| # | 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] |
✓ |
✓ |
✗ |
5.189 |
|
| \(2\) |
\begin{align*}
y^{\prime }&=x^{2}+y^{2}-1 \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_Riccati] |
✗ |
✓ |
✗ |
24.063 |
|
| \(3\) |
\begin{align*}
y^{\prime }&=x^{2}+y^{2} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[[_Riccati, _special]] |
✓ |
✓ |
✗ |
6.224 |
|
| \(4\) |
\begin{align*}
y^{\prime }&=1+x^{2}+y^{2}+x^{2} y^{4} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
1.309 |
|
| \(5\) |
\begin{align*}
y^{\prime }&=\frac {-{\mathrm e}^{-x}+x}{x +{\mathrm e}^{y}} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
1.881 |
|
| \(6\) |
\begin{align*}
{\mathrm e}^{x} \sin \left (y\right )+3 y-\left (3 x -{\mathrm e}^{x} \sin \left (y\right )\right ) y^{\prime }&=0 \\
\end{align*} |
[‘x=_G(y,y’)‘] |
✗ |
✗ |
✗ |
9.454 |
|
| \(7\) |
\begin{align*}
x \ln \left (x \right )+y x +\left (y \ln \left (x \right )+y x \right ) y^{\prime }&=0 \\
\end{align*} |
[[_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
27.126 |
|
| \(8\) |
\begin{align*}
y^{\prime }&=\frac {x^{2}+y^{2}}{\sin \left (x \right )} \\
\end{align*} |
[_Riccati] |
✗ |
✗ |
✗ |
10.178 |
|
| \(9\) |
\begin{align*}
y^{\prime }&=\frac {y+{\mathrm e}^{x}}{x^{2}+y^{2}} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
2.470 |
|
| \(10\) |
\begin{align*}
y^{\prime }&=\tan \left (y x \right ) \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✗ |
1.139 |
|
| \(11\) |
\begin{align*}
y^{\prime }&=\frac {x^{2}+y^{2}}{\ln \left (y x \right )} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
3.995 |
|
| \(12\) |
\begin{align*}
y^{\prime }&=\left (x^{2}+y^{2}\right ) y^{{1}/{3}} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
1.861 |
|
| \(13\) |
\begin{align*}
y^{\prime }&=\ln \left (1+x^{2}+y^{2}\right ) \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
1.281 |
|
| \(14\) |
\begin{align*}
y^{\prime }&=\sqrt {x^{2}+y^{2}} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
3.092 |
|
| \(15\) |
\begin{align*}
y^{\prime }&=\left (x^{2}+y^{2}\right )^{2} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
1.487 |
|
| \(16\) |
\begin{align*}
2 x^{2}+8 y x +y^{2}+\left (2 x^{2}+\frac {x y^{3}}{3}\right ) y^{\prime }&=0 \\
\end{align*} |
[_rational] |
✗ |
✗ |
✗ |
2.958 |
|
| \(17\) |
\begin{align*}
y \sin \left (y x \right )+x y^{2} \cos \left (y x \right )+\left (x \sin \left (y x \right )+x y^{2} \cos \left (y x \right )\right ) y^{\prime }&=0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
5.747 |
|
| \(18\) |
\begin{align*}
y^{\prime }&=y^{2}+\cos \left (t^{2}\right ) \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_Riccati] |
✗ |
✗ |
✗ |
29.204 |
|
| \(19\) |
\begin{align*}
y^{\prime }&=1+y+y^{2} \cos \left (t \right ) \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_Riccati] |
✓ |
✗ |
✗ |
26.187 |
|
| \(20\) |
\begin{align*}
y^{\prime }&={\mathrm e}^{-t^{2}}+y^{2} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_Riccati] |
✗ |
✗ |
✗ |
29.401 |
|
| \(21\) |
\begin{align*}
y^{\prime }&={\mathrm e}^{-t^{2}}+y^{2} \\
y \left (1\right ) &= 0 \\
\end{align*} |
[_Riccati] |
✗ |
✗ |
✗ |
28.523 |
|
| \(22\) |
\begin{align*}
y^{\prime }&={\mathrm e}^{-t^{2}}+y^{2} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_Riccati] |
✗ |
✗ |
✗ |
28.663 |
|
| \(23\) |
\begin{align*}
y^{\prime }&=y+{\mathrm e}^{-y}+{\mathrm e}^{-t} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
2.017 |
|
| \(24\) |
\begin{align*}
y^{\prime }&=y^{3}+{\mathrm e}^{-5 t} \\
y \left (0\right ) &= {\frac {2}{5}} \\
\end{align*} |
[_Abel] |
✗ |
✗ |
✗ |
1.876 |
|
| \(25\) |
\begin{align*}
y^{\prime }&=\left (4 y+{\mathrm e}^{-t^{2}}\right ) {\mathrm e}^{2 y} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
2.529 |
|
| \(26\) |
\begin{align*}
y^{\prime }&={\mathrm e}^{-t}+\ln \left (1+y^{2}\right ) \\
y \left (0\right ) &= 0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
2.954 |
|
| \(27\) |
\begin{align*}
2 t \cos \left (y\right )+3 t^{2} y+\left (2 t^{2}+2 y\right ) y^{\prime }&=0 \\
y \left (0\right ) &= 1 \\
\end{align*} |
[‘x=_G(y,y’)‘] |
✗ |
✗ |
✗ |
44.401 |
|
| \(28\) |
\begin{align*}
y^{\prime }&=t^{2}+y^{2} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[[_Riccati, _special]] |
✓ |
✓ |
✗ |
10.951 |
|
| \(29\) |
\begin{align*}
y^{\prime }&=1+y+y^{2} \cos \left (t \right ) \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_Riccati] |
✓ |
✗ |
✗ |
19.711 |
|
| \(30\) |
\begin{align*}
y^{\prime }&={\mathrm e}^{-t^{2}}+y^{2} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_Riccati] |
✗ |
✗ |
✗ |
29.798 |
|
| \(31\) |
\begin{align*}
y^{\prime }&={\mathrm e}^{-t^{2}}+y^{2} \\
y \left (1\right ) &= 0 \\
\end{align*} |
[_Riccati] |
✗ |
✗ |
✗ |
30.997 |
|
| \(32\) |
\begin{align*}
y^{\prime }&={\mathrm e}^{-t^{2}}+y^{2} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_Riccati] |
✗ |
✗ |
✗ |
29.601 |
|
| \(33\) |
\begin{align*}
y^{\prime }&=y+{\mathrm e}^{-y}+{\mathrm e}^{-t} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
1.463 |
|
| \(34\) |
\begin{align*}
y^{\prime }&=y^{3}+{\mathrm e}^{-5 t} \\
y \left (0\right ) &= {\frac {2}{5}} \\
\end{align*} |
[_Abel] |
✗ |
✗ |
✗ |
1.596 |
|
| \(35\) |
\begin{align*}
y^{\prime }&=\left (4 y+{\mathrm e}^{-t^{2}}\right ) {\mathrm e}^{2 y} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
1.987 |
|
| \(36\) |
\begin{align*}
y^{\prime }&={\mathrm e}^{-t}+\ln \left (1+y^{2}\right ) \\
y \left (0\right ) &= 0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
2.058 |
|
| \(37\) |
\begin{align*}
y^{\prime }&=y+{\mathrm e}^{-y}+2 t \\
y \left (0\right ) &= 0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
7.798 |
|
| \(38\) |
\begin{align*}
y^{\prime }&=\frac {t^{2}+y^{2}}{1+t +y^{2}} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_rational] |
✗ |
✗ |
✗ |
2.932 |
|
| \(39\) |
\begin{align*}
x y^{2}+2 y+\left (2 y^{3}-x^{2} y+2 x \right ) y^{\prime }&=0 \\
\end{align*} |
[_rational] |
✗ |
✗ |
✗ |
32.862 |
|
| \(40\) |
\begin{align*}
y-x^{2} \sqrt {x^{2}-y^{2}}-x y^{\prime }&=0 \\
y \left (1\right ) &= 1 \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✗ |
✗ |
✗ |
38.757 |
|
| \(41\) |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime }+y x&=x \left (-x^{2}+1\right ) \sqrt {y} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✗ |
2.059 |
|
| \(42\) |
\begin{align*}
1+\left (2 y-x^{2}\right ) {y^{\prime }}^{2}-2 x^{2} y {y^{\prime }}^{2}&=0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
10.668 |
|
| \(43\) |
\begin{align*}
x y {y^{\prime }}^{2}+\left (y x -1\right ) y^{\prime }&=y \\
\end{align*} |
[_rational] |
✗ |
✗ |
✗ |
45.158 |
|
| \(44\) |
\begin{align*}
y^{\prime }+p \left (x \right ) y+q \left (x \right ) y^{2}&=r \left (x \right ) \\
\end{align*} |
[_Riccati] |
✗ |
✗ |
✗ |
11.063 |
|
| \(45\) |
\begin{align*}
y \,{\mathrm e}^{y x}+\left (2 y-x \,{\mathrm e}^{y x}\right ) y^{\prime }&=0 \\
\end{align*} |
[‘x=_G(y,y’)‘] |
✗ |
✗ |
✗ |
2.921 |
|
| \(46\) |
\begin{align*}
y^{2} \left (x^{2}+1\right )+y+\left (1+2 y x \right ) y^{\prime }&=0 \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
13.098 |
|
| \(47\) |
\begin{align*}
2 y^{2}-4 x +5&=\left (4-2 y+4 y x \right ) y^{\prime } \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
23.849 |
|
| \(48\) |
\begin{align*}
x^{2}+y^{3}+y+\left (x^{3}+y^{2}-x \right ) y^{\prime }&=0 \\
\end{align*} |
[_rational] |
✗ |
✗ |
✗ |
4.714 |
|
| \(49\) |
\begin{align*}
y^{\prime }&=f \left (x \right )+a y+b y^{2} \\
\end{align*} |
[_Riccati] |
✗ |
✗ |
✗ |
5.418 |
|
| \(50\) |
\begin{align*}
y^{\prime }&=f \left (x \right )+g \left (x \right ) y+a y^{2} \\
\end{align*} |
[_Riccati] |
✗ |
✗ |
✗ |
6.923 |
|
| \(51\) |
\begin{align*}
y^{\prime }&=f \left (x \right )+g \left (x \right ) y+h \left (x \right ) y^{2} \\
\end{align*} |
[_Riccati] |
✗ |
✗ |
✗ |
12.605 |
|
| \(52\) |
\begin{align*}
y^{\prime }+\left (a x +y\right ) y^{2}&=0 \\
\end{align*} |
[_Abel] |
✓ |
✓ |
✗ |
10.120 |
|
| \(53\) |
\begin{align*}
y^{\prime }&=\left (a \,{\mathrm e}^{x}+y\right ) y^{2} \\
\end{align*} |
[_Abel] |
✓ |
✓ |
✗ |
7.318 |
|
| \(54\) |
\begin{align*}
y^{\prime }+3 a \left (2 x +y\right ) y^{2}&=0 \\
\end{align*} |
[_Abel] |
✓ |
✓ |
✗ |
10.317 |
|
| \(55\) |
\begin{align*}
y^{\prime }&=f \left (x \right )+g \left (x \right ) y+h \left (x \right ) y^{n} \\
\end{align*} |
[_Chini] |
✗ |
✗ |
✗ |
6.024 |
|
| \(56\) |
\begin{align*}
y^{\prime }&=\tan \left (x \right ) \left (\tan \left (y\right )+\sec \left (x \right ) \sec \left (y\right )\right ) \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✓ |
11.130 |
|
| \(57\) |
\begin{align*}
y^{\prime }&=\left (1+\cos \left (x \right ) \sin \left (y\right )\right ) \tan \left (y\right ) \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✓ |
✓ |
7.634 |
|
| \(58\) |
\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)]‘]] |
✓ |
✓ |
✗ |
13.417 |
|
| \(59\) |
\begin{align*}
2 y^{\prime }&=2 \sin \left (y\right )^{2} \tan \left (y\right )-x \sin \left (2 y\right ) \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✓ |
✗ |
68.343 |
|
| \(60\) |
\begin{align*}
x y^{\prime }&=y-x \left (x -y\right ) \sqrt {x^{2}+y^{2}} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✗ |
13.348 |
|
| \(61\) |
\begin{align*}
x y^{\prime }&=\sin \left (x -y\right ) \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
53.626 |
|
| \(62\) |
\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)]‘]] |
✓ |
✓ |
✗ |
7.566 |
|
| \(63\) |
\begin{align*}
x^{2} y^{\prime }&=a \,x^{2} y^{2}-a y^{3} \\
\end{align*} |
[_rational, _Abel] |
✓ |
✓ |
✗ |
7.342 |
|
| \(64\) |
\begin{align*}
x^{2} y^{\prime }+a y^{2}+b \,x^{2} y^{3}&=0 \\
\end{align*} |
[_rational, _Abel] |
✓ |
✓ |
✗ |
8.747 |
|
| \(65\) |
\begin{align*}
x^{2} y^{\prime }&=\sec \left (y\right )+3 x \tan \left (y\right ) \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✗ |
23.125 |
|
| \(66\) |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime }&=n \left (y^{2}-2 y x +1\right ) \\
\end{align*} |
[_rational, _Riccati] |
✓ |
✓ |
✗ |
5.230 |
|
| \(67\) |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime }&=1+y^{2}-2 x y \left (1+y^{2}\right ) \\
\end{align*} |
[_rational, _Abel] |
✓ |
✓ |
✗ |
63.955 |
|
| \(68\) |
\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’)‘] |
✓ |
✓ |
✗ |
32.566 |
|
| \(69\) |
\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] |
✓ |
✓ |
✗ |
22.363 |
|
| \(70\) |
\begin{align*}
x^{7} y^{\prime }+5 x^{3} y^{2}+2 \left (x^{2}+1\right ) y^{3}&=0 \\
\end{align*} |
[_rational, _Abel] |
✓ |
✓ |
✗ |
30.792 |
|
| \(71\) |
\begin{align*}
x^{k} y^{\prime }&=a \,x^{m}+b y^{n} \\
\end{align*} |
[_Chini] |
✗ |
✗ |
✗ |
7.270 |
|
| \(72\) |
\begin{align*}
y y^{\prime }+x^{3}+y&=0 \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
✗ |
✗ |
16.599 |
|
| \(73\) |
\begin{align*}
y y^{\prime }+f \left (x \right )&=g \left (x \right ) y \\
\end{align*} |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
✗ |
✗ |
16.115 |
|
| \(74\) |
\begin{align*}
y y^{\prime }+x +f \left (x^{2}+y^{2}\right ) g \left (x \right )&=0 \\
\end{align*} |
[NONE] |
✓ |
✓ |
✗ |
13.006 |
|
| \(75\) |
\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‘]] |
✓ |
✓ |
✗ |
38.056 |
|
| \(76\) |
\begin{align*}
x \left (y+a \right ) y^{\prime }+b x +c y&=0 \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
30.566 |
|
| \(77\) |
\begin{align*}
\left (a +x \left (x +y\right )\right ) y^{\prime }&=b \left (x +y\right ) y \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
46.471 |
|
| \(78\) |
\begin{align*}
\left (1-x^{2} y\right ) y^{\prime }-1+x y^{2}&=0 \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✗ |
75.559 |
|
| \(79\) |
\begin{align*}
x^{7} y y^{\prime }&=2 x^{2}+2+5 x^{3} y \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✗ |
49.641 |
|
| \(80\) |
\begin{align*}
\left (x +2 y+y^{2}\right ) y^{\prime }+y \left (y+1\right )+\left (x +y\right )^{2} y^{2}&=0 \\
\end{align*} |
[_rational] |
✓ |
✓ |
✗ |
13.826 |
|
| \(81\) |
\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]‘]] |
✓ |
✓ |
✗ |
46.066 |
|
| \(82\) |
\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] |
✓ |
✓ |
✗ |
9.586 |
|
| \(83\) |
\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] |
✓ |
✓ |
✗ |
18.379 |
|
| \(84\) |
\begin{align*}
{y^{\prime }}^{2}&=f \left (x \right )^{2} \left (y-u \left (x \right )\right )^{2} \left (y-a \right ) \left (y-b \right ) \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
33.445 |
|
| \(85\) |
\begin{align*}
{y^{\prime }}^{2} x^{2}+x \left (x^{2}+y x -2 y\right ) y^{\prime }+\left (1-x \right ) \left (x^{2}-y\right ) y&=0 \\
\end{align*} |
[_rational] |
✗ |
✗ |
✗ |
104.534 |
|
| \(86\) |
\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)]‘]] |
✓ |
✓ |
✗ |
62.017 |
|
| \(87\) |
\begin{align*}
x y^{2} {y^{\prime }}^{2}+\left (a -x^{3}-y^{3}\right ) y^{\prime }+x^{2} y&=0 \\
\end{align*} |
[_rational] |
✓ |
✓ |
✗ |
289.033 |
|
| \(88\) |
\begin{align*}
x y^{2} {y^{\prime }}^{3}-y^{3} {y^{\prime }}^{2}+x \left (x^{2}+1\right ) y^{\prime }-x^{2} y&=0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✓ |
✗ |
525.321 |
|
| \(89\) |
\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)]‘]] |
✓ |
✓ |
✓ |
11.914 |
|
| \(90\) |
\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)]‘]] |
✓ |
✓ |
✓ |
10.320 |
|
| \(91\) |
\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)]‘]] |
✓ |
✓ |
✓ |
10.750 |
|
| \(92\) |
\begin{align*}
x^{2} \left ({y^{\prime }}^{6}+3 y^{4}+3 y^{2}+1\right )&=a^{2} \\
\end{align*} |
[_rational] |
✗ |
✗ |
✗ |
1.658 |
|
| \(93\) |
\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] |
✓ |
✓ |
✗ |
31.371 |
|
| \(94\) |
\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] |
✓ |
✓ |
✗ |
11.735 |
|
| \(95\) |
\begin{align*}
x^{2} y^{\prime }+x y^{3}+a y^{2}&=0 \\
\end{align*} |
[_rational, _Abel] |
✓ |
✓ |
✗ |
7.488 |
|
| \(96\) |
\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] |
✓ |
✓ |
✗ |
14.408 |
|
| \(97\) |
\begin{align*}
s^{\prime }&=t \ln \left (s^{2 t}\right )+8 t^{2} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✓ |
✗ |
4.750 |
|
| \(98\) |
\begin{align*}
s^{2}+s^{\prime }&=\frac {s+1}{s t} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class C‘]] |
✗ |
✗ |
✗ |
21.899 |
|
| \(99\) |
\begin{align*}
x^{\prime }+x t&={\mathrm e}^{x} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
8.019 |
|
| \(100\) |
\begin{align*}
x x^{\prime }+x t^{2}&=\sin \left (t \right ) \\
\end{align*} |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
✗ |
✗ |
69.973 |
|
| \(101\) |
\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‘]] |
✓ |
✓ |
✗ |
23.428 |
|
| \(102\) |
\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‘]] |
✓ |
✓ |
✗ |
16.207 |
|
| \(103\) |
\begin{align*}
1+\frac {1}{1+x^{2}+4 y x +y^{2}}+\left (\frac {1}{\sqrt {y}}+\frac {1}{1+x^{2}+2 y x +y^{2}}\right ) y^{\prime }&=0 \\
\end{align*} |
[_rational] |
✗ |
✗ |
✗ |
51.046 |
|
| \(104\) |
\begin{align*}
\sqrt {\frac {y}{x}}+\cos \left (x \right )+\left (\sqrt {\frac {x}{y}}+\sin \left (y\right )\right ) y^{\prime }&=0 \\
\end{align*} |
[NONE] |
✗ |
✓ |
✗ |
59.987 |
|
| \(105\) |
\begin{align*}
\sin \left (x^{\prime }\right )+y^{3} x&=\sin \left (y \right ) \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
25.509 |
|
| \(106\) |
\begin{align*}
y^{\prime }&=x^{2}+y^{2} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[[_Riccati, _special]] |
✓ |
✓ |
✗ |
11.805 |
|
| \(107\) |
\begin{align*}
y^{\prime }&=6 \sqrt {y}+5 x^{3} \\
y \left (-1\right ) &= 4 \\
\end{align*} |
[_Chini] |
✗ |
✗ |
✗ |
3.691 |
|
| \(108\) |
\begin{align*}
y^{\prime }&=x^{2}-y^{2} \\
y \left (0\right ) &= 2 \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✗ |
7.348 |
|
| \(109\) |
\begin{align*}
y^{\prime }&={\mathrm e}^{-\frac {x y^{2}}{100}} \\
y \left (-6\right ) &= 0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
1.714 |
|
| \(110\) |
\begin{align*}
y^{\prime }&={\mathrm e}^{-\frac {x y^{2}}{100}} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
0.971 |
|
| \(111\) |
\begin{align*}
y^{\prime }&={\mathrm e}^{-\frac {x y^{2}}{100}} \\
y \left (0\right ) &= -4 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
0.980 |
|
| \(112\) |
\begin{align*}
y^{\prime }&={\mathrm e}^{-\frac {x y^{2}}{100}} \\
y \left (8\right ) &= -4 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
0.984 |
|
| \(113\) |
\begin{align*}
x y^{\prime }-4 y&=x^{6} {\mathrm e}^{x} \\
y \left (0\right ) &= y_{0} \\
\end{align*} |
[_linear] |
✗ |
✗ |
✗ |
3.981 |
|
| \(114\) |
\begin{align*}
x \ln \left (x \right ) y^{\prime }+y&=3 x^{3} \\
y \left (1\right ) &= 0 \\
\end{align*} |
[_linear] |
✗ |
✗ |
✓ |
0.738 |
|
| \(115\) |
\begin{align*}
2 y^{2}-4 x +5&=\left (4-2 y+4 y x \right ) y^{\prime } \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
25.234 |
|
| \(116\) |
\begin{align*}
y^{\prime }&=y+x \,{\mathrm e}^{y} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
10.323 |
|
| \(117\) |
\begin{align*}
y^{\prime }&=\sqrt {1-x^{2}-y^{2}} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
2.369 |
|
| \(118\) |
\begin{align*}
{y^{\prime }}^{2}+y^{2}&=\sec \left (x \right )^{4} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
46.897 |
|
| \(119\) |
\begin{align*}
y^{\prime }&=\frac {y x +3 x -2 y+6}{y x -3 x -2 y+6} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
11.898 |
|
| \(120\) |
\begin{align*}
y^{\prime }&=\cos \left (x \right )+\frac {y^{2}}{x} \\
\end{align*} |
[_Riccati] |
✗ |
✗ |
✗ |
5.302 |
|
| \(121\) |
\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] |
✓ |
✓ |
✗ |
5.312 |
|
| \(122\) |
\begin{align*}
y^{\prime }+y^{3}+a x y^{2}&=0 \\
\end{align*} |
[_Abel] |
✓ |
✓ |
✗ |
3.705 |
|
| \(123\) |
\begin{align*}
y^{\prime }-y^{3}-a \,{\mathrm e}^{x} y^{2}&=0 \\
\end{align*} |
[_Abel] |
✓ |
✓ |
✗ |
4.006 |
|
| \(124\) |
\begin{align*}
y^{\prime }+3 a y^{3}+6 a x y^{2}&=0 \\
\end{align*} |
[_Abel] |
✓ |
✓ |
✗ |
4.018 |
|
| \(125\) |
\begin{align*}
y^{\prime }-x \left (x +2\right ) y^{3}-y^{2} \left (x +3\right )&=0 \\
\end{align*} |
[_Abel] |
✓ |
✓ |
✗ |
4.694 |
|
| \(126\) |
\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] |
✓ |
✓ |
✗ |
12.160 |
|
| \(127\) |
\begin{align*}
y^{\prime }+2 \left (a^{2} x^{3}-b^{2} x \right ) y^{3}+3 b y^{2}&=0 \\
\end{align*} |
[_Abel] |
✓ |
✓ |
✗ |
7.477 |
|
| \(128\) |
\begin{align*}
y^{\prime }-a \left (x^{n}-x \right ) y^{3}-y^{2}&=0 \\
\end{align*} |
[_Abel] |
✗ |
✗ |
✗ |
31.420 |
|
| \(129\) |
\begin{align*}
y^{\prime }-\left (a \,x^{n}+b x \right ) y^{3}-c y^{2}&=0 \\
\end{align*} |
[_Abel] |
✗ |
✗ |
✗ |
32.123 |
|
| \(130\) |
\begin{align*}
y^{\prime }-f_{3} \left (x \right ) y^{3}-f_{2} \left (x \right ) y^{2}-f_{1} \left (x \right ) y-f_{0} \left (x \right )&=0 \\
\end{align*} |
[_Abel] |
✗ |
✗ |
✗ |
6.557 |
|
| \(131\) |
\begin{align*}
y^{\prime }-\left (y-f \left (x \right )\right ) \left (y-g \left (x \right )\right ) \left (y-\frac {a f \left (x \right )+b g \left (x \right )}{a +b}\right ) h \left (x \right )-\frac {f^{\prime }\left (x \right ) \left (y-g \left (x \right )\right )}{f \left (x \right )-g \left (x \right )}-\frac {g^{\prime }\left (x \right ) \left (y-f \left (x \right )\right )}{g \left (x \right )-f \left (x \right )}&=0 \\
\end{align*} |
[_Abel] |
✓ |
✓ |
✗ |
12.534 |
|
| \(132\) |
\begin{align*}
y^{\prime }-f \left (x \right ) y^{n}-g \left (x \right ) y-h \left (x \right )&=0 \\
\end{align*} |
[_Chini] |
✗ |
✗ |
✗ |
2.143 |
|
| \(133\) |
\begin{align*}
y^{\prime }-f \left (x \right ) y^{a}-g \left (x \right ) y^{b}&=0 \\
\end{align*} |
[NONE] |
✗ |
✗ |
✗ |
1.914 |
|
| \(134\) |
\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] |
✓ |
✓ |
✗ |
35.631 |
|
| \(135\) |
\begin{align*}
y^{\prime }-f \left (x \right ) \left (y-g \left (x \right )\right ) \sqrt {\left (y-a \right ) \left (y-b \right )}&=0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
6.558 |
|
| \(136\) |
\begin{align*}
y^{\prime }+f \left (x \right ) \cos \left (a y\right )+g \left (x \right ) \sin \left (a y\right )+h \left (x \right )&=0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
5.530 |
|
| \(137\) |
\begin{align*}
y^{\prime }+f \left (x \right ) \sin \left (y\right )+\left (1-f^{\prime }\left (x \right )\right ) \cos \left (y\right )-f^{\prime }\left (x \right )-1&=0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✗ |
2.633 |
|
| \(138\) |
\begin{align*}
y^{\prime }+2 \tan \left (y\right ) \tan \left (x \right )-1&=0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✗ |
3.281 |
|
| \(139\) |
\begin{align*}
y^{\prime }-a \left (\tan \left (y\right )^{2}+1\right )+\tan \left (y\right ) \tan \left (x \right )&=0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
6.791 |
|
| \(140\) |
\begin{align*}
y^{\prime }-\tan \left (y x \right )&=0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✗ |
✗ |
1.167 |
|
| \(141\) |
\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)]‘]] |
✓ |
✓ |
✗ |
6.713 |
|
| \(142\) |
\begin{align*}
2 y^{\prime }-3 y^{2}-4 a y-b -c \,{\mathrm e}^{-2 a x}&=0 \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✗ |
30.573 |
|
| \(143\) |
\begin{align*}
x y^{\prime }+y^{3}+3 x y^{2}&=0 \\
\end{align*} |
[_rational, _Abel] |
✓ |
✓ |
✗ |
8.128 |
|
| \(144\) |
\begin{align*}
x y^{\prime }-x \left (-x +y\right ) \sqrt {x^{2}+y^{2}}-y&=0 \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✗ |
9.529 |
|
| \(145\) |
\begin{align*}
x y^{\prime }-\sin \left (x -y\right )&=0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
51.100 |
|
| \(146\) |
\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)]‘]] |
✓ |
✓ |
✗ |
5.757 |
|
| \(147\) |
\begin{align*}
x^{2} y^{\prime }+a y^{3}-a \,x^{2} y^{2}&=0 \\
\end{align*} |
[_rational, _Abel] |
✓ |
✓ |
✗ |
2.976 |
|
| \(148\) |
\begin{align*}
x^{2} y^{\prime }+x y^{3}+a y^{2}&=0 \\
\end{align*} |
[_rational, _Abel] |
✓ |
✓ |
✗ |
9.863 |
|
| \(149\) |
\begin{align*}
x^{2} y^{\prime }+y^{3} a \,x^{2}+b y^{2}&=0 \\
\end{align*} |
[_rational, _Abel] |
✓ |
✓ |
✗ |
3.938 |
|
| \(150\) |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime }+\left (1+y^{2}\right ) \left (2 y x -1\right )&=0 \\
\end{align*} |
[_rational, _Abel] |
✓ |
✓ |
✗ |
54.425 |
|
| \(151\) |
\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’)‘] |
✓ |
✓ |
✗ |
28.882 |
|
| \(152\) |
\begin{align*}
\left (x^{2}-1\right ) y^{\prime }+a \left (y^{2}-2 y x +1\right )&=0 \\
\end{align*} |
[_rational, _Riccati] |
✓ |
✓ |
✗ |
3.056 |
|
| \(153\) |
\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] |
✓ |
✓ |
✗ |
17.177 |
|
| \(154\) |
\begin{align*}
x^{7} y^{\prime }+5 x^{3} y^{2}+2 \left (x^{2}+1\right ) y^{3}&=0 \\
\end{align*} |
[_rational, _Abel] |
✓ |
✓ |
✗ |
25.794 |
|
| \(155\) |
\begin{align*}
y y^{\prime }+x^{3}+y&=0 \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
✗ |
✗ |
7.210 |
|
| \(156\) |
\begin{align*}
y y^{\prime }+a y+\frac {\left (a^{2}-1\right ) x}{4}+b \,x^{n}&=0 \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
✗ |
✗ |
103.133 |
|
| \(157\) |
\begin{align*}
y y^{\prime }+a y+b \,{\mathrm e}^{x}-2 a&=0 \\
\end{align*} |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
✗ |
✗ |
20.273 |
|
| \(158\) |
\begin{align*}
y y^{\prime }+x +f \left (x^{2}+y^{2}\right ) g \left (x \right )&=0 \\
\end{align*} |
[NONE] |
✓ |
✓ |
✗ |
11.499 |
|
| \(159\) |
\begin{align*}
x y y^{\prime }-y^{2}+y x +x^{3}-2 x^{2}&=0 \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
32.525 |
|
| \(160\) |
\begin{align*}
x \left (y+a \right ) y^{\prime }+b y+c x&=0 \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
17.536 |
|
| \(161\) |
\begin{align*}
\left (x^{2} y-1\right ) y^{\prime }-x y^{2}+1&=0 \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✗ |
64.009 |
|
| \(162\) |
\begin{align*}
\left (x^{2} y-1\right ) y^{\prime }+8 x y^{2}-8&=0 \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
76.093 |
|
| \(163\) |
\begin{align*}
x \left (y x +x^{4}-1\right ) y^{\prime }-y \left (y x -x^{4}-1\right )&=0 \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✗ |
33.186 |
|
| \(164\) |
\begin{align*}
\left (x +2 y+y^{2}\right ) y^{\prime }+y \left (y+1\right )+\left (x +y\right )^{2} y^{2}&=0 \\
\end{align*} |
[_rational] |
✓ |
✓ |
✗ |
7.046 |
|
| \(165\) |
\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] |
✓ |
✓ |
✗ |
7.639 |
|
| \(166\) |
\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’)‘] |
✓ |
✓ |
✓ |
37.694 |
|
| \(167\) |
\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’)‘] |
✓ |
✓ |
✓ |
61.663 |
|
| \(168\) |
\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’)‘] |
✓ |
✓ |
✓ |
43.100 |
|
| \(169\) |
\begin{align*}
\left (2 x^{2}+1\right ) {y^{\prime }}^{2}+\left (y^{2}+2 y x +x^{2}+2\right ) y^{\prime }+2 y^{2}+1&=0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✓ |
✗ |
55.872 |
|
| \(170\) |
\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)]‘]] |
✓ |
✓ |
✗ |
19.344 |
|
| \(171\) |
\begin{align*}
\left ({y^{\prime }}^{2}+y^{2}\right ) \cos \left (x \right )^{4}-a^{2}&=0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
25.104 |
|
| \(172\) |
\begin{align*}
\left (a y-x^{2}\right ) {y^{\prime }}^{2}+2 x y {y^{\prime }}^{2}-y^{2}&=0 \\
\end{align*} |
[_rational] |
✗ |
✗ |
✗ |
5.094 |
|
| \(173\) |
\begin{align*}
x y {y^{\prime }}^{2}+\left (x^{22}-y^{2}+a \right ) y^{\prime }-y x&=0 \\
\end{align*} |
[_rational] |
✗ |
✗ |
✗ |
67.270 |
|
| \(174\) |
\begin{align*}
\left (a y^{2}+b x +c \right ) {y^{\prime }}^{2}-b y y^{\prime }+d y^{2}&=0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✓ |
✗ |
58.429 |
|
| \(175\) |
\begin{align*}
x y^{2} {y^{\prime }}^{2}-\left (y^{3}+x^{3}-a \right ) y^{\prime }+x^{2} y&=0 \\
\end{align*} |
[_rational] |
✓ |
✓ |
✗ |
182.073 |
|
| \(176\) |
\begin{align*}
x^{2} \left (x y^{2}-1\right ) {y^{\prime }}^{2}+2 x^{2} y^{2} \left (-x +y\right ) y^{\prime }-y^{2} \left (x^{2} y-1\right )&=0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
34.230 |
|
| \(177\) |
\begin{align*}
\left (y^{4}-a^{2} x^{2}\right ) {y^{\prime }}^{2}+2 a^{2} x y y^{\prime }+y^{2} \left (y^{2}-a^{2}\right )&=0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
28.383 |
|
| \(178\) |
\begin{align*}
x^{2} \left (x^{2} y^{4}-1\right ) {y^{\prime }}^{2}+2 x^{3} y^{3} \left (y^{2}-x^{2}\right ) y^{\prime }-y^{2} \left (y^{2} x^{4}-1\right )&=0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
31.692 |
|
| \(179\) |
\begin{align*}
\left (a^{2} \sqrt {x^{2}+y^{2}}-x^{2}\right ) {y^{\prime }}^{2}+2 x y y^{\prime }+a^{2} \sqrt {x^{2}+y^{2}}-y^{2}&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
100.556 |
|
| \(180\) |
\begin{align*}
\left (a \left (x^{2}+y^{2}\right )^{{3}/{2}}-x^{2}\right ) {y^{\prime }}^{2}+2 x y y^{\prime }+a \left (x^{2}+y^{2}\right )^{{3}/{2}}-y^{2}&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
74.567 |
|
| \(181\) |
\begin{align*}
f \left (x^{2}+y^{2}\right ) \left (1+{y^{\prime }}^{2}\right )-\left (x y^{\prime }-y\right )^{2}&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
28.815 |
|
| \(182\) |
\begin{align*}
{y^{\prime }}^{2}-\left (x^{2}+x y^{2}+y^{4}\right ) {y^{\prime }}^{2}+\left (x y^{6}+x^{2} y^{4}+x^{3} y^{2}\right ) y^{\prime }-x^{3} y^{6}&=0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
77.909 |
|
| \(183\) |
\begin{align*}
x y^{2} {y^{\prime }}^{3}-y^{3} {y^{\prime }}^{2}+x \left (x^{2}+1\right ) y^{\prime }-x^{2} y&=0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✓ |
✗ |
494.707 |
|
| \(184\) |
\begin{align*}
x^{n -1} {y^{\prime }}^{n}-n x y^{\prime }+y&=0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✗ |
3.881 |
|
| \(185\) |
\begin{align*}
y \sqrt {1+{y^{\prime }}^{2}}-a y y^{\prime }-a x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✗ |
0.124 |
|
| \(186\) |
\begin{align*}
f \left (x^{2}+y^{2}\right ) \sqrt {1+{y^{\prime }}^{2}}-x y^{\prime }+y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
37.400 |
|
| \(187\) |
\begin{align*}
a \,x^{n} f \left (y^{\prime }\right )+x y^{\prime }-y&=0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✗ |
2.609 |
|
| \(188\) |
\begin{align*}
f \left ({y^{\prime }}^{2} x \right )+2 x y^{\prime }-y&=0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✗ |
1.339 |
|
| \(189\) |
\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)]‘]] |
✓ |
✓ |
✗ |
5.140 |
|
| \(190\) |
\begin{align*}
y^{\prime }&=\frac {1+2 F \left (\frac {1+4 x^{2} y}{4 x^{2}}\right ) x}{2 x^{3}} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
✓ |
✗ |
4.466 |
|
| \(191\) |
\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)]‘]] |
✓ |
✓ |
✗ |
4.607 |
|
| \(192\) |
\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)]‘]] |
✓ |
✓ |
✗ |
5.941 |
|
| \(193\) |
\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)]‘]] |
✓ |
✓ |
✗ |
4.825 |
|
| \(194\) |
\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)]‘]] |
✓ |
✓ |
✗ |
6.003 |
|
| \(195\) |
\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)]‘]] |
✓ |
✓ |
✗ |
5.493 |
|
| \(196\) |
\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)]‘]] |
✓ |
✓ |
✗ |
11.855 |
|
| \(197\) |
\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] |
✓ |
✓ |
✗ |
5.142 |
|
| \(198\) |
\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)]‘]] |
✓ |
✓ |
✗ |
4.993 |
|
| \(199\) |
\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’)‘] |
✓ |
✓ |
✗ |
4.480 |
|
| \(200\) |
\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)]‘]] |
✓ |
✓ |
✗ |
9.784 |
|
| \(201\) |
\begin{align*}
y^{\prime }&=\frac {F \left (\frac {\left (y+3\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)]‘]] |
✓ |
✓ |
✗ |
11.569 |
|
| \(202\) |
\begin{align*}
y^{\prime }&=\frac {\left (y+1\right ) \left (\left (y-\ln \left (y+1\right )-\ln \left (x \right )\right ) x +1\right )}{y x} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✓ |
26.967 |
|
| \(203\) |
\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’)‘] |
✓ |
✓ |
✗ |
5.510 |
|
| \(204\) |
\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)]‘]] |
✓ |
✓ |
✗ |
1.895 |
|
| \(205\) |
\begin{align*}
y^{\prime }&=\frac {1+2 x^{5} \sqrt {1+4 x^{2} y}}{2 x^{3}} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✗ |
9.953 |
|
| \(206\) |
\begin{align*}
y^{\prime }&=-\left (-\ln \left (\ln \left (y\right )\right )+\ln \left (x \right )\right ) y \\
\end{align*} |
[‘x=_G(y,y’)‘] |
✓ |
✓ |
✗ |
5.681 |
|
| \(207\) |
\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’)‘] |
✓ |
✓ |
✗ |
6.520 |
|
| \(208\) |
\begin{align*}
y^{\prime }&=\frac {y}{\ln \left (\ln \left (y\right )\right )-\ln \left (x \right )+1} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✗ |
7.814 |
|
| \(209\) |
\begin{align*}
y^{\prime }&=\frac {1+2 \sqrt {1+4 x^{2} y}\, x^{4}}{2 x^{3}} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✗ |
9.844 |
|
| \(210\) |
\begin{align*}
y^{\prime }&=-\frac {x^{3} \left (\sqrt {a}\, x +\sqrt {a}-2 \sqrt {a \,x^{4}+8 y}\right ) \sqrt {a}}{2 \left (x +1\right )} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
✓ |
✗ |
20.740 |
|
| \(211\) |
\begin{align*}
y^{\prime }&=-\frac {\left (\sqrt {a}\, x^{4}+\sqrt {a}\, x^{3}-2 \sqrt {a \,x^{4}+8 y}\right ) \sqrt {a}}{2 \left (x +1\right )} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
✓ |
✓ |
2.299 |
|
| \(212\) |
\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)]‘]] |
✓ |
✓ |
✗ |
8.136 |
|
| \(213\) |
\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’)‘] |
✓ |
✓ |
✗ |
198.205 |
|
| \(214\) |
\begin{align*}
y^{\prime }&=\frac {x +1+2 x^{6} \sqrt {1+4 x^{2} y}}{2 x^{3} \left (x +1\right )} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✗ |
10.836 |
|
| \(215\) |
\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)]‘]] |
✓ |
✓ |
✗ |
19.180 |
|
| \(216\) |
\begin{align*}
y^{\prime }&=\frac {y+\sqrt {x^{2}+y^{2}}\, x^{2}}{x} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✗ |
15.028 |
|
| \(217\) |
\begin{align*}
y^{\prime }&=\frac {-x^{2}+1+4 x^{3} \sqrt {x^{2}-2 x +1+8 y}}{4 x +4} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
✓ |
✗ |
11.620 |
|
| \(218\) |
\begin{align*}
y^{\prime }&=\frac {y+x^{3} \sqrt {x^{2}+y^{2}}}{x} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✗ |
7.003 |
|
| \(219\) |
\begin{align*}
y^{\prime }&=\frac {x +1+2 \sqrt {1+4 x^{2} y}\, x^{3}}{2 x^{3} \left (x +1\right )} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✗ |
9.301 |
|
| \(220\) |
\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)]‘]] |
✓ |
✓ |
✗ |
15.580 |
|
| \(221\) |
\begin{align*}
y^{\prime }&=-\frac {\left (-\ln \left (-1+y\right )+\ln \left (y+1\right )+2 \ln \left (x \right )\right ) x \left (y+1\right )^{2}}{8} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✗ |
32.878 |
|
| \(222\) |
\begin{align*}
y^{\prime }&=\frac {\left (-\ln \left (-1+y\right )+\ln \left (y+1\right )+2 \ln \left (x \right )\right )^{2} x \left (y+1\right )^{2}}{16} \\
\end{align*} |
[‘x=_G(y,y’)‘] |
✓ |
✓ |
✗ |
36.172 |
|
| \(223\) |
\begin{align*}
y^{\prime }&=\frac {2 a x +2 a +x^{3} \sqrt {-y^{2}+4 a x}}{\left (x +1\right ) y} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✗ |
48.090 |
|
| \(224\) |
\begin{align*}
y^{\prime }&=-\frac {\left (x \ln \left (y\right )+\ln \left (y\right )-1\right ) y}{x +1} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
12.161 |
|
| \(225\) |
\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)]‘]] |
✓ |
✓ |
✗ |
11.834 |
|
| \(226\) |
\begin{align*}
y^{\prime }&=\frac {-x^{2}+x +2+2 x^{3} \sqrt {x^{2}-4 x +4 y}}{2 x +2} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
✓ |
✗ |
11.467 |
|
| \(227\) |
\begin{align*}
y^{\prime }&=\frac {3 x^{4}+3 x^{3}+\sqrt {9 x^{4}-4 y^{3}}}{\left (x +1\right ) y^{2}} \\
\end{align*} |
[_rational] |
✓ |
✓ |
✗ |
102.932 |
|
| \(228\) |
\begin{align*}
y^{\prime }&=\frac {x^{3} \left (3 x +3+\sqrt {9 x^{4}-4 y^{3}}\right )}{\left (x +1\right ) y^{2}} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✗ |
201.472 |
|
| \(229\) |
\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)]‘]] |
✓ |
✓ |
✗ |
13.186 |
|
| \(230\) |
\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)]‘]] |
✓ |
✓ |
✗ |
13.037 |
|
| \(231\) |
\begin{align*}
y^{\prime }&=\frac {\left (-x \ln \left (y\right )-\ln \left (y\right )+x^{3}\right ) y}{x +1} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
5.949 |
|
| \(232\) |
\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 (x +1\right )} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✗ |
76.715 |
|
| \(233\) |
\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 (x +1\right )} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✗ |
46.159 |
|
| \(234\) |
\begin{align*}
y^{\prime }&=\frac {\left (x +1+x^{4} \ln \left (y\right )\right ) y \ln \left (y\right )}{x \left (x +1\right )} \\
\end{align*} |
[‘x=_G(y,y’)‘] |
✓ |
✓ |
✓ |
6.821 |
|
| \(235\) |
\begin{align*}
y^{\prime }&=\frac {\left (2 x +2+x^{3} y\right ) y}{\left (-1+2 x +\ln \left (y\right )\right ) \left (x +1\right )} \\
\end{align*} |
[‘x=_G(y,y’)‘] |
✓ |
✓ |
✗ |
7.050 |
|
| \(236\) |
\begin{align*}
y^{\prime }&=-\frac {\left (x \ln \left (y\right )+\ln \left (y\right )-x \right ) y}{x \left (x +1\right )} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
23.225 |
|
| \(237\) |
\begin{align*}
y^{\prime }&=\frac {\left (-x \ln \left (y\right )-\ln \left (y\right )+x^{4}\right ) y}{x \left (x +1\right )} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
6.505 |
|
| \(238\) |
\begin{align*}
y^{\prime }&=\frac {\left (x +1+x \ln \left (y\right )\right ) \ln \left (y\right ) y}{x \left (x +1\right )} \\
\end{align*} |
[‘x=_G(y,y’)‘] |
✓ |
✓ |
✓ |
19.699 |
|
| \(239\) |
\begin{align*}
y^{\prime }&=\frac {y x +y+x \sqrt {x^{2}+y^{2}}}{x \left (x +1\right )} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✗ |
17.450 |
|
| \(240\) |
\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)]‘]] |
✓ |
✓ |
✗ |
4.803 |
|
| \(241\) |
\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)]‘]] |
✓ |
✓ |
✗ |
6.769 |
|
| \(242\) |
\begin{align*}
y^{\prime }&=\frac {-x \sin \left (2 y\right )-\sin \left (2 y\right )+\cos \left (2 y\right ) x^{4}+x^{4}}{2 x \left (x +1\right )} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✗ |
11.468 |
|
| \(243\) |
\begin{align*}
y^{\prime }&=\frac {y x +y+x^{4} \sqrt {x^{2}+y^{2}}}{x \left (x +1\right )} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✗ |
12.446 |
|
| \(244\) |
\begin{align*}
y^{\prime }&=\frac {-x \sin \left (2 y\right )-\sin \left (2 y\right )+x \cos \left (2 y\right )+x}{2 x \left (x +1\right )} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✗ |
78.584 |
|
| \(245\) |
\begin{align*}
y^{\prime }&=-\frac {1}{-x -\textit {\_F1} \left (y-\ln \left (x \right )\right ) y \,{\mathrm e}^{y}} \\
\end{align*} |
[NONE] |
✓ |
✓ |
✗ |
5.293 |
|
| \(246\) |
\begin{align*}
y^{\prime }&=\frac {x^{3} {\mathrm e}^{y}+x^{4}+y \,{\mathrm e}^{y}-{\mathrm e}^{y} \ln \left (x +{\mathrm e}^{y}\right )+y x -\ln \left (x +{\mathrm e}^{y}\right ) x +x}{x^{2}} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✗ |
34.917 |
|
| \(247\) |
\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)]‘]] |
✓ |
✓ |
✗ |
17.834 |
|
| \(248\) |
\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)]‘]] |
✓ |
✓ |
✗ |
15.220 |
|
| \(249\) |
\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’)‘] |
✓ |
✓ |
✓ |
10.228 |
|
| \(250\) |
\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)]‘]] |
✓ |
✓ |
✗ |
11.155 |
|
| \(251\) |
\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’)‘] |
✓ |
✓ |
✓ |
9.768 |
|
| \(252\) |
\begin{align*}
y^{\prime }&=\frac {\left (3 x y^{2}+x +3 y^{2}\right ) y}{\left (x +6 y^{2}\right ) x \left (x +1\right )} \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✗ |
16.263 |
|
| \(253\) |
\begin{align*}
y^{\prime }&=-\frac {-y+x^{3} \sqrt {x^{2}+y^{2}}-x^{2} \sqrt {x^{2}+y^{2}}\, y}{x} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✗ |
10.651 |
|
| \(254\) |
\begin{align*}
y^{\prime }&=\frac {1+2 \sqrt {1+4 x^{2} y}\, x^{3}+2 x^{5} \sqrt {1+4 x^{2} y}+2 x^{6} \sqrt {1+4 x^{2} y}}{2 x^{3}} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✗ |
12.410 |
|
| \(255\) |
\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’)‘] |
✓ |
✓ |
✗ |
34.824 |
|
| \(256\) |
\begin{align*}
y^{\prime }&=-\frac {-y+x^{4} \sqrt {x^{2}+y^{2}}-x^{3} \sqrt {x^{2}+y^{2}}\, y}{x} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✗ |
10.486 |
|
| \(257\) |
\begin{align*}
y^{\prime }&=\frac {\left (x^{4}+3 x y^{2}+3 y^{2}\right ) y}{\left (x +6 y^{2}\right ) x \left (x +1\right )} \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✗ |
6.465 |
|
| \(258\) |
\begin{align*}
y^{\prime }&=-\frac {1}{-\left (y^{3}\right )^{{2}/{3}} x -\textit {\_F1} \left (y^{3}-3 \ln \left (x \right )\right ) \left (y^{3}\right )^{{1}/{3}} x} \\
\end{align*} |
[NONE] |
✗ |
✗ |
✗ |
4.492 |
|
| \(259\) |
\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] |
✓ |
✓ |
✗ |
40.640 |
|
| \(260\) |
\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] |
✓ |
✓ |
✗ |
4.951 |
|
| \(261\) |
\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)]‘]] |
✓ |
✓ |
✗ |
12.211 |
|
| \(262\) |
\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)]‘]] |
✓ |
✓ |
✗ |
7.103 |
|
| \(263\) |
\begin{align*}
y^{\prime }&=-\frac {x}{2}+1+\sqrt {x^{2}-4 x +4 y}+x^{2} \sqrt {x^{2}-4 x +4 y}+x^{3} \sqrt {x^{2}-4 x +4 y} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
✓ |
✗ |
12.706 |
|
| \(264\) |
\begin{align*}
y^{\prime }&=\frac {1}{\sin \left (x \right )}+\textit {\_F1} \left (y-\ln \left (\sin \left (x \right )\right )+\ln \left (1+\cos \left (x \right )\right )\right ) \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
✗ |
10.151 |
|
| \(265\) |
\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] |
✓ |
✓ |
✗ |
9.724 |
|
| \(266\) |
\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] |
✓ |
✓ |
✗ |
8.921 |
|
| \(267\) |
\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] |
✓ |
✓ |
✗ |
5.675 |
|
| \(268\) |
\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)]‘]] |
✓ |
✓ |
✗ |
13.030 |
|
| \(269\) |
\begin{align*}
y^{\prime }&=-\frac {-x -\textit {\_F1} \left (y^{2}-2 x \right )}{\sqrt {y^{2}}\, x} \\
\end{align*} |
[NONE] |
✓ |
✓ |
✗ |
5.438 |
|
| \(270\) |
\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)]‘]] |
✓ |
✓ |
✗ |
6.327 |
|
| \(271\) |
\begin{align*}
y^{\prime }&=\frac {y+x \sqrt {x^{2}+y^{2}}+x^{3} \sqrt {x^{2}+y^{2}}+x^{4} \sqrt {x^{2}+y^{2}}}{x} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✗ |
✓ |
✗ |
11.702 |
|
| \(272\) |
\begin{align*}
y^{\prime }&=\left (\frac {\ln \left (-1+y\right ) y}{\left (1-y\right ) \ln \left (x \right ) x}-\frac {\ln \left (-1+y\right )}{\left (1-y\right ) \ln \left (x \right ) x}-f \left (x \right )\right ) \left (1-y\right ) \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✗ |
8.295 |
|
| \(273\) |
\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)]‘]] |
✓ |
✓ |
✗ |
16.278 |
|
| \(274\) |
\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)]‘]] |
✓ |
✓ |
✗ |
7.546 |
|
| \(275\) |
\begin{align*}
y^{\prime }&=-\frac {-y x -y+x^{5} \sqrt {x^{2}+y^{2}}-x^{4} \sqrt {x^{2}+y^{2}}\, y}{x \left (x +1\right )} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✗ |
14.825 |
|
| \(276\) |
\begin{align*}
y^{\prime }&=-\frac {-y x -y+\sqrt {x^{2}+y^{2}}\, x^{2}-x \sqrt {x^{2}+y^{2}}\, y}{x \left (x +1\right )} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✗ |
16.106 |
|
| \(277\) |
\begin{align*}
y^{\prime }&=-\frac {i \left (32 i x +64+64 y^{4}+32 x^{2} y^{2}+4 x^{4}+64 y^{6}+48 x^{2} y^{4}+12 y^{2} x^{4}+x^{6}\right )}{128 y} \\
\end{align*} |
[_rational] |
✗ |
✗ |
✗ |
11.740 |
|
| \(278\) |
\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)]‘]] |
✓ |
✓ |
✗ |
39.689 |
|
| \(279\) |
\begin{align*}
y^{\prime }&=-\frac {i \left (i x +1+x^{4}+2 x^{2} y^{2}+y^{4}+x^{6}+3 y^{2} x^{4}+3 x^{2} y^{4}+y^{6}\right )}{y} \\
\end{align*} |
[_rational] |
✗ |
✗ |
✗ |
11.488 |
|
| \(280\) |
\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 (x +1\right )} \\
\end{align*} |
[NONE] |
✓ |
✓ |
✗ |
12.141 |
|
| \(281\) |
\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 (x +1\right )} \\
\end{align*} |
[NONE] |
✓ |
✓ |
✗ |
12.539 |
|
| \(282\) |
\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 (x +1\right )} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✗ |
9.599 |
|
| \(283\) |
\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 (x +1\right )} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✗ |
8.187 |
|
| \(284\) |
\begin{align*}
y^{\prime }&=-\frac {-y+\sqrt {x^{2}+y^{2}}\, x^{2}-x \sqrt {x^{2}+y^{2}}\, y+x^{4} \sqrt {x^{2}+y^{2}}-x^{3} \sqrt {x^{2}+y^{2}}\, y+x^{5} \sqrt {x^{2}+y^{2}}-x^{4} \sqrt {x^{2}+y^{2}}\, y}{x} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✗ |
18.749 |
|
| \(285\) |
\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] |
✓ |
✓ |
✗ |
12.221 |
|
| \(286\) |
\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] |
✓ |
✓ |
✓ |
15.538 |
|
| \(287\) |
\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] |
✓ |
✓ |
✓ |
14.797 |
|
| \(288\) |
\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 (x -1\right )}{x} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘], _Abel] |
✓ |
✓ |
✗ |
18.353 |
|
| \(289\) |
\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] |
✓ |
✓ |
✗ |
27.891 |
|
| \(290\) |
\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] |
✓ |
✓ |
✗ |
27.312 |
|
| \(291\) |
\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] |
✓ |
✓ |
✗ |
41.385 |
|
| \(292\) |
\begin{align*}
\left (x^{2}-1\right ) y^{\prime }+\lambda \left (y^{2}-2 y x +1\right )&=0 \\
\end{align*} |
[_rational, _Riccati] |
✓ |
✓ |
✗ |
4.285 |
|
| \(293\) |
\begin{align*}
\left (a \,x^{2}+b \right ) y^{\prime }+\alpha y^{2}+\beta x y+\gamma &=0 \\
\end{align*} |
[_rational, _Riccati] |
✓ |
✓ |
✗ |
506.861 |
|
| \(294\) |
\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] |
✓ |
✓ |
✗ |
26.872 |
|
| \(295\) |
\begin{align*}
y^{\prime }&=\sigma y^{2}+a +b \,{\mathrm e}^{\lambda x}+c \,{\mathrm e}^{2 \lambda x} \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✗ |
7.562 |
|
| \(296\) |
\begin{align*}
y^{\prime }&=y^{2}+a \,{\mathrm e}^{2 \lambda x} \left ({\mathrm e}^{\lambda x}+b \right )^{n}-\frac {\lambda ^{2}}{4} \\
\end{align*} |
[_Riccati] |
✓ |
✗ |
✗ |
34.092 |
|
| \(297\) |
\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] |
✓ |
✓ |
✗ |
27.215 |
|
| \(298\) |
\begin{align*}
y^{\prime }&=a \,x^{n} y^{2}-a b \,x^{n} {\mathrm e}^{\lambda x} y+b \lambda \,{\mathrm e}^{\lambda x} \\
\end{align*} |
[_Riccati] |
✗ |
✓ |
✗ |
12.270 |
|
| \(299\) |
\begin{align*}
y^{\prime }&=a \,x^{n} y^{2}-a \,x^{n} \left (b \,{\mathrm e}^{\lambda x}+c \right ) y+c \,x^{n} \\
\end{align*} |
[_Riccati] |
✗ |
✗ |
✗ |
13.459 |
|
| \(300\) |
\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] |
✓ |
✓ |
✗ |
36.176 |
|
| \(301\) |
\begin{align*}
y^{\prime }&=y^{2}+\lambda a -a \left (a +\lambda \right ) \tanh \left (\lambda x \right )^{2} \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✗ |
7.733 |
|
| \(302\) |
\begin{align*}
y^{\prime }&=y^{2}+3 \lambda a -\lambda ^{2}-a \left (a +\lambda \right ) \tanh \left (\lambda x \right )^{2} \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✗ |
29.556 |
|
| \(303\) |
\begin{align*}
y^{\prime }&=y^{2}+\lambda a -a \left (a +\lambda \right ) \coth \left (\lambda x \right )^{2} \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✗ |
7.776 |
|
| \(304\) |
\begin{align*}
y^{\prime }&=y^{2}-\lambda ^{2}+3 \lambda a -a \left (a +\lambda \right ) \coth \left (\lambda x \right )^{2} \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✗ |
35.279 |
|
| \(305\) |
\begin{align*}
2 y^{\prime }&=\left (\lambda +a -\sin \left (\lambda x \right ) a \right ) y^{2}+\lambda -a -\sin \left (\lambda x \right ) a \\
\end{align*} |
[_Riccati] |
✓ |
✗ |
✗ |
107.712 |
|
| \(306\) |
\begin{align*}
y^{\prime }&=y^{2}+\lambda a +a \left (\lambda -a \right ) \tan \left (\lambda x \right )^{2} \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✗ |
6.098 |
|
| \(307\) |
\begin{align*}
y^{\prime }&=y^{2}+\lambda ^{2}+3 \lambda a +a \left (\lambda -a \right ) \tan \left (\lambda x \right )^{2} \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✗ |
47.328 |
|
| \(308\) |
\begin{align*}
y^{\prime }&=y^{2}+\lambda a +a \left (\lambda -a \right ) \cot \left (\lambda x \right )^{2} \\
\end{align*} |
[_Riccati] |
✓ |
✗ |
✗ |
6.049 |
|
| \(309\) |
\begin{align*}
y^{\prime }&=y^{2}+\lambda ^{2}+3 \lambda a +a \left (\lambda -a \right ) \cot \left (\lambda x \right )^{2} \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✗ |
76.852 |
|
| \(310\) |
\begin{align*}
y^{\prime }&=y^{2}-2 a b \cot \left (a x \right ) y+b^{2}-a^{2} \\
\end{align*} |
[_Riccati] |
✓ |
✗ |
✗ |
56.072 |
|
| \(311\) |
\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] |
✓ |
✓ |
✗ |
41.582 |
|
| \(312\) |
\begin{align*}
y^{\prime }&=y^{2}-\frac {\lambda ^{2}}{2}-\frac {3 \lambda ^{2} \tan \left (\lambda x \right )^{2}}{4}+a \cos \left (\lambda x \right )^{2} \sin \left (\lambda x \right )^{n} \\
\end{align*} |
[_Riccati] |
✓ |
✗ |
✗ |
50.523 |
|
| \(313\) |
\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] |
✓ |
✓ |
✗ |
72.161 |
|
| \(314\) |
\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] |
✓ |
✓ |
✗ |
86.013 |
|
| \(315\) |
\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] |
✓ |
✓ |
✗ |
43.747 |
|
| \(316\) |
\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] |
✓ |
✓ |
✗ |
89.800 |
|
| \(317\) |
\begin{align*}
y^{\prime }&=f \left (x \right ) y^{2}-a \tanh \left (\lambda x \right )^{2} \left (a f \left (x \right )+\lambda \right )+\lambda a \\
\end{align*} |
[_Riccati] |
✗ |
✗ |
✗ |
82.390 |
|
| \(318\) |
\begin{align*}
y^{\prime }&=f \left (x \right ) y^{2}-a \coth \left (\lambda x \right )^{2} \left (a f \left (x \right )+\lambda \right )+\lambda a \\
\end{align*} |
[_Riccati] |
✗ |
✗ |
✗ |
86.537 |
|
| \(319\) |
\begin{align*}
y^{\prime }&=f \left (x \right ) y^{2}-a^{2} f \left (x \right )+a \lambda \sinh \left (\lambda x \right )-a^{2} f \left (x \right ) \sinh \left (\lambda x \right )^{2} \\
\end{align*} |
[_Riccati] |
✗ |
✗ |
✗ |
34.543 |
|
| \(320\) |
\begin{align*}
x y^{\prime }&=f \left (x \right ) y^{2}+a -a^{2} f \left (x \right ) \ln \left (x \right )^{2} \\
\end{align*} |
[_Riccati] |
✗ |
✗ |
✗ |
12.415 |
|
| \(321\) |
\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] |
✓ |
✓ |
✗ |
22.111 |
|
| \(322\) |
\begin{align*}
y^{\prime }&=f \left (x \right ) y^{2}-a x \ln \left (x \right ) f \left (x \right ) y+a \ln \left (x \right )+a \\
\end{align*} |
[_Riccati] |
✗ |
✗ |
✗ |
25.814 |
|
| \(323\) |
\begin{align*}
y^{\prime }&=f \left (x \right ) y^{2}-a^{2} f \left (x \right )+a \lambda \sin \left (\lambda x \right )+a^{2} f \left (x \right ) \sin \left (\lambda x \right )^{2} \\
\end{align*} |
[_Riccati] |
✗ |
✗ |
✗ |
37.438 |
|
| \(324\) |
\begin{align*}
y^{\prime }&=f \left (x \right ) y^{2}-a^{2} f \left (x \right )+a \lambda \cos \left (\lambda x \right )+a^{2} f \left (x \right ) \cos \left (\lambda x \right )^{2} \\
\end{align*} |
[_Riccati] |
✗ |
✗ |
✗ |
38.082 |
|
| \(325\) |
\begin{align*}
y^{\prime }&=f \left (x \right ) y^{2}-a \tan \left (\lambda x \right )^{2} \left (a f \left (x \right )-\lambda \right )+\lambda a \\
\end{align*} |
[_Riccati] |
✗ |
✗ |
✗ |
89.300 |
|
| \(326\) |
\begin{align*}
y^{\prime }&=f \left (x \right ) y^{2}-a \cot \left (\lambda x \right )^{2} \left (a f \left (x \right )-\lambda \right )+\lambda a \\
\end{align*} |
[_Riccati] |
✗ |
✗ |
✗ |
106.123 |
|
| \(327\) |
\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] |
✓ |
✓ |
✗ |
8.971 |
|
| \(328\) |
\begin{align*}
f \left (x \right )^{2} y^{\prime }-f^{\prime }\left (x \right ) y^{2}+g \left (x \right ) \left (y-f \left (x \right )\right )&=0 \\
\end{align*} |
[_Riccati] |
✗ |
✗ |
✗ |
29.293 |
|
| \(329\) |
\begin{align*}
y^{\prime }&=y^{2}+a^{2} f \left (a x +b \right ) \\
\end{align*} |
[_Riccati] |
✗ |
✗ |
✗ |
5.818 |
|
| \(330\) |
\begin{align*}
y^{\prime }&=y^{2}+\frac {f \left (\frac {1}{x}\right )}{x^{4}} \\
\end{align*} |
[_Riccati] |
✗ |
✗ |
✗ |
6.931 |
|
| \(331\) |
\begin{align*}
x^{2} y^{\prime }&=x^{4} f \left (x \right ) y^{2}+1 \\
\end{align*} |
[_Riccati] |
✗ |
✗ |
✗ |
8.598 |
|
| \(332\) |
\begin{align*}
x^{2} y^{\prime }&=y^{2} x^{4}+x^{2 n} f \left (a \,x^{n}+b \right )-\frac {n^{2}}{4}+\frac {1}{4} \\
\end{align*} |
[_Riccati] |
✗ |
✗ |
✗ |
44.309 |
|
| \(333\) |
\begin{align*}
y^{\prime }&=f \left (x \right ) y^{2}+g \left (x \right ) y+h \left (x \right ) \\
\end{align*} |
[_Riccati] |
✗ |
✗ |
✗ |
13.063 |
|
| \(334\) |
\begin{align*}
x^{2} y^{\prime }&=x^{2} y^{2}+f \left (a \ln \left (x \right )+b \right )+\frac {1}{4} \\
\end{align*} |
[_Riccati] |
✗ |
✗ |
✗ |
12.049 |
|
| \(335\) |
\begin{align*}
y y^{\prime }-y&=-\frac {2 x}{9}+A +\frac {B}{\sqrt {x}} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✗ |
178.790 |
|
| \(336\) |
\begin{align*}
y y^{\prime }-y&=2 A \left (\sqrt {x}+4 A +\frac {3 A^{2}}{\sqrt {x}}\right ) \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✗ |
✗ |
117.497 |
|
| \(337\) |
\begin{align*}
y y^{\prime }-y&=A x +\frac {B}{x}-\frac {B^{2}}{x^{3}} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✗ |
✗ |
42.132 |
|
| \(338\) |
\begin{align*}
y y^{\prime }-y&=\frac {A}{x}-\frac {A^{2}}{x^{3}} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✗ |
36.711 |
|
| \(339\) |
\begin{align*}
y y^{\prime }-y&=A +B \,{\mathrm e}^{-\frac {2 x}{A}} \\
\end{align*} |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✗ |
✗ |
41.391 |
|
| \(340\) |
\begin{align*}
y y^{\prime }-y&=A \left ({\mathrm e}^{\frac {2 x}{A}}-1\right ) \\
\end{align*} |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✗ |
✗ |
58.596 |
|
| \(341\) |
\begin{align*}
y y^{\prime }-y&=-\frac {2 x}{9}+6 A^{2} \left (1+\frac {2 A}{\sqrt {x}}\right ) \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✗ |
108.650 |
|
| \(342\) |
\begin{align*}
y y^{\prime }-y&=\frac {\left (2 m +1\right ) x}{4 m^{2}}+\frac {A}{x}-\frac {A^{2}}{x^{3}} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✗ |
✗ |
52.898 |
|
| \(343\) |
\begin{align*}
y y^{\prime }-y&=\frac {4}{9} x +2 A \,x^{2}+2 A^{2} x^{3} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✗ |
60.192 |
|
| \(344\) |
\begin{align*}
y y^{\prime }-y&=-\frac {3 x}{16}+\frac {5 A}{x^{{1}/{3}}}-\frac {12 A^{2}}{x^{{5}/{3}}} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
98.482 |
|
| \(345\) |
\begin{align*}
y y^{\prime }-y&=\frac {A}{x} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✗ |
111.070 |
|
| \(346\) |
\begin{align*}
y y^{\prime }-y&=-\frac {x}{4}+\frac {A \left (\sqrt {x}+5 A +\frac {3 A^{2}}{\sqrt {x}}\right )}{4} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✗ |
✗ |
164.078 |
|
| \(347\) |
\begin{align*}
y y^{\prime }-y&=\frac {2 a^{2}}{\sqrt {8 a^{2}+x^{2}}} \\
\end{align*} |
[[_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✗ |
✗ |
66.569 |
|
| \(348\) |
\begin{align*}
y y^{\prime }-y&=\frac {3 x}{8}+\frac {3 \sqrt {a^{2}+x^{2}}}{8}-\frac {a^{2}}{16 \sqrt {a^{2}+x^{2}}} \\
\end{align*} |
[[_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
157.621 |
|
| \(349\) |
\begin{align*}
y y^{\prime }-y&=-\frac {4 x}{25}+\frac {A}{\sqrt {x}} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✗ |
✗ |
103.614 |
|
| \(350\) |
\begin{align*}
y y^{\prime }-y&=-\frac {9 x}{100}+\frac {A}{x^{{5}/{3}}} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✗ |
114.122 |
|
| \(351\) |
\begin{align*}
y y^{\prime }-y&=-\frac {12 x}{49}+\frac {2 A \left (5 \sqrt {x}+34 A +\frac {15 A^{2}}{\sqrt {x}}\right )}{49} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✗ |
✗ |
162.286 |
|
| \(352\) |
\begin{align*}
y y^{\prime }-y&=-\frac {12 x}{49}+\frac {A \left (25 \sqrt {x}+41 A +\frac {10 A^{2}}{\sqrt {x}}\right )}{98} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✗ |
✗ |
168.394 |
|
| \(353\) |
\begin{align*}
y y^{\prime }-y&=-\frac {2 x}{9}+\frac {A}{\sqrt {x}} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✗ |
76.910 |
|
| \(354\) |
\begin{align*}
y y^{\prime }-y&=-\frac {12 x}{49}+\frac {6 A \left (-3 \sqrt {x}+23 A +\frac {12 A^{2}}{\sqrt {x}}\right )}{49} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
139.533 |
|
| \(355\) |
\begin{align*}
y y^{\prime }-y&=-\frac {30 x}{121}+\frac {3 A \left (21 \sqrt {x}+35 A +\frac {6 A^{2}}{\sqrt {x}}\right )}{242} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
173.875 |
|
| \(356\) |
\begin{align*}
y y^{\prime }-y&=-\frac {3 x}{16}+\frac {A}{x^{{5}/{3}}} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
103.210 |
|
| \(357\) |
\begin{align*}
y y^{\prime }-y&=-\frac {12 x}{49}+\frac {4 A \left (-10 \sqrt {x}+27 A +\frac {10 A^{2}}{\sqrt {x}}\right )}{49} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
154.270 |
|
| \(358\) |
\begin{align*}
y y^{\prime }-y&=\frac {A}{\sqrt {x}} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✗ |
58.050 |
|
| \(359\) |
\begin{align*}
y y^{\prime }-y&=A \left (n +2\right ) \left (\sqrt {x}+2 \left (n +2\right ) A +\frac {\left (n +1\right ) \left (n +3\right ) A^{2}}{\sqrt {x}}\right ) \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✗ |
✗ |
272.079 |
|
| \(360\) |
\begin{align*}
y y^{\prime }-y&=A \left (n +2\right ) \left (\sqrt {x}+2 \left (n +2\right ) A +\frac {\left (2 n +3\right ) A^{2}}{\sqrt {x}}\right ) \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✗ |
✗ |
234.694 |
|
| \(361\) |
\begin{align*}
y y^{\prime }-y&=A \sqrt {x}+2 A^{2}+\frac {B}{\sqrt {x}} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✗ |
✗ |
160.362 |
|
| \(362\) |
\begin{align*}
y y^{\prime }-y&=2 A^{2}-A \sqrt {x} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✗ |
✗ |
81.391 |
|
| \(363\) |
\begin{align*}
y y^{\prime }-y&=-\frac {x}{4}+\frac {6 A \left (\sqrt {x}+8 A +\frac {5 A^{2}}{\sqrt {x}}\right )}{49} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
139.636 |
|
| \(364\) |
\begin{align*}
y y^{\prime }-y&=-\frac {6 x}{25}+\frac {6 A \left (2 \sqrt {x}+7 A +\frac {4 A^{2}}{\sqrt {x}}\right )}{25} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
155.432 |
|
| \(365\) |
\begin{align*}
y y^{\prime }-y&=-\frac {3 x}{16}+\frac {3 A}{x^{{1}/{3}}}-\frac {12 A^{2}}{x^{{5}/{3}}} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✗ |
✗ |
104.700 |
|
| \(366\) |
\begin{align*}
y y^{\prime }-y&=\frac {9 x}{32}+\frac {15 \sqrt {b^{2}+x^{2}}}{32}+\frac {3 b^{2}}{64 \sqrt {b^{2}+x^{2}}} \\
\end{align*} |
[[_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
156.392 |
|
| \(367\) |
\begin{align*}
y y^{\prime }-y&=A \,x^{2}-\frac {9}{625 A} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✗ |
48.828 |
|
| \(368\) |
\begin{align*}
y y^{\prime }-y&=-\frac {6}{25} x -A \,x^{2} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✗ |
64.923 |
|
| \(369\) |
\begin{align*}
y y^{\prime }-y&=\frac {6}{25} x -A \,x^{2} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✗ |
64.764 |
|
| \(370\) |
\begin{align*}
y y^{\prime }-y&=\frac {63 x}{4}+\frac {A}{x^{{5}/{3}}} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
111.898 |
|
| \(371\) |
\begin{align*}
y y^{\prime }-y&=2 x +2 A \left (10 \sqrt {x}+31 A +\frac {30 A^{2}}{\sqrt {x}}\right ) \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✗ |
✗ |
163.618 |
|
| \(372\) |
\begin{align*}
y y^{\prime }-y&=2 x +2 A \left (-10 \sqrt {x}+19 A +\frac {30 A^{2}}{\sqrt {x}}\right ) \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
159.896 |
|
| \(373\) |
\begin{align*}
y y^{\prime }-y&=-\frac {12 x}{49}+\frac {A \left (5 \sqrt {x}+262 A +\frac {65 A^{2}}{\sqrt {x}}\right )}{49} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✗ |
✗ |
202.002 |
|
| \(374\) |
\begin{align*}
y y^{\prime }-y&=-\frac {12 x}{49}+A \sqrt {x} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✗ |
✗ |
109.806 |
|
| \(375\) |
\begin{align*}
y y^{\prime }-y&=20 x +\frac {A}{\sqrt {x}} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
87.689 |
|
| \(376\) |
\begin{align*}
y y^{\prime }-y&=-\frac {10 x}{49}+\frac {2 A \left (4 \sqrt {x}+61 A +\frac {12 A^{2}}{\sqrt {x}}\right )}{49} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✗ |
✗ |
184.507 |
|
| \(377\) |
\begin{align*}
y y^{\prime }-y&=-\frac {12 x}{49}+\frac {2 A \left (\sqrt {x}+166 A +\frac {55 A^{2}}{\sqrt {x}}\right )}{49} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✗ |
✗ |
188.651 |
|
| \(378\) |
\begin{align*}
y y^{\prime }-y&=-\frac {4 x}{25}+\frac {A \left (7 \sqrt {x}+49 A +\frac {6 A^{2}}{\sqrt {x}}\right )}{50} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
162.208 |
|
| \(379\) |
\begin{align*}
y y^{\prime }-y&=\frac {15 x}{4}+\frac {6 A}{x^{{1}/{3}}}-\frac {3 A^{2}}{x^{{5}/{3}}} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
109.430 |
|
| \(380\) |
\begin{align*}
y y^{\prime }-y&=-\frac {3 x}{16}+\frac {A}{x^{{1}/{3}}}+\frac {B}{x^{{5}/{3}}} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
197.048 |
|
| \(381\) |
\begin{align*}
y y^{\prime }-y&=\frac {k}{\sqrt {A \,x^{2}+B x +c}} \\
\end{align*} |
[[_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
130.661 |
|
| \(382\) |
\begin{align*}
y y^{\prime }-y&=-\frac {6 x}{25}+\frac {4 B^{2} \left (\left (2-A \right ) x^{{1}/{3}}-\frac {3 B \left (2 A +1\right )}{2}+\frac {B^{2} \left (1-3 A \right )}{x^{{1}/{3}}}-\frac {A \,B^{3}}{x^{{2}/{3}}}\right )}{75} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✗ |
✗ |
462.855 |
|
| \(383\) |
\begin{align*}
y y^{\prime }-y&=a x +b \,x^{m} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
✗ |
✗ |
87.310 |
|
| \(384\) |
\begin{align*}
y y^{\prime }-y&=a^{2} \lambda \,{\mathrm e}^{2 \lambda x}-a \left (b \lambda +1\right ) {\mathrm e}^{\lambda x}+b \\
\end{align*} |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
✗ |
✗ |
87.598 |
|
| \(385\) |
\begin{align*}
y y^{\prime }-y&=a^{2} f^{\prime }\left (x \right ) f^{\prime \prime }\left (x \right )-\frac {\left (f \left (x \right )+b \right )^{2} f^{\prime \prime }\left (x \right )}{{f^{\prime }\left (x \right )}^{3}} \\
\end{align*} |
[[_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
28.864 |
|
| \(386\) |
\begin{align*}
y y^{\prime }&=\left (a x +b \right ) y+1 \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✗ |
73.809 |
|
| \(387\) |
\begin{align*}
y y^{\prime }&=\frac {y}{\left (a x +b \right )^{2}}+1 \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✗ |
51.981 |
|
| \(388\) |
\begin{align*}
y y^{\prime }&=\left (a -\frac {1}{a x}\right ) y+1 \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✗ |
106.410 |
|
| \(389\) |
\begin{align*}
y y^{\prime }&=\frac {3 y}{\sqrt {a \,x^{{3}/{2}}+8 x}}+1 \\
\end{align*} |
[[_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✗ |
✗ |
106.117 |
|
| \(390\) |
\begin{align*}
y y^{\prime }&=\left (\frac {a}{x^{{2}/{3}}}-\frac {2}{3 a \,x^{{1}/{3}}}\right ) y+1 \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✗ |
✗ |
104.989 |
|
| \(391\) |
\begin{align*}
y y^{\prime }&=a \,{\mathrm e}^{\lambda x} y+1 \\
\end{align*} |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✗ |
25.826 |
|
| \(392\) |
\begin{align*}
y y^{\prime }&=\left (a \,{\mathrm e}^{\lambda x}+b \,{\mathrm e}^{-\lambda x}\right ) y+1 \\
\end{align*} |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
✗ |
✗ |
47.483 |
|
| \(393\) |
\begin{align*}
y y^{\prime }&=a y \cosh \left (x \right )+1 \\
\end{align*} |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
✗ |
✗ |
72.296 |
|
| \(394\) |
\begin{align*}
y y^{\prime }&=a \cos \left (\lambda x \right ) y+1 \\
\end{align*} |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
✗ |
✗ |
49.659 |
|
| \(395\) |
\begin{align*}
y y^{\prime }&=a \sin \left (\lambda x \right ) y+1 \\
\end{align*} |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
✗ |
✗ |
77.891 |
|
| \(396\) |
\begin{align*}
y y^{\prime }&=\left (a x +3 b \right ) y+x^{3} c -a b \,x^{2}-2 b^{2} x \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✗ |
✗ |
72.455 |
|
| \(397\) |
\begin{align*}
2 y y^{\prime }&=\left (7 a x +5 b \right ) y-3 a^{2} x^{3}-2 c \,x^{2}-3 b^{2} x \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✗ |
✗ |
83.497 |
|
| \(398\) |
\begin{align*}
y y^{\prime }&=\left (\left (3-m \right ) x -1\right ) y-\left (m -1\right ) a x \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
✗ |
✗ |
187.392 |
|
| \(399\) |
\begin{align*}
y y^{\prime }+x \left (a \,x^{2}+b \right ) y+x&=0 \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✗ |
99.705 |
|
| \(400\) |
\begin{align*}
y y^{\prime }+a \left (1-\frac {1}{x}\right ) y&=a^{2} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✗ |
100.633 |
|
| \(401\) |
\begin{align*}
y y^{\prime }-a \left (1-\frac {b}{x}\right ) y&=a^{2} b \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✗ |
104.627 |
|
| \(402\) |
\begin{align*}
y y^{\prime }&=x^{n -1} \left (\left (1+2 n \right ) x +a n \right ) y-n \,x^{2 n} \left (x +a \right ) \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✗ |
✗ |
148.565 |
|
| \(403\) |
\begin{align*}
y y^{\prime }&=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‘]] |
✓ |
✓ |
✗ |
268.816 |
|
| \(404\) |
\begin{align*}
y y^{\prime }-\frac {a \left (x \left (m -1\right )+1\right ) y}{x}&=\frac {a^{2} \left (m x +1\right ) \left (x -1\right )}{x} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✗ |
✗ |
66.132 |
|
| \(405\) |
\begin{align*}
y y^{\prime }-a \left (1-\frac {b}{\sqrt {x}}\right ) y&=\frac {a^{2} b}{\sqrt {x}} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✗ |
91.795 |
|
| \(406\) |
\begin{align*}
y y^{\prime }+\frac {a \left (6 x -1\right ) y}{2 x}&=-\frac {a^{2} \left (x -1\right ) \left (4 x -1\right )}{2 x} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✗ |
✗ |
77.925 |
|
| \(407\) |
\begin{align*}
y y^{\prime }-\frac {a \left (1+\frac {2 b}{x^{2}}\right ) y}{2}&=\frac {a^{2} \left (3 x +\frac {4 b}{x}\right )}{16} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
80.878 |
|
| \(408\) |
\begin{align*}
y y^{\prime }+\frac {a \left (13 x -18\right ) y}{15 x^{{7}/{5}}}&=-\frac {4 a^{2} \left (x -1\right ) \left (-6+x \right )}{15 x^{{9}/{5}}} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
147.414 |
|
| \(409\) |
\begin{align*}
y y^{\prime }+\frac {a \left (1+5 x \right ) y}{2 \sqrt {x}}&=a^{2} \left (-x^{2}+1\right ) \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
141.103 |
|
| \(410\) |
\begin{align*}
y y^{\prime }+\frac {a \left (7 x -12\right ) y}{10 x^{{7}/{5}}}&=-\frac {a^{2} \left (x -1\right ) \left (x -16\right )}{10 x^{{9}/{5}}} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✗ |
✗ |
145.724 |
|
| \(411\) |
\begin{align*}
y y^{\prime }+\frac {3 a \left (13 x -8\right ) y}{20 x^{{7}/{5}}}&=-\frac {a^{2} \left (x -1\right ) \left (27 x -32\right )}{20 x^{{9}/{5}}} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
147.806 |
|
| \(412\) |
\begin{align*}
y y^{\prime }-\frac {a \left (x +1\right ) y}{2 x^{{7}/{4}}}&=\frac {a^{2} \left (x -1\right ) \left (5+3 x \right )}{4 x^{{5}/{2}}} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✗ |
✗ |
205.729 |
|
| \(413\) |
\begin{align*}
y y^{\prime }-\frac {a \left (4 x +3\right ) y}{14 x^{{8}/{7}}}&=-\frac {a^{2} \left (x -1\right ) \left (16 x +5\right )}{14 x^{{9}/{7}}} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
170.075 |
|
| \(414\) |
\begin{align*}
y y^{\prime }+\frac {a \left (13 x -3\right ) y}{6 x^{{2}/{3}}}&=-\frac {a^{2} \left (x -1\right ) \left (5 x -1\right )}{6 x^{{1}/{3}}} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
120.849 |
|
| \(415\) |
\begin{align*}
y y^{\prime }-\frac {a \left (5 x -4\right ) y}{x^{4}}&=\frac {a^{2} \left (x -1\right ) \left (3 x -1\right )}{x^{7}} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✗ |
✗ |
90.870 |
|
| \(416\) |
\begin{align*}
y y^{\prime }-\frac {2 a \left (3 x -10\right ) y}{5 x^{4}}&=\frac {a^{2} \left (x -1\right ) \left (8 x -5\right )}{5 x^{7}} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
128.085 |
|
| \(417\) |
\begin{align*}
y y^{\prime }+\frac {a \left (39 x -4\right ) y}{42 x^{{9}/{7}}}&=-\frac {a^{2} \left (x -1\right ) \left (9 x -1\right )}{42 x^{{11}/{7}}} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
169.372 |
|
| \(418\) |
\begin{align*}
y y^{\prime }+\frac {a \left (x -2\right ) y}{x}&=\frac {2 a^{2} \left (x -1\right )}{x} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✗ |
✗ |
99.185 |
|
| \(419\) |
\begin{align*}
y y^{\prime }+\frac {a \left (3 x -2\right ) y}{x}&=-\frac {2 a^{2} \left (x -1\right )^{2}}{x} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
101.948 |
|
| \(420\) |
\begin{align*}
y y^{\prime }+\frac {a \left (1-\frac {b}{x^{2}}\right ) y}{x}&=\frac {a^{2} b}{x} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
79.772 |
|
| \(421\) |
\begin{align*}
y y^{\prime }-\frac {a \left (3 x -4\right ) y}{4 x^{{5}/{2}}}&=\frac {a^{2} \left (x -1\right ) \left (x +2\right )}{4 x^{4}} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
113.210 |
|
| \(422\) |
\begin{align*}
y y^{\prime }+\frac {a \left (33 x +2\right ) y}{30 x^{{6}/{5}}}&=-\frac {a^{2} \left (x -1\right ) \left (9 x -4\right )}{30 x^{{7}/{5}}} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✗ |
✗ |
140.775 |
|
| \(423\) |
\begin{align*}
y y^{\prime }-\frac {a \left (x -8\right ) y}{8 x^{{5}/{2}}}&=-\frac {a^{2} \left (x -1\right ) \left (3 x -4\right )}{8 x^{4}} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
114.625 |
|
| \(424\) |
\begin{align*}
y y^{\prime }-\frac {a \left (6 x -13\right ) y}{13 x^{{5}/{2}}}&=-\frac {a^{2} \left (x -1\right ) \left (x -13\right )}{26 x^{4}} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
136.582 |
|
| \(425\) |
\begin{align*}
y y^{\prime }-\frac {2 a \left (3 x +2\right ) y}{5 x^{{8}/{5}}}&=\frac {a^{2} \left (x -1\right ) \left (8 x +1\right )}{5 x^{{11}/{5}}} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
151.667 |
|
| \(426\) |
\begin{align*}
y y^{\prime }-\frac {6 a \left (1+4 x \right ) y}{5 x^{{7}/{5}}}&=\frac {a^{2} \left (x -1\right ) \left (27 x +8\right )}{5 x^{{9}/{5}}} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
153.632 |
|
| \(427\) |
\begin{align*}
y y^{\prime }-\frac {a \left (x +4\right ) y}{5 x^{{8}/{5}}}&=\frac {a^{2} \left (x -1\right ) \left (7+3 x \right )}{5 x^{{3}/{5}}} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
143.569 |
|
| \(428\) |
\begin{align*}
y y^{\prime }-\frac {a \left (x +4\right ) y}{5 x^{{8}/{5}}}&=\frac {a^{2} \left (x -1\right ) \left (7+3 x \right )}{5 x^{{11}/{5}}} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✗ |
✗ |
145.727 |
|
| \(429\) |
\begin{align*}
y y^{\prime }-\frac {a \left (2 x -1\right ) y}{x^{{5}/{2}}}&=\frac {a^{2} \left (x -1\right ) \left (1+3 x \right )}{2 x^{4}} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✗ |
✗ |
117.318 |
|
| \(430\) |
\begin{align*}
y y^{\prime }+\frac {a \left (-6+x \right ) y}{5 x^{{7}/{5}}}&=\frac {2 a^{2} \left (x -1\right ) \left (x +4\right )}{5 x^{{9}/{5}}} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✗ |
✗ |
153.290 |
|
| \(431\) |
\begin{align*}
y y^{\prime }-\frac {3 a y}{x^{{7}/{4}}}&=\frac {a^{2} \left (x -1\right ) \left (x -9\right )}{4 x^{{5}/{2}}} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✗ |
✗ |
153.186 |
|
| \(432\) |
\begin{align*}
y y^{\prime }-\frac {a \left (\left (1+k \right ) x -1\right ) y}{x^{2}}&=\frac {a^{2} \left (1+k \right ) \left (x -1\right )}{x^{2}} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✗ |
✗ |
234.345 |
|
| \(433\) |
\begin{align*}
y y^{\prime }-\left (\left (2 n -1\right ) x -a n \right ) x^{-1-n} y&=n \left (x -a \right ) x^{-2 n} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✗ |
✗ |
212.486 |
|
| \(434\) |
\begin{align*}
y y^{\prime }-a \left (\frac {n +2}{n}+b \,x^{n}\right ) y&=-\frac {a^{2} x \left (\frac {n +1}{n}+b \,x^{n}\right )}{n} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✗ |
✗ |
219.167 |
|
| \(435\) |
\begin{align*}
y y^{\prime }&=\left (a \,{\mathrm e}^{x}+b \right ) y+c \,{\mathrm e}^{2 x}-a b \,{\mathrm e}^{x}-b^{2} \\
\end{align*} |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✗ |
✗ |
95.444 |
|
| \(436\) |
\begin{align*}
y y^{\prime }&=\left (a \,{\mathrm e}^{\lambda x}+b \right ) y+c \left (a^{2} {\mathrm e}^{2 \lambda x}+a b \left (\lambda x +1\right ) {\mathrm e}^{\lambda x}+b^{2} \lambda x \right ) \\
\end{align*} |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✗ |
198.299 |
|
| \(437\) |
\begin{align*}
y y^{\prime }&={\mathrm e}^{\lambda x} \left (2 a \lambda x +a +b \right ) y-{\mathrm e}^{2 \lambda x} \left (a^{2} \lambda \,x^{2}+a b x +c \right ) \\
\end{align*} |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✗ |
✗ |
332.758 |
|
| \(438\) |
\begin{align*}
y y^{\prime }&={\mathrm e}^{a x} \left (2 a \,x^{2}+b +2 x \right ) y+{\mathrm e}^{2 a x} \left (-a \,x^{4}-b \,x^{2}+c \right ) \\
\end{align*} |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
✗ |
✗ |
189.659 |
|
| \(439\) |
\begin{align*}
y y^{\prime }+a \left (2 b x +1\right ) {\mathrm e}^{b x} y&=-a^{2} b \,x^{2} {\mathrm e}^{2 b x} \\
\end{align*} |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✗ |
63.804 |
|
| \(440\) |
\begin{align*}
y y^{\prime }-a \left (1+2 n +2 n \left (n +1\right ) x \right ) {\mathrm e}^{\left (n +1\right ) x} y&=-a^{2} n \left (n +1\right ) \left (n x +1\right ) x \,{\mathrm e}^{2 \left (n +1\right ) x} \\
\end{align*} |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✗ |
✗ |
125.184 |
|
| \(441\) |
\begin{align*}
y y^{\prime }+a \left (1+2 b \sqrt {x}\right ) {\mathrm e}^{2 b \sqrt {x}} y&=-a^{2} b \,x^{{3}/{2}} {\mathrm e}^{4 b \sqrt {x}} \\
\end{align*} |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✗ |
✗ |
95.601 |
|
| \(442\) |
\begin{align*}
y y^{\prime }&=\left (2 \ln \left (x \right )+a +1\right ) y+x \left (-\ln \left (x \right )^{2}-a \ln \left (x \right )+b \right ) \\
\end{align*} |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✗ |
✗ |
84.477 |
|
| \(443\) |
\begin{align*}
y y^{\prime }&=\left (2 \ln \left (x \right )^{2}+2 \ln \left (x \right )+a \right ) y+x \left (-\ln \left (x \right )^{4}-a \ln \left (x \right )^{2}+b \right ) \\
\end{align*} |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
✗ |
✗ |
108.746 |
|
| \(444\) |
\begin{align*}
y y^{\prime }&=a x \cos \left (\lambda \,x^{2}\right ) y+x \\
\end{align*} |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
✗ |
✗ |
116.960 |
|
| \(445\) |
\begin{align*}
x y y^{\prime }&=a y^{2}+b y+c \,x^{n}+s \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
125.014 |
|
| \(446\) |
\begin{align*}
x y y^{\prime }&=-n y^{2}+a \left (1+2 n \right ) x y+b y-a^{2} n \,x^{2}-a b x +c \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✗ |
✗ |
84.415 |
|
| \(447\) |
\begin{align*}
2 x y y^{\prime }&=\left (1-n \right ) y^{2}+\left (a \left (1+2 n \right ) x +2 n -1\right ) y-a^{2} n \,x^{2}-b x -n \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✗ |
✗ |
139.290 |
|
| \(448\) |
\begin{align*}
\left (a x y-a k y+b x -b k \right ) y^{\prime }&=c y^{2}+d x y+\left (-d k +b \right ) y \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✗ |
✗ |
102.620 |
|
| \(449\) |
\begin{align*}
\left (A x y+B \,x^{2}+k x \right ) y^{\prime }&=A y^{2}+c x y+d \,x^{2}+\left (-A \beta +k \right ) y-c \beta x -k \beta \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✗ |
✗ |
151.098 |
|
| \(450\) |
\begin{align*}
\left (A x y+A k y+B \,x^{2}+B k x \right ) y^{\prime }&=c y^{2}+d x y+k \left (d -B \right ) y \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✗ |
✗ |
150.506 |
|
| \(451\) |
\begin{align*}
\left (\left (a x +c \right ) y+\left (1-n \right ) x^{2}+\left (2 n -1\right ) x -n \right ) y^{\prime }&=2 a y^{2}+2 y x \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✗ |
✗ |
297.907 |
|
| \(452\) |
\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‘]] |
✓ |
✓ |
✗ |
481.081 |
|
| \(453\) |
\begin{align*}
x \left (2 a x y+b \right ) y^{\prime }&=-4 a \,x^{2} y^{2}-3 b x y+c \,x^{2}+k \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
64.003 |
|
| \(454\) |
\begin{align*}
\left (y x +a \,x^{n}+b \,x^{2}\right ) y^{\prime }&=y^{2}+c \,x^{n}+b x y \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✗ |
330.362 |
|
| \(455\) |
\begin{align*}
y y^{\prime }&=-n y^{2}+a \left (1+2 n \right ) {\mathrm e}^{x} y+b y-a^{2} n \,{\mathrm e}^{2 x}-a b \,{\mathrm e}^{x}+c \\
\end{align*} |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
✗ |
✗ |
147.957 |
|
| \(456\) |
\begin{align*}
y^{\prime }&=-y^{3}+3 a^{2} x^{2} y-2 a^{3} x^{3}+a \\
\end{align*} |
[_Abel] |
✓ |
✓ |
✗ |
7.639 |
|
| \(457\) |
\begin{align*}
y^{\prime }&=-y^{3}+\left (a x +b \right ) y^{2} \\
\end{align*} |
[_Abel] |
✓ |
✓ |
✗ |
22.721 |
|
| \(458\) |
\begin{align*}
y^{\prime }&=-y^{3}+\frac {y^{2}}{\left (a x +b \right )^{2}} \\
\end{align*} |
[_rational, _Abel] |
✓ |
✓ |
✗ |
22.800 |
|
| \(459\) |
\begin{align*}
y^{\prime }&=a x y^{3}+2 a b \,x^{2} y^{2}-b -2 a \,b^{3} x^{4} \\
\end{align*} |
[_Abel] |
✗ |
✗ |
✗ |
15.780 |
|
| \(460\) |
\begin{align*}
9 y^{\prime }&=-x^{m} \left (a \,x^{1-m}+b \right )^{2 \lambda +1} y^{3}-x^{-2 m} \left (9 a +2+9 b m \,x^{m -1}\right ) \left (a \,x^{1-m}+b \right )^{-\lambda -2} \\
\end{align*} |
[_Abel] |
✗ |
✗ |
✗ |
30.228 |
|
| \(461\) |
\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] |
✓ |
✓ |
✗ |
7.292 |
|
| \(462\) |
\begin{align*}
y^{\prime }&=-\left (a x +b \,x^{m}\right ) y^{3}+y^{2} \\
\end{align*} |
[_Abel] |
✗ |
✗ |
✗ |
69.344 |
|
| \(463\) |
\begin{align*}
y^{\prime }&=\frac {y^{3}}{\sqrt {a \,x^{2}+b x +c}}+y^{2} \\
\end{align*} |
[_Abel] |
✗ |
✗ |
✗ |
86.231 |
|
| \(464\) |
\begin{align*}
y^{\prime }&=-y^{3}+a \,{\mathrm e}^{\lambda x} y^{2} \\
\end{align*} |
[_Abel] |
✓ |
✓ |
✗ |
16.252 |
|
| \(465\) |
\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] |
✓ |
✓ |
✗ |
7.339 |
|
| \(466\) |
\begin{align*}
\left (x^{2}+y^{2}\right ) \left (y y^{\prime }+x \right )&=\left (x^{2}+y^{2}+x \right ) \left (x y^{\prime }-y\right ) \\
\end{align*} |
[_rational] |
✓ |
✓ |
✗ |
5.239 |
|
| \(467\) |
\begin{align*}
x^{3} y^{4}+x^{2} y^{3}+x y^{2}+y+\left (x^{4} y^{3}-x^{3} y^{2}-x^{3} y+x \right ) y^{\prime }&=0 \\
\end{align*} |
[_rational] |
✗ |
✗ |
✗ |
3.338 |
|
| \(468\) |
\begin{align*}
\left (x -y^{\prime }-y\right )^{2}&=x^{2} \left (2 y x -x^{2} y^{\prime }\right ) \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
66.469 |
|
| \(469\) |
\begin{align*}
x x^{\prime }&=1-x t \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✗ |
15.672 |
|
| \(470\) |
\begin{align*}
{x^{\prime }}^{2}+x t&=\sqrt {t +1} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
60.183 |
|
| \(471\) |
\begin{align*}
3 x^{2} y+2-\left (y+x^{3}\right ) y^{\prime }&=0 \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
✗ |
✗ |
8.102 |
|
| \(472\) |
\begin{align*}
y^{\prime }&=x y^{3}+x^{2} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_Abel] |
✗ |
✗ |
✗ |
7.918 |
|
| \(473\) |
\begin{align*}
y^{\prime }&=\sin \left (y x \right ) \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
1.782 |
|
| \(474\) |
\begin{align*}
y^{\prime }&=t \ln \left (y^{2 t}\right )+t^{2} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✓ |
✗ |
20.394 |
|
| \(475\) |
\begin{align*}
y^{\prime }&=\ln \left (y x \right ) \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
2.298 |
|
| \(476\) |
\begin{align*}
{y^{\prime }}^{2}+x y {y^{\prime }}^{2}&=\ln \left (x \right ) \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
41.583 |
|
| \(477\) |
\begin{align*}
y^{\prime }&=x^{3}+y^{3} \\
\end{align*} |
[_Abel] |
✗ |
✗ |
✗ |
3.108 |
|
| \(478\) |
\begin{align*}
y^{\prime }&=\frac {1}{\sqrt {15-x^{2}-y^{2}}} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
5.828 |
|
| \(479\) |
\begin{align*}
y^{\prime }&=2 y^{3}+t^{2} \\
y \left (0\right ) &= -{\frac {1}{2}} \\
\end{align*} |
[_Abel] |
✗ |
✗ |
✗ |
3.229 |
|
| \(480\) |
\begin{align*}
y^{\prime }&=\left (y-3\right ) \left (\sin \left (y\right ) \sin \left (t \right )+\cos \left (t \right )+1\right ) \\
y \left (0\right ) &= 4 \\
\end{align*} |
[‘x=_G(y,y’)‘] |
✗ |
✗ |
✗ |
16.783 |
|
| \(481\) |
\begin{align*}
y^{\prime }&=\left (-1+y\right ) \left (-2+y\right ) \left (y-{\mathrm e}^{\frac {t}{2}}\right ) \\
\end{align*} |
[_Abel] |
✗ |
✗ |
✗ |
12.544 |
|
| \(482\) |
\begin{align*}
\sin \left (x +y\right )-y y^{\prime }&=0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
62.884 |
|
| \(483\) |
\begin{align*}
y^{2} y^{\prime }+3 x^{2} y&=\sin \left (x \right ) \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
45.574 |
|
| \(484\) |
\begin{align*}
4 x \left (x^{2}+y^{2}\right )-5 y+4 y \left (x^{2}+y^{2}-5 x \right ) y^{\prime }&=0 \\
\end{align*} |
[_rational] |
✗ |
✗ |
✗ |
60.570 |
|
| \(485\) |
\begin{align*}
y^{\prime }+t^{2}&=\frac {1}{y^{2}} \\
\end{align*} |
[_rational] |
✗ |
✗ |
✗ |
13.817 |
|
| \(486\) |
\begin{align*}
1-y^{2} \cos \left (y t \right )+\left (t y \cos \left (y t \right )+\sin \left (y t \right )\right ) y^{\prime }&=0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
10.402 |
|
| \(487\) |
\begin{align*}
\frac {1}{t^{2}+1}-y^{2}-2 t y y^{\prime }&=0 \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_exact, _rational, _Bernoulli] |
✗ |
✗ |
✗ |
71.054 |
|
| \(488\) |
\begin{align*}
y^{\prime }&=\sin \left (y\right )-\cos \left (x \right ) \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
3.239 |
|
| \(489\) |
\begin{align*}
y^{\prime }&=\sin \left (y x \right ) \\
y \left (0\right ) &= 0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✗ |
1.558 |
|
| \(490\) |
\begin{align*}
x^{2} \cos \left (y\right ) y^{\prime }+1&=0 \\
y \left (\infty \right ) &= \frac {16 \pi }{3} \\
\end{align*} |
[_separable] |
✓ |
✗ |
✗ |
123.111 |
|
| \(491\) |
\begin{align*}
x^{2} y^{\prime }+\cos \left (2 y\right )&=1 \\
y \left (\infty \right ) &= \frac {10 \pi }{3} \\
\end{align*} |
[_separable] |
✓ |
✗ |
✗ |
59.645 |
|
| \(492\) |
\begin{align*}
x^{2} y^{\prime }+\sin \left (2 y\right )&=1 \\
y \left (\infty \right ) &= \frac {11 \pi }{4} \\
\end{align*} |
[_separable] |
✓ |
✗ |
✓ |
72.735 |
|
| \(493\) |
\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)]‘]] |
✓ |
✓ |
✗ |
11.263 |
|
| \(494\) |
\begin{align*}
y^{\prime }&=y \left ({\mathrm e}^{x}+\ln \left (y\right )\right ) \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
8.025 |
|
| \(495\) |
\begin{align*}
y^{\prime }+x \sin \left (2 y\right )&=2 x \,{\mathrm e}^{-x^{2}} \cos \left (y\right )^{2} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✗ |
23.944 |
|
| \(496\) |
\begin{align*}
y^{\prime }&=\sqrt {1-t^{2}-y^{2}} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
16.949 |
|
| \(497\) |
\begin{align*}
y^{\prime }&=\frac {\ln \left (y t \right )}{1-t^{2}+y^{2}} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
27.565 |
|
| \(498\) |
\begin{align*}
y^{\prime }&=\left (t^{2}+y^{2}\right )^{{3}/{2}} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
15.624 |
|
| \(499\) |
\begin{align*}
{\mathrm e}^{x} \sin \left (y\right )+3 y-\left (3 x -{\mathrm e}^{x} \sin \left (y\right )\right ) y^{\prime }&=0 \\
\end{align*} |
[‘x=_G(y,y’)‘] |
✗ |
✗ |
✗ |
26.735 |
|
| \(500\) |
\begin{align*}
\frac {4 x^{3}}{y^{2}}+\frac {12}{y}+3 \left (\frac {x}{y^{2}}+4 y\right ) y^{\prime }&=0 \\
\end{align*} |
[_rational] |
✗ |
✗ |
✗ |
12.285 |
|
| \(501\) |
\begin{align*}
\left (x^{2}-x^{3}+3 x y^{2}+2 y^{3}\right ) y^{\prime }+2 x^{3}+3 x^{2} y+y^{2}-y^{3}&=0 \\
\end{align*} |
[_rational] |
✓ |
✓ |
✗ |
17.619 |
|
| \(502\) |
\begin{align*}
y&={y^{\prime }}^{2}-x y^{\prime }+\frac {x^{3}}{2} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
77.798 |
|
| \(503\) |
\begin{align*}
\left (x y^{\prime }-y\right )^{2}&=a \left (1+{y^{\prime }}^{2}\right ) \left (x^{2}+y^{2}\right )^{{3}/{2}} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
204.188 |
|
| \(504\) |
\begin{align*}
\left (x y^{\prime }-y\right )^{2}&={y^{\prime }}^{2}-\frac {2 y y^{\prime }}{x}+1 \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✗ |
98.914 |
|
| \(505\) |
\begin{align*}
\left (1-y^{2}+\frac {y^{4}}{x^{2}}\right ) {y^{\prime }}^{2}-\frac {2 y y^{\prime }}{x}+\frac {y^{2}}{x^{2}}&=0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✗ |
✗ |
299.332 |
|
| \(506\) |
\begin{align*}
y^{\prime }-\frac {\tan \left (y\right )}{x +1}&=\left (x +1\right ) {\mathrm e}^{x} \sec \left (y\right ) \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✓ |
33.743 |
|
| \(507\) |
\begin{align*}
y^{\prime }+\frac {y \ln \left (y\right )}{x}&=\frac {y}{x^{2}}-\ln \left (y\right )^{2} \\
\end{align*} |
[‘x=_G(y,y’)‘] |
✗ |
✗ |
✗ |
24.520 |
|
| \(508\) |
\begin{align*}
y^{\prime }&={\mathrm e}^{x -y} \left ({\mathrm e}^{x}-{\mathrm e}^{y}\right ) \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
✓ |
✓ |
9.343 |
|
| \(509\) |
\begin{align*}
\left (x y^{\prime }-y\right )^{2}&=a \left (1+{y^{\prime }}^{2}\right ) \left (x^{2}+y^{2}\right )^{{3}/{2}} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
168.915 |
|
| \(510\) |
\begin{align*}
\left (x y^{\prime }-y\right )^{2}&={y^{\prime }}^{2}-\frac {2 y y^{\prime }}{x}+1 \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✗ |
97.241 |
|
| \(511\) |
\begin{align*}
x y {y^{\prime }}^{2}+\left (x^{2}+y^{2}-h^{2}\right ) y^{\prime }-y x&=0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
133.563 |
|
| \(512\) |
\begin{align*}
\left (x^{2} y^{\prime }+y^{2}\right ) \left (x y^{\prime }+y\right )&=\left (y^{\prime }+1\right )^{2} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
58.789 |
|
| \(513\) |
\begin{align*}
\left (x y \sin \left (y x \right )+\cos \left (y x \right )\right ) y+\left (x y \sin \left (y x \right )-\cos \left (y x \right )\right ) y^{\prime }&=0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
19.892 |
|
| \(514\) |
\begin{align*}
3 x^{2} y^{4}+2 y x +\left (2 x^{3} y^{2}-x^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[_rational] |
✗ |
✗ |
✗ |
34.928 |
|
| \(515\) |
\begin{align*}
3 y {y^{\prime }}^{2}-2 x y y^{\prime }+4 y^{2}-x^{2}&=0 \\
\end{align*} |
[_rational] |
✗ |
✗ |
✗ |
255.404 |
|
| \(516\) |
\begin{align*}
\left (1-y^{2}+\frac {y^{4}}{x^{2}}\right ) {y^{\prime }}^{2}-\frac {2 y y^{\prime }}{x}+\frac {y^{2}}{x^{2}}&=0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✗ |
✗ |
293.472 |
|
| \(517\) |
\begin{align*}
\left (2 x^{2}+1\right ) {y^{\prime }}^{2}+\left (y^{2}+2 y x +x^{2}+2\right ) y^{\prime }+2 y^{2}+1&=0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✓ |
✗ |
120.121 |
|
| \(518\) |
\begin{align*}
3 x^{2}+6 x y^{2}+\left (6 x^{2}+4 y^{3}\right ) y^{\prime }&=0 \\
\end{align*} |
[_rational] |
✗ |
✗ |
✗ |
26.129 |
|
| \(519\) |
\begin{align*}
y^{\prime }&=x^{3}+y^{3} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_Abel] |
✗ |
✗ |
✗ |
12.630 |
|
| \(520\) |
\begin{align*}
y^{\prime }&=x +\sqrt {1+y^{2}} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✓ |
✗ |
45.546 |
|
| \(521\) |
\begin{align*}
x^{\prime }&=t^{2} x^{4}+1 \\
x \left (0\right ) &= 0 \\
\end{align*} |
[_Chini] |
✗ |
✗ |
✗ |
13.087 |
|
| \(522\) |
\begin{align*}
x^{\prime }&=\sin \left (x t \right ) \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
4.378 |
|
| \(523\) |
\begin{align*}
x^{\prime }&=\arctan \left (x\right )+t \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
39.113 |
|
| \(524\) |
\begin{align*}
x^{2}+y^{2}+\left (a x y+y^{4}\right ) y^{\prime }&=0 \\
\end{align*} |
[_rational] |
✗ |
✗ |
✗ |
59.565 |
|
| \(525\) |
\begin{align*}
{x^{\prime }}^{2}&=x^{2}+t^{2}-1 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
44.142 |
|
| \(526\) |
\begin{align*}
\frac {x^{2}}{y}+y^{2}-\left (\frac {x^{3}}{y^{2}}+y x +y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[_rational] |
✓ |
✗ |
✗ |
20.517 |
|
| \(527\) |
\begin{align*}
y^{\prime }&=1+x +x^{2} \cos \left (x \right )-\left (1+4 x \cos \left (x \right )\right ) y+2 y^{2} \cos \left (x \right ) \\
\end{align*} |
[_Riccati] |
✗ |
✗ |
✗ |
137.664 |
|
| \(528\) |
\begin{align*}
\frac {x^{2}}{y}+y^{2}-\left (\frac {x^{3}}{y^{2}}+y x +y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[_rational] |
✓ |
✗ |
✗ |
20.091 |
|
| \(529\) |
\begin{align*}
x y^{\prime }-y&=x^{2} \sqrt {x^{2}-y^{2}} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✗ |
52.347 |
|
| \(530\) |
\begin{align*}
a x y-b +\left (c x y-d \right ) x y^{\prime }&=0 \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
86.265 |
|
| \(531\) |
\begin{align*}
y^{\prime }&=\sin \left (y\right ) x +{\mathrm e}^{x} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
16.209 |
|
| \(532\) |
\begin{align*}
1+y x +y y^{\prime }&=0 \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✗ |
142.749 |
|
| \(533\) |
\begin{align*}
{| y^{\prime }|}+1&=0 \\
\end{align*} |
[_sym_implicit] |
✓ |
✗ |
✗ |
0.325 |
|
| \(534\) |
\begin{align*}
y^{\prime }&=x^{2}+y^{2} \\
y \left (0\right ) &= 2 \\
\end{align*} |
[[_Riccati, _special]] |
✓ |
✓ |
✗ |
91.779 |
|
| \(535\) |
\begin{align*}
y^{\prime }&=y \csc \left (x \right ) \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✗ |
✗ |
✗ |
49.074 |
|
| \(536\) |
\begin{align*}
y^{\prime }&=\frac {1}{\sqrt {x^{2}+4 y^{2}-4}} \\
y \left (3\right ) &= 2 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
24.682 |
|
| \(537\) |
\begin{align*}
U^{\prime }&=\frac {U+1}{\sqrt {s}+\sqrt {s U}} \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✗ |
66.487 |
|
| \(538\) |
\begin{align*}
x^{2}+y \left (x -y\right )^{2} \tan \left (\frac {y}{x}\right )-\left (x^{2}+x \left (x -y\right )^{2} \tan \left (\frac {y}{x}\right )\right ) y^{\prime }&=0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✗ |
132.289 |
|
| \(539\) |
\begin{align*}
y^{\prime }&=\sqrt {\sin \left (x \right )+y}-\cos \left (x \right ) \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
✓ |
39.455 |
|
| \(540\) |
\begin{align*}
x y^{\prime }+y&=3 \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✗ |
✗ |
✓ |
211.237 |
|
| \(541\) |
\begin{align*}
y^{\prime }&=x^{2}+y^{2} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[[_Riccati, _special]] |
✓ |
✓ |
✗ |
93.716 |
|
| \(542\) |
\begin{align*}
y y^{\prime }&=x^{2}+y \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
✗ |
✗ |
77.502 |
|
| \(543\) |
\begin{align*}
y^{2} y^{\prime }+y \tan \left (x \right )&=\sin \left (x \right )^{3} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
117.594 |
|
| \(544\) |
\begin{align*}
{\mathrm e}^{x} \cos \left (y\right )-x^{2}+\left ({\mathrm e}^{y} \sin \left (x \right )+y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[NONE] |
✗ |
✗ |
✗ |
90.727 |
|
| \(545\) |
\begin{align*}
2 x -3 y+\left (7 y^{2}+x^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[_rational] |
✗ |
✗ |
✗ |
55.146 |
|
| \(546\) |
\begin{align*}
y x +1+y^{2} y^{\prime }&=0 \\
\end{align*} |
[_rational] |
✗ |
✗ |
✗ |
111.970 |
|
| \(547\) |
\begin{align*}
2 x^{3} y+\left (2 x^{2} y^{2}+2 y^{4}+\ln \left (y\right )\right ) y^{\prime }&=0 \\
\end{align*} |
[‘x=_G(y,y’)‘] |
✗ |
✗ |
✗ |
117.408 |
|
| \(548\) |
\begin{align*}
y^{\prime }&=\frac {y x +3}{5 x -y} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
✗ |
✗ |
106.313 |
|
| \(549\) |
\begin{align*}
y^{\prime }&=\frac {2 y x +3 y}{x^{2}+2 y^{2}} \\
\end{align*} |
[_rational] |
✗ |
✗ |
✗ |
41.565 |
|
| \(550\) |
\begin{align*}
\frac {8 x^{4} y+12 x^{3} y^{2}+2}{2 x +3 y}+\frac {\left (2 x^{5}+3 x^{4} y+3\right ) y^{\prime }}{x^{2} y^{4}+1}&=0 \\
\end{align*} |
[_rational] |
✗ |
✗ |
✗ |
68.326 |
|
| \(551\) |
\begin{align*}
x^{2} y+\left (x^{2}-y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[_rational] |
✗ |
✗ |
✗ |
40.078 |
|
| \(552\) |
\begin{align*}
x^{3}+y^{2}+\left (y x -3 x^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
67.807 |
|
| \(553\) |
\begin{align*}
x +\sin \left (y\right )-\cos \left (y\right )-x \cos \left (y\right ) \left (2 \sin \left (y\right ) x +1\right ) y^{\prime }&=0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
183.086 |
|
| \(554\) |
\begin{align*}
\left (-x^{2}+1\right ) y^{2}+x \left (x^{2} y^{2}+2 x +y\right ) y^{\prime }&=0 \\
\end{align*} |
[_rational] |
✗ |
✗ |
✗ |
19.808 |
|
| \(555\) |
\begin{align*}
\left (x^{2} y^{2}-1\right ) y+x \left (x^{2} y+2 x +y\right ) y^{\prime }&=0 \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class C‘]] |
✗ |
✗ |
✗ |
109.472 |
|
| \(556\) |
\begin{align*}
y \left (x \tan \left (x \right )+\ln \left (y\right )\right )+\tan \left (x \right ) y^{\prime }&=0 \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
57.309 |
|
| \(557\) |
\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’)‘] |
✓ |
✓ |
✓ |
22.465 |
|
| \(558\) |
\begin{align*}
{y^{\prime }}^{2}+4 x^{4} y^{\prime }-12 x^{4} y&=0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
293.428 |
|
| \(559\) |
\begin{align*}
y+2 t +2 t y y^{\prime }&=0 \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
181.960 |
|
| \(560\) |
\begin{align*}
2 t^{2}-y+\left (t +y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[_rational] |
✗ |
✗ |
✗ |
16.439 |
|
| \(561\) |
\begin{align*}
y^{\prime }&=6 \sqrt {y}+5 x^{3} \\
y \left (-1\right ) &= 4 \\
\end{align*} |
[_Chini] |
✗ |
✗ |
✗ |
27.074 |
|
| \(562\) |
\begin{align*}
y^{\prime }&=x^{2}-y^{2} \\
y \left (0\right ) &= 2 \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✗ |
86.093 |
|
| \(563\) |
\begin{align*}
y^{\prime }&={\mathrm e}^{-\frac {x y^{2}}{100}} \\
y \left (-6\right ) &= 0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
6.242 |
|
| \(564\) |
\begin{align*}
y^{\prime }&={\mathrm e}^{-\frac {x y^{2}}{100}} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
5.797 |
|
| \(565\) |
\begin{align*}
y^{\prime }&={\mathrm e}^{-\frac {x y^{2}}{100}} \\
y \left (0\right ) &= -4 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
5.846 |
|
| \(566\) |
\begin{align*}
y^{\prime }&={\mathrm e}^{-\frac {x y^{2}}{100}} \\
y \left (8\right ) &= -4 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
5.863 |
|
| \(567\) |
\begin{align*}
y^{\prime }&=x^{2}+y^{2} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[[_Riccati, _special]] |
✓ |
✓ |
✗ |
93.786 |
|
| \(568\) |
\begin{align*}
y^{\prime }-2 y x&=6 y \,{\mathrm e}^{y^{2}} \\
\end{align*} |
[‘x=_G(y,y’)‘] |
✗ |
✗ |
✗ |
44.191 |
|
| \(569\) |
\begin{align*}
y^{\prime }&=\sin \left (y\right )-\cos \left (x \right ) \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
2.362 |
|
| \(570\) |
\begin{align*}
x^{2} y^{\prime }+\cos \left (2 y\right )&=1 \\
y \left (\infty \right ) &= \frac {5 \pi }{4} \\
\end{align*} |
[_separable] |
✓ |
✗ |
✗ |
9.183 |
|
| \(571\) |
\begin{align*}
\left (x +1\right ) y^{\prime }&=-1+y \\
y \left (\infty \right ) &= y_{0} \\
\end{align*} |
[_separable] |
✓ |
✗ |
✓ |
6.156 |
|
| \(572\) |
\begin{align*}
y^{\prime }&=2 x \left (\pi +y\right ) \\
y \left (\infty \right ) &= y_{0} \\
\end{align*} |
[_separable] |
✓ |
✗ |
✓ |
7.970 |
|
| \(573\) |
\begin{align*}
x^{2} y^{\prime }+\sin \left (2 y\right )&=1 \\
y \left (\infty \right ) &= \frac {11 \pi }{4} \\
\end{align*} |
[_separable] |
✓ |
✗ |
✓ |
20.300 |
|
| \(574\) |
\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’)‘] |
✓ |
✓ |
✗ |
16.284 |
|
| \(575\) |
\begin{align*}
y^{\prime }-2 y x&=\cos \left (x \right )-2 x \sin \left (x \right ) \\
y \left (\infty \right ) &= y_{0} \\
\end{align*} |
[_linear] |
✓ |
✗ |
✓ |
9.645 |
|
| \(576\) |
\begin{align*}
2 \sqrt {x}\, y^{\prime }-y&=-\sin \left (\sqrt {x}\right )-\cos \left (\sqrt {x}\right ) \\
y \left (\infty \right ) &= y_{0} \\
\end{align*} |
[_linear] |
✓ |
✗ |
✓ |
11.652 |
|
| \(577\) |
\begin{align*}
y^{\prime }-y \ln \left (2\right )&=2^{\sin \left (x \right )} \left (\cos \left (x \right )-1\right ) \ln \left (2\right ) \\
y \left (\infty \right ) &= y_{0} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✗ |
✓ |
11.688 |
|
| \(578\) |
\begin{align*}
2 x^{2} y^{\prime }-y x&=2 x \cos \left (x \right )-2 \sin \left (x \right ) \\
y \left (\infty \right ) &= 0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✗ |
5.767 |
|
| \(579\) |
\begin{align*}
\left (x^{2}+1\right ) \ln \left (x^{2}+1\right ) y^{\prime }-2 y x&=\ln \left (x^{2}+1\right )-2 x \arctan \left (x \right ) \\
y \left (-\infty \right ) &= -\frac {\pi }{2} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
52.217 |
|
| \(580\) |
\begin{align*}
\cos \left (y\right ) y^{\prime }&=\sin \left (x +y\right ) \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
6.092 |
|
| \(581\) |
\begin{align*}
y^{\prime }&=\frac {\left (x +1\right )^{2}-2 y}{2 y} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
✗ |
✗ |
9.193 |
|
| \(582\) |
\begin{align*}
y^{\prime }+y&={\mathrm e}^{x}-\sin \left (y\right ) \\
\end{align*} |
[‘x=_G(y,y’)‘] |
✗ |
✗ |
✗ |
3.159 |
|
| \(583\) |
\begin{align*}
\left (\cos \left (x +y\right )+\sin \left (x -y\right )\right ) y^{\prime }&=\cos \left (2 x \right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✗ |
21.828 |
|
| \(584\) |
\begin{align*}
\ln \left (y^{x}\right ) y^{\prime }&=3 x^{2} y \\
y \left (2\right ) &= {\mathrm e}^{3} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✓ |
✗ |
4.895 |
|
| \(585\) |
\begin{align*}
4 y x +2 x^{2}+y+\left (2 x^{2}+3 y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[_rational] |
✗ |
✗ |
✗ |
1.516 |
|
| \(586\) |
\begin{align*}
\frac {1}{x}+y^{\prime }&=\frac {2}{x^{3} y^{{4}/{3}}} \\
\end{align*} |
[_rational] |
✗ |
✗ |
✗ |
1.980 |
|
| \(587\) |
\begin{align*}
y^{\prime }&=\sin \left (y x \right ) \\
y \left (\frac {\pi }{2}\right ) &= 1 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
1.308 |
|
| \(588\) |
\begin{align*}
y^{\prime }&=x^{2}-y^{2}+\frac {8 x}{y} \\
y \left (3\right ) &= -1 \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class C‘]] |
✗ |
✗ |
✗ |
8.492 |
|
| \(589\) |
\begin{align*}
y^{\prime }&=\cos \left ({\mathrm e}^{y x}\right ) \\
y \left (0\right ) &= -4 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
2.077 |
|
| \(590\) |
\begin{align*}
x^{2} y^{\prime }-2 \cos \left (2 y\right )&=1 \\
y \left (\infty \right ) &= \frac {9 \pi }{4} \\
\end{align*} |
[_separable] |
✓ |
✗ |
✓ |
26.970 |
|
| \(591\) |
\begin{align*}
3 y^{2} y^{\prime }+16 x&=2 x y^{3} \\
y \left (\infty \right ) &= y_{0} \\
\end{align*} |
[_separable] |
✓ |
✗ |
✗ |
19.071 |
|
| \(592\) |
\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)]‘]] |
✓ |
✓ |
✓ |
3.602 |
|
| \(593\) |
\begin{align*}
y \left (x +y^{2}\right )+x^{2} \left (-1+y\right ) y^{\prime }&=0 \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
✗ |
18.607 |
|
| \(594\) |
\begin{align*}
x^{2}-y+x \left (y+1\right ) y^{\prime }&=0 \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✗ |
✗ |
6.477 |
|
| \(595\) |
\begin{align*}
y^{\prime }&=y^{2}-3 x^{2}-1 \\
y \left (0\right ) &= 1 \\
\end{align*} |
|
✗ |
✓ |
✗ |
80.907 |
|
| \(596\) |
\begin{align*}
x^{3}-2 x y^{2}+3 x^{2} y y^{\prime }&=x y^{\prime }-y \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✗ |
49.469 |
|
| \(597\) |
\begin{align*}
x y^{\prime }&=\left (x^{2}+\tan \left (y\right )\right ) \cos \left (y\right )^{2} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✓ |
✗ |
7.541 |
|
| \(598\) |
\begin{align*}
y^{\prime }&=\frac {\left (3 x +y^{3}-1\right )^{2}}{y^{2}} \\
\end{align*} |
[_rational] |
✓ |
✓ |
✓ |
16.329 |
|
| \(599\) |
\begin{align*}
x y y^{\prime }-x^{2} \sqrt {1+y^{2}}&=\left (x +1\right ) \left (1+y^{2}\right ) \\
\end{align*} |
[‘x=_G(y,y’)‘] |
✓ |
✓ |
✓ |
14.511 |
|
| \(600\) |
\begin{align*}
\left (3 y x +x +y\right ) y+\left (4 y x +x +2 y\right ) x y^{\prime }&=0 \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✗ |
27.272 |
|
| \(601\) |
\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]‘]] |
✓ |
✓ |
✓ |
3.635 |
|