y \\
y^{\prime }&=x \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.081 |
|
| \(1065\) |
\begin{align*}
x^{\prime }&=2 x y \\
y^{\prime }&=3 y^{2}-x^{2} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.084 |
|
| \(1066\) |
\begin{align*}
x^{\prime }&=x^{2} \\
y^{\prime }&=2 y^{2}-x y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.082 |
|
| \(1067\) |
\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 |
✓ |
✓ |
✓ |
0.144 |
|
| \(1068\) |
\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 |
✓ |
✓ |
✓ |
0.165 |
|
| \(1069\) |
\begin{align*}
2 y^{\prime \prime \prime }+x y^{\prime \prime }+2 y^{\prime }+x y&=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]] |
✓ |
✓ |
✗ |
0.252 |
|
| \(1070\) |
\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 |
✓ |
✓ |
✗ |
0.136 |
|
| \(1071\) |
\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]] |
✓ |
✓ |
✗ |
4.012 |
|
| \(1072\) |
\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]] |
✓ |
✓ |
✗ |
0.732 |
|
| \(1073\) |
\begin{align*}
1+x y+y^{\prime } y&=0 \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✗ |
297.357 |
|
| \(1074\) |
\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 |
✓ |
✓ |
✓ |
0.071 |
|
| \(1075\) |
\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 |
✓ |
✓ |
✓ |
0.086 |
|
| \(1076\) |
\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 |
✓ |
✓ |
✗ |
0.125 |
|
| \(1077\) |
\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 |
✓ |
✓ |
✓ |
0.061 |
|
| \(1078\) |
\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 |
✓ |
✓ |
✓ |
0.119 |
|
| \(1079\) |
\begin{align*}
y^{\prime }&=y^{2}+x^{2} \\
y \left (0\right ) &= 2 \\
\end{align*} |
[[_Riccati, _special]] |
✓ |
✓ |
✗ |
172.194 |
|
| \(1080\) |
\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)]‘]] |
✓ |
✓ |
✗ |
122.749 |
|
| \(1081\) |
\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’)‘] |
✓ |
✓ |
✗ |
183.758 |
|
| \(1082\) |
\begin{align*}
y^{\prime }&=\sqrt {\sin \left (x \right )+y}-\cos \left (x \right ) \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
✓ |
165.441 |
|
| \(1083\) |
\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]] |
✓ |
✓ |
✗ |
139.569 |
|
| \(1084\) |
\begin{align*}
y^{\prime \prime \prime }&=\frac {24 x +24 y}{x^{3}} \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
0.173 |
|
| \(1085\) |
\begin{align*}
x y^{\prime \prime \prime }+2 x y^{\prime \prime }-x y^{\prime }-2 x y&=1 \\
\end{align*} |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
0.153 |
|
| \(1086\) |
\begin{align*}
y^{\prime \prime }&=x \\
y^{\prime \prime }&=y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.129 |
|
| \(1087\) |
\begin{align*}
y^{\prime \prime }&=x-2 \\
y^{\prime \prime }&=2+y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.132 |
|
| \(1088\) |
\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 |
✓ |
✓ |
✓ |
0.109 |
|
| \(1089\) |
\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 |
✓ |
✓ |
✓ |
0.106 |
|
| \(1090\) |
\begin{align*}
x^{\prime }&=y z \\
y^{\prime }&=x z \\
z^{\prime }&=x y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.118 |
|
| \(1091\) |
\begin{align*}
x^{\prime }&=x y \\
y^{\prime }&=1+y^{2} \\
z^{\prime }&=z \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.114 |
|
| \(1092\) |
\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 |
✓ |
✓ |
✓ |
0.073 |
|
| \(1093\) |
\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 |
✓ |
✓ |
✓ |
0.072 |
|
| \(1094\) |
\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 |
✓ |
✓ |
✓ |
0.072 |
|
| \(1095\) |
\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 |
✓ |
✓ |
✓ |
0.077 |
|
| \(1096\) |
\begin{align*}
x^{\prime \prime }&=y+4 \,{\mathrm e}^{-2 t} \\
y^{\prime \prime }&=x-{\mathrm e}^{-2 t} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.137 |
|
| \(1097\) |
\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 |
✓ |
✓ |
✓ |
0.130 |
|
| \(1098\) |
\begin{align*}
y^{\prime }&=y^{2}+x^{2} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[[_Riccati, _special]] |
✓ |
✓ |
✗ |
175.376 |
|
| \(1099\) |
\begin{align*}
y^{\prime \prime \prime }+x^{2} y&={\mathrm e}^{x} \\
\end{align*} |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✗ |
0.145 |
|
| \(1100\) |
\begin{align*}
x y^{\prime \prime \prime }+4 x y^{\prime \prime }-x y&=1 \\
\end{align*} |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✗ |
0.142 |
|
| \(1101\) |
\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 |
✓ |
✓ |
✓ |
0.200 |
|
| \(1102\) |
\begin{align*}
y^{\prime \prime \prime }-y \sin \left (x \right )&=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]] |
✓ |
✓ |
✗ |
0.110 |
|
| \(1103\) |
\begin{align*}
y^{\prime \prime \prime \prime }-\ln \left (1+x \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]] |
✓ |
✓ |
✗ |
0.436 |
|
| \(1104\) |
\begin{align*}
y^{\prime \prime \prime }-3 x^{2} y^{\prime }+2 x 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]] |
✓ |
✓ |
✗ |
0.113 |
|
| \(1105\) |
\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]] |
✓ |
✓ |
✗ |
0.114 |
|
| \(1106\) |
\begin{align*}
y^{\prime \prime \prime }+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✗ |
0.094 |
|
| \(1107\) |
\begin{align*}
y^{\prime \prime \prime }-2 x y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.097 |
|
| \(1108\) |
\begin{align*}
x_{1}^{\prime }&=x_{1}+\left (-t +1\right ) x_{2} \\
x_{2}^{\prime }&=\frac {x_{1}}{t}-x_{2} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.088 |
|
| \(1109\) |
\begin{align*}
x^{\prime } t&=3 x-2 y \\
t y^{\prime }&=x+y-t^{2} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.086 |
|
| \(1110\) |
\begin{align*}
x^{\prime } t&=3 x-2 y \\
t y^{\prime }&=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 |
✓ |
✓ |
✓ |
0.100 |
|
| \(1111\) |
\begin{align*}
x^{\prime }&=y^{2}-x^{2} \\
y^{\prime }&=2 x y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.094 |
|
| \(1112\) |
\begin{align*}
x^{\prime }&=y \\
y^{\prime }&=-\sin \left (x\right ) \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.078 |
|
| \(1113\) |
\begin{align*}
x^{\prime }&=y \\
y^{\prime }&=-4 \sin \left (x\right ) \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.091 |
|
| \(1114\) |
\begin{align*}
x^{\prime }&=x-x y \\
y^{\prime }&=-y+x y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.084 |
|
| \(1115\) |
\begin{align*}
x_{1}^{\prime }&=x_{2} \\
x_{2}^{\prime }&=\sin \left (x_{1}\right ) \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.077 |
|
| \(1116\) |
\begin{align*}
x_{1}^{\prime }&=x_{2} \\
x_{2}^{\prime }&=x_{1}-x_{1}^{3} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.080 |
|
| \(1117\) |
\begin{align*}
x^{\prime }&=x-x y \\
y^{\prime }&=-y+x y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.079 |
|
| \(1118\) |
\begin{align*}
x^{\prime }&=x^{2}-x \\
y^{\prime }&=-3 y+x y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.081 |
|
| \(1119\) |
\begin{align*}
x^{\prime }&=x-x y \\
y^{\prime }&=-y+x y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.081 |
|
| \(1120\) |
\begin{align*}
y^{\prime }&=-2 \\
z^{\prime }&=x \,{\mathrm e}^{2 x +y} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.159 |
|
| \(1121\) |
\begin{align*}
y^{\prime } y&=-x \\
y z^{\prime }&=2 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.095 |
|
| \(1122\) |
\begin{align*}
x y^{\prime }&=y \\
z^{\prime }&=3 y-x \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.117 |
|
| \(1123\) |
\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]] |
✓ |
✓ |
✗ |
0.162 |
|
| \(1124\) |
\begin{align*}
\left (-x^{4}+1\right ) y^{\prime \prime \prime }-24 x y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_3rd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✗ |
0.144 |
|
| \(1125\) |
\begin{align*}
x^{2} y^{\prime \prime \prime }-y^{\prime }+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.112 |
|
| \(1126\) |
\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)]‘]] |
✓ |
✓ |
✓ |
97.137 |
|
| \(1127\) |
\begin{align*}
y^{\prime }&=\tan \left (y\right ) \cot \left (x \right )-\cos \left (x \right ) \sec \left (y\right ) \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✓ |
68.766 |
|
| \(1128\) |
\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]] |
✓ |
✓ |
✗ |
790.796 |
|
| \(1129\) |
\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 |
✓ |
✓ |
✓ |
0.068 |
|
| \(1130\) |
\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 |
✓ |
✓ |
✓ |
0.109 |
|
| \(1131\) |
\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 |
✓ |
✓ |
✓ |
0.111 |
|
| \(1132\) |
\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 |
✓ |
✓ |
✓ |
0.084 |
|
| \(1133\) |
\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 |
✓ |
✓ |
✓ |
0.119 |
|
| \(1134\) |
\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 |
✓ |
✓ |
✓ |
0.109 |
|
| \(1135\) |
\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 |
✓ |
✓ |
✓ |
0.109 |
|
| \(1136\) |
\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 |
✓ |
✓ |
✗ |
0.115 |
|
| \(1137\) |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }+\sin \left (t \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
27.648 |
|
| \(1138\) |
\begin{align*}
t y^{\prime \prime \prime }+3 y^{\prime \prime }+t y^{\prime }+y&=0 \\
\end{align*}
Using Laplace transform method. |
[[_3rd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✗ |
0.154 |
|
| \(1139\) |
\begin{align*}
\left (\cos \left (2 t \right )+1\right ) y^{\prime \prime }-4 y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
12.453 |
|
| \(1140\) |
\begin{align*}
y_{1}^{\prime }&=y_{2} \\
y_{2}^{\prime }&=y_{1} y_{2} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.144 |
|
| \(1141\) |
\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 |
✓ |
✓ |
✓ |
0.152 |
|
| \(1142\) |
\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 |
✓ |
✓ |
✓ |
0.112 |
|
| \(1143\) |
\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 |
✓ |
✓ |
✓ |
0.148 |
|
| \(1144\) |
\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 |
✓ |
✓ |
✓ |
0.153 |
|
| \(1145\) |
\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 |
✓ |
✓ |
✓ |
0.149 |
|
| \(1146\) |
\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 |
✓ |
✓ |
✓ |
0.150 |
|
| \(1147\) |
\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 |
✓ |
✓ |
✗ |
0.147 |
|
| \(1148\) |
\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 |
✓ |
✓ |
✗ |
0.148 |
|
| \(1149\) |
\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 |
✓ |
✓ |
✓ |
0.164 |
|
| \(1150\) |
\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 |
✓ |
✓ |
✓ |
0.156 |
|
| \(1151\) |
\begin{align*}
\left (1-x \right ) y^{\prime \prime }-4 x y^{\prime }+5 y&=\cos \left (x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✗ |
50.376 |
|
| \(1152\) |
\begin{align*}
\sin \left (t \right ) y^{\prime \prime \prime }-\cos \left (t \right ) y^{\prime }&=2 \\
\end{align*} |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
✗ |
5.043 |
|
| \(1153\) |
\begin{align*}
x^{\prime \prime }&=4 y+{\mathrm e}^{t} \\
y^{\prime \prime }&=4 x-{\mathrm e}^{t} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.188 |
|
| \(1154\) |
\begin{align*}
y^{\prime }&=x^{2}-y^{2} \\
y \left (0\right ) &= 2 \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✗ |
109.538 |
|
| \(1155\) |
\begin{align*}
y^{\prime }&=y^{2}+x^{2} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[[_Riccati, _special]] |
✓ |
✓ |
✗ |
186.438 |
|
| \(1156\) |
\begin{align*}
y^{\prime \prime }-y+5 y^{\prime }&=t \\
2 y^{\prime }-x^{\prime \prime }+4 x&=2 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.233 |
|
| \(1157\) |
\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 |
✓ |
✓ |
✓ |
0.164 |
|
| \(1158\) |
\begin{align*}
x^{\prime \prime }&=y \\
y^{\prime \prime }&=x \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.179 |
|
| \(1159\) |
\begin{align*}
x^{\prime }&=\frac {1}{y} \\
y^{\prime }&=\frac {1}{x} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.162 |
|
| \(1160\) |
\begin{align*}
y^{\prime }+x \sin \left (2 y\right )&=x \,{\mathrm e}^{-x^{2}} \cos \left (y\right )^{2} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✗ |
109.691 |
|
| \(1161\) |
\begin{align*}
\left (x^{2}+1\right ) \ln \left (x^{2}+1\right ) y^{\prime }-2 x y&=\ln \left (x^{2}+1\right )-2 x \arctan \left (x \right ) \\
y \left (-\infty \right ) &= -\frac {\pi }{2} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
265.334 |
|
| \(1162\) |
\begin{align*}
y \left (1+\ln \left (y\right )\right ) y^{\prime \prime }+{y^{\prime }}^{2}&=2 x y \,{\mathrm e}^{x^{2}} \\
\end{align*} |
[[_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✗ |
4.158 |
|
| \(1163\) |
\begin{align*}
{y^{\prime \prime }}^{2}-y^{\prime } y^{\prime \prime \prime }&=\frac {{y^{\prime }}^{2}}{x^{2}} \\
\end{align*} |
[[_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
2.085 |
|
| \(1164\) |
\begin{align*}
x y^{\prime } \left (y y^{\prime \prime }-{y^{\prime }}^{2}\right )-y {y^{\prime }}^{2}&=x^{4} y^{3} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_poly_yn]] |
✓ |
✓ |
✗ |
9.991 |
|
| \(1165\) |
\begin{align*}
x^{4} y^{\prime \prime }&=\left (y-x y^{\prime }\right )^{3} \\
y \left (1\right ) &= 1 \\
y^{\prime }\left (1\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
1.460 |
|
| \(1166\) |
\begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&=4 \,{\mathrm e}^{-x} \\
y \left (\infty \right ) &= 0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
54.073 |
|
| \(1167\) |
\begin{align*}
x \left (1-x \ln \left (x \right )\right ) y^{\prime \prime }+\left (1+x^{2} \ln \left (x \right )\right ) y^{\prime }-\left (1+x \right ) y&=\left (1-x \ln \left (x \right )\right )^{2} {\mathrm e}^{x} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✗ |
256.622 |
|
| \(1168\) |
\begin{align*}
4 x y^{\prime \prime }+2 y^{\prime }+y&=\frac {6+x}{x^{2}} \\
y \left (\infty \right ) &= 0 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✗ |
222.705 |
|
| \(1169\) |
\begin{align*}
x^{3} \left (\ln \left (x \right )-1\right ) y^{\prime \prime }-x^{2} y^{\prime }+x y&=2 \ln \left (x \right ) \\
y \left (\infty \right ) &= 0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
154.792 |
|
| \(1170\) |
\begin{align*}
2 y^{\prime \prime }+4 x y^{\prime \prime \prime }+x^{2} y^{\prime \prime \prime \prime }&=0 \\
y \left (1\right ) &= 0 \\
y^{\prime }\left (1\right ) &= 0 \\
y \left (0\right ) &= y_{0} \\
\end{align*} |
[[_high_order, _missing_y]] |
✓ |
✓ |
✓ |
10.426 |
|
| \(1171\) |
\begin{align*}
x^{\prime }&=x \cos \left (t \right ) \\
2 y^{\prime }&=\left ({\mathrm e}^{t}+{\mathrm e}^{-t}\right ) y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.144 |
|
| \(1172\) |
\begin{align*}
x^{\prime }&=\frac {1}{y} \\
y^{\prime }&=\frac {1}{x} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.162 |
|
| \(1173\) |
\begin{align*}
x^{\prime } t&=t -2 x \\
t y^{\prime }&=t x+t y+2 x-t \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
0.096 |
|
| \(1174\) |
\begin{align*}
\left (\cos \left (x +y\right )+\sin \left (x -y\right )\right ) y^{\prime }&=\cos \left (2 x \right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✗ |
159.933 |
|
| \(1175\) |
\begin{align*}
x^{\prime }&=x-\frac {x y}{2} \\
y^{\prime }&=2 x y-\frac {6 y}{5} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✗ |
0.145 |
|
| \(1176\) |
\begin{align*}
\left (x^{3}+3 \ln \left (y\right )\right ) y&=x y^{\prime } \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
89.864 |
|
| \(1177\) |
\begin{align*}
y \left (x +y^{2}\right )+x^{2} \left (y-1\right ) y^{\prime }&=0 \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
✗ |
280.107 |
|
| \(1178\) |
\begin{align*}
x^{3}-2 x y^{2}+3 x^{2} y y^{\prime }&=-y+x y^{\prime } \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✗ |
186.388 |
|
| \(1179\) |
\begin{align*}
y^{\prime }&=\frac {\left (3 x +y^{3}-1\right )^{2}}{y^{2}} \\
\end{align*} |
[_rational] |
✓ |
✓ |
✓ |
244.022 |
|
| \(1180\) |
\begin{align*}
x y y^{\prime }-x^{2} \sqrt {1+y^{2}}&=\left (1+x \right ) \left (1+y^{2}\right ) \\
\end{align*} |
[‘x=_G(y,y’)‘] |
✓ |
✓ |
✓ |
223.886 |
|
| \(1181\) |
\begin{align*}
\left (3 x y+x +y\right ) y+\left (4 x y+x +2 y\right ) x y^{\prime }&=0 \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✗ |
292.425 |
|
| \(1182\) |
\begin{align*}
x^{2}-1+\left (x^{2} y^{2}+x^{3}+x \right ) y^{\prime }&=0 \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
✓ |
66.754 |
|
| \(1183\) |
\begin{align*}
y y^{\prime \prime \prime }&=y^{\prime } y^{\prime \prime } \\
\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]] |
✓ |
✓ |
✗ |
0.242 |
|
| \(1184\) |
\begin{align*}
-y^{\prime }+x y^{\prime \prime }&=x^{2} y y^{\prime } \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✗ |
4.638 |
|
| \(1185\) |
\begin{align*}
y y^{\prime \prime }&={y^{\prime }}^{2}+15 y^{2} \sqrt {x} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✗ |
1.553 |
|
| \(1186\) |
\begin{align*}
x^{2} y y^{\prime \prime }&=\left (y-x y^{\prime }\right )^{2} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✗ |
2.819 |
|
| \(1187\) |
\begin{align*}
y^{\prime \prime }+\frac {y^{\prime }}{x}+\frac {y}{x^{2}}&=\frac {{y^{\prime }}^{2}}{y} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✗ |
3.048 |
|
| \(1188\) |
\begin{align*}
y \left (x y^{\prime \prime }+y^{\prime }\right )&=x {y^{\prime }}^{2} \left (1-x \right ) \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
2.734 |
|
| \(1189\) |
\begin{align*}
x^{2} y y^{\prime \prime }+{y^{\prime }}^{2}&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
✓ |
✗ |
0.853 |
|
| \(1190\) |
\begin{align*}
x^{2} \left ({y^{\prime }}^{2}-2 y y^{\prime \prime }\right )&=y^{2} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✗ |
1.192 |
|
| \(1191\) |
\begin{align*}
x y y^{\prime \prime }&=y^{\prime } \left (y+y^{\prime }\right ) \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
2.475 |
|
| \(1192\) |
\begin{align*}
4 x^{2} y^{3} y^{\prime \prime }&=x^{2}-y^{4} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
3.540 |
|
| \(1193\) |
\begin{align*}
x^{3} y^{\prime \prime }&=\left (y-x y^{\prime }\right ) \left (y-x y^{\prime }-x \right ) \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✗ |
10.482 |
|
| \(1194\) |
\begin{align*}
\frac {y^{2}}{x^{2}}+{y^{\prime }}^{2}&=3 x y^{\prime \prime }+\frac {2 y y^{\prime }}{x} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✗ |
15.597 |
|
| \(1195\) |
\begin{align*}
y^{\prime \prime }&=\left (2 x y-\frac {5}{x}\right ) y^{\prime }+4 y^{2}-\frac {4 y}{x^{2}} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✗ |
4.145 |
|
| \(1196\) |
\begin{align*}
x^{2} \left (2 y y^{\prime \prime }-{y^{\prime }}^{2}\right )&=1-2 x y y^{\prime } \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
✗ |
2.811 |
|
| \(1197\) |
\begin{align*}
x^{2} \left (y y^{\prime \prime }-{y^{\prime }}^{2}\right )+x y y^{\prime }&=\left (2 x y^{\prime }-3 y\right ) \sqrt {x^{3}} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✗ |
5.502 |
|
| \(1198\) |
\begin{align*}
x^{4} \left ({y^{\prime }}^{2}-2 y y^{\prime \prime }\right )&=4 x^{3} y y^{\prime }+1 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
✗ |
6.179 |
|
| \(1199\) |
\begin{align*}
y^{\prime } y+x y y^{\prime \prime }-{y^{\prime }}^{2} x&=x^{3} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
2.478 |
|
| \(1200\) |
\begin{align*}
{y^{\prime \prime }}^{2}-y^{\prime } y^{\prime \prime \prime }&=\frac {{y^{\prime }}^{2}}{x^{2}} \\
\end{align*} |
[[_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
2.271 |
|
| \(1201\) |
\begin{align*}
y^{\prime } y+2 x^{2} y^{\prime \prime }&={y^{\prime }}^{2} x \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_poly_yn], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✗ |
5.564 |
|
| \(1202\) |
\begin{align*}
{y^{\prime }}^{2}+2 x y y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
✓ |
✗ |
0.791 |
|
| \(1203\) |
\begin{align*}
2 x y^{2} \left (x y^{\prime \prime }+y^{\prime }\right )+1&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
✗ |
2.500 |
|
| \(1204\) |
\begin{align*}
y \left (y^{\prime }+2 x y^{\prime \prime }\right )&={y^{\prime }}^{2} x +1 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
✗ |
2.663 |
|
| \(1205\) |
\begin{align*}
y^{\prime \prime }+2 y {y^{\prime }}^{2}&=\left (2 x +\frac {1}{x}\right ) y^{\prime } \\
\end{align*} |
[_Liouville, [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✗ |
4.077 |
|
| \(1206\) |
\begin{align*}
y y^{\prime \prime }&={y^{\prime }}^{2}+2 x y^{2} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✗ |
0.849 |
|
| \(1207\) |
\begin{align*}
2 y y^{\prime \prime \prime }&=y^{\prime } \\
\end{align*} |
[[_3rd_order, _missing_x], [_3rd_order, _exact, _nonlinear], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2]] |
✓ |
✓ |
✗ |
0.216 |
|
| \(1208\) |
\begin{align*}
y^{2} y^{\prime \prime \prime }&={y^{\prime }}^{3} \\
\end{align*} |
[[_3rd_order, _missing_x], [_3rd_order, _exact, _nonlinear], [_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.229 |
|
| \(1209\) |
\begin{align*}
x^{2} y y^{\prime \prime }+1&=x \left (1-y\right ) y^{\prime } \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
✗ |
4.203 |
|
| \(1210\) |
\begin{align*}
y y^{\prime \prime }&=2 {y^{\prime }}^{2} x \\
y \left (2\right ) &= 2 \\
y^{\prime }\left (2\right ) &= {\frac {1}{2}} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
1.236 |
|
| \(1211\) |
\begin{align*}
\left (2 x +3\right )^{3} y^{\prime \prime \prime }+3 \left (2 x +3\right ) y^{\prime }-6 y&=0 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.165 |
|
| \(1212\) |
\begin{align*}
y-x y^{\prime }-y^{\prime \prime }+x y^{\prime \prime \prime }&=0 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.159 |
|
| \(1213\) |
\begin{align*}
\left (x^{2}-2 x +3\right ) y^{\prime \prime \prime }-\left (x^{2}+1\right ) y^{\prime \prime }+2 x y^{\prime }-2 y&=0 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.185 |
|
| \(1214\) |
\begin{align*}
y^{\prime \prime }-2 x y^{\prime }+\left (1+x \right )^{2} y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
39.368 |
|
| \(1215\) |
\begin{align*}
y^{\prime \prime }-2 \,{\mathrm e}^{x} y^{\prime }+y \,{\mathrm e}^{2 x}&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
54.872 |
|
| \(1216\) |
\begin{align*}
y^{\prime \prime }-2 \left (-1+x \right ) y^{\prime }+x^{2} y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
49.620 |
|
| \(1217\) |
\begin{align*}
y^{\prime \prime }+\left (x^{4}+1\right ) y&=0 \\
\end{align*} |
[_Titchmarsh] |
✓ |
✓ |
✗ |
37.583 |
|
| \(1218\) |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime \prime }-y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
41.131 |
|
| \(1219\) |
\begin{align*}
y^{\prime \prime \prime }-x y^{\prime \prime }+\left (x -2\right ) y^{\prime }+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_3rd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✗ |
0.112 |
|