| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
x^{2} y^{\prime \prime }+\left (-x^{2}+x \right ) y^{\prime }-\left (x +1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.934 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+2 y^{\prime } x -\left (x^{2}+2\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.823 |
|
| \begin{align*}
y^{\prime \prime } x -2 y^{\prime } x -y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.306 |
|
| \begin{align*}
y^{\prime \prime } x +2 y^{\prime }-y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.821 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-x^{2} y^{\prime }+2 \left (x -1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
1.477 |
|
| \begin{align*}
y^{\prime \prime } x +y^{\prime }-y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.371 |
|
| \begin{align*}
y^{\prime }&=a f \left (x \right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.193 |
|
| \begin{align*}
y^{\prime }&=x +\sin \left (x \right )+y \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.971 |
|
| \begin{align*}
y^{\prime }&=x^{2}+3 \cosh \left (x \right )+2 y \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.570 |
|
| \begin{align*}
y^{\prime }&=x^{2}+3 \cosh \left (x \right )-2 y \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.563 |
|
| \begin{align*}
y^{\prime }&=a +b x +c y \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.033 |
|
| \begin{align*}
y^{\prime }&=a \cos \left (b x +c \right )+k y \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.122 |
|
| \begin{align*}
y^{\prime }&=a \sin \left (b x +c \right )+k y \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.452 |
|
| \begin{align*}
y^{\prime }&=a +b \,{\mathrm e}^{k x}+c y \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.588 |
|
| \begin{align*}
y^{\prime }&=x \left (x^{2}-y\right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.247 |
|
| \begin{align*}
y^{\prime }&=x \left ({\mathrm e}^{-x^{2}}+a y\right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.265 |
|
| \begin{align*}
y^{\prime }&=x^{2} \left (a \,x^{3}+b y\right ) \\
\end{align*} | [_linear] | ✓ | ✓ | ✓ | ✓ | 3.649 |
|
| \begin{align*}
y^{\prime }&=a \,x^{n} y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.378 |
|
| \begin{align*}
y^{\prime }&=\cos \left (x \right ) \sin \left (x \right )+y \cos \left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.629 |
|
| \begin{align*}
y^{\prime }&=\cos \left (x \right ) \sin \left (x \right )-y \cos \left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.607 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{\sin \left (x \right )}+y \cos \left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.431 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{-\sin \left (x \right )}+y \cos \left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.504 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{\sin \left (x \right )}-y \cos \left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.082 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{-\sin \left (x \right )}-y \cos \left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.448 |
|
| \begin{align*}
y^{\prime }&=\cot \left (x \right ) y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.112 |
|
| \begin{align*}
y^{\prime }&=1-\cot \left (x \right ) y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.589 |
|
| \begin{align*}
y^{\prime }&=x \csc \left (x \right )-\cot \left (x \right ) y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.876 |
|
| \begin{align*}
y^{\prime }&=\left (2 \csc \left (2 x \right )+\cot \left (x \right )\right ) y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.914 |
|
| \begin{align*}
y^{\prime }&=-\cot \left (x \right ) y+\sec \left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.953 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{x} \sin \left (x \right )+\cot \left (x \right ) y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.823 |
|
| \begin{align*}
y^{\prime }+\csc \left (x \right )+2 \cot \left (x \right ) y&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.252 |
|
| \begin{align*}
y^{\prime }&=2 \csc \left (2 x \right ) \sec \left (x \right )^{2}-2 y \cot \left (2 x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.909 |
|
| \begin{align*}
y^{\prime }&=2 \cot \left (x \right )^{2} \cos \left (2 x \right )-2 y \csc \left (2 x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✗ |
3.382 |
|
| \begin{align*}
y^{\prime }&=2 \csc \left (2 x \right ) \left (\sin \left (x \right )^{3}+y\right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✗ |
3.623 |
|
| \begin{align*}
y^{\prime }&=2 \csc \left (2 x \right ) \left (1-\tan \left (x \right )^{2}+y\right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✗ |
3.249 |
|
| \begin{align*}
y^{\prime }&=y \sec \left (x \right ) \\
\end{align*} | [_separable] | ✓ | ✓ | ✓ | ✓ | 2.474 |
|
| \begin{align*}
y^{\prime }+\tan \left (x \right )&=\left (1-y\right ) \sec \left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.666 |
|
| \begin{align*}
y^{\prime }&=\tan \left (x \right ) y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.255 |
|
| \begin{align*}
y^{\prime }&=\cos \left (x \right )+\tan \left (x \right ) y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.490 |
|
| \begin{align*}
y^{\prime }&=\cos \left (x \right )-\tan \left (x \right ) y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.004 |
|
| \begin{align*}
y^{\prime }&=\sec \left (x \right )-\tan \left (x \right ) y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.846 |
|
| \begin{align*}
y^{\prime }&=\sin \left (2 x \right )+\tan \left (x \right ) y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.601 |
|
| \begin{align*}
y^{\prime }&=\sin \left (2 x \right )-\tan \left (x \right ) y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.550 |
|
| \begin{align*}
y^{\prime }&=\sin \left (x \right )+2 \tan \left (x \right ) y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.569 |
|
| \begin{align*}
y^{\prime }&=2+2 \sec \left (2 x \right )+2 y \tan \left (2 x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.273 |
|
| \begin{align*}
y^{\prime }&=\csc \left (x \right )+3 \tan \left (x \right ) y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.549 |
|
| \begin{align*}
y^{\prime }&=\left (a +\cos \left (\ln \left (x \right )\right )+\sin \left (\ln \left (x \right )\right )\right ) y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.257 |
|
| \begin{align*}
y^{\prime }&=6 \,{\mathrm e}^{2 x}-y \tanh \left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.690 |
|
| \begin{align*}
y^{\prime }&=f \left (x \right ) f^{\prime }\left (x \right )+y f^{\prime }\left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
0.332 |
|
| \begin{align*}
y^{\prime }&=f \left (x \right ) f^{\prime }\left (x \right )-y f^{\prime }\left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
0.306 |
|
| \begin{align*}
y^{\prime }&=f \left (x \right )+g \left (x \right ) y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.720 |
|
| \begin{align*}
y^{\prime }&=x^{2}-y^{2} \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✓ |
✗ |
5.334 |
|
| \begin{align*}
y^{\prime }+f \left (x \right )^{2}&=f^{\prime }\left (x \right )+y^{2} \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✗ |
✗ |
1.316 |
|
| \begin{align*}
y^{\prime }+1-x&=y \left (x +y\right ) \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✓ |
✗ |
2.599 |
|
| \begin{align*}
y^{\prime }&=\left (x +y\right )^{2} \\
\end{align*} | [[_homogeneous, ‘class C‘], _Riccati] | ✓ | ✓ | ✓ | ✓ | 1.481 |
|
| \begin{align*}
y^{\prime }&=\left (x -y\right )^{2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
✓ |
✓ |
✓ |
1.286 |
|
| \begin{align*}
y^{\prime }&=3 y-3 x +3+\left (x -y\right )^{2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
✓ |
✓ |
✓ |
2.539 |
|
| \begin{align*}
y^{\prime }&=2 x -\left (x^{2}+1\right ) y+y^{2} \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✓ |
✗ |
2.256 |
|
| \begin{align*}
y^{\prime }&=x \left (x^{3}+2\right )-\left (2 x^{2}-y\right ) y \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Riccati] |
✓ |
✓ |
✓ |
✓ |
1.447 |
|
| \begin{align*}
y^{\prime }&=1+x \left (-x^{3}+2\right )+\left (2 x^{2}-y\right ) y \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Riccati] |
✓ |
✓ |
✓ |
✓ |
1.720 |
|
| \begin{align*}
y^{\prime }&=\cos \left (x \right )-\left (-y+\sin \left (x \right )\right ) y \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✓ |
✗ |
0.325 |
|
| \begin{align*}
y^{\prime }&=\cos \left (2 x \right )+\left (\sin \left (2 x \right )+y\right ) y \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✓ |
✗ |
1.245 |
|
| \begin{align*}
y^{\prime }&=f \left (x \right )+x f \left (x \right ) y+y^{2} \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✓ |
✗ |
3.003 |
|
| \begin{align*}
y^{\prime }&=\left (3+x -4 y\right )^{2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
✓ |
✓ |
✓ |
6.497 |
|
| \begin{align*}
y^{\prime }&=\left (1+4 x +9 y\right )^{2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
✓ |
✓ |
✓ |
15.109 |
|
| \begin{align*}
y^{\prime }&=3 a +3 b x +3 b y^{2} \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✓ |
✗ |
0.205 |
|
| \begin{align*}
y^{\prime }&=a +b y^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.490 |
|
| \begin{align*}
y^{\prime }&=a x +b y^{2} \\
\end{align*} |
[[_Riccati, _special]] |
✓ |
✓ |
✓ |
✗ |
35.309 |
|
| \begin{align*}
y^{\prime }&=a +b x +c y^{2} \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✓ |
✗ |
0.175 |
|
| \begin{align*}
y^{\prime }&=a \,x^{n -1}+b \,x^{2 n}+c y^{2} \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✓ |
✗ |
1.514 |
|
| \begin{align*}
y^{\prime }&=a \,x^{n}+b y^{2} \\
\end{align*} |
[[_Riccati, _special]] |
✓ |
✓ |
✓ |
✗ |
33.747 |
|
| \begin{align*}
y^{\prime }&=a_{0} +a_{1} y+a_{2} y^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
3.138 |
|
| \begin{align*}
y^{\prime }&=f \left (x \right )+a y+b y^{2} \\
\end{align*} |
[_Riccati] |
✗ |
✗ |
✗ |
✗ |
1.969 |
|
| \begin{align*}
y^{\prime }&=1+a \left (x -y\right ) y \\
\end{align*} | [_Riccati] | ✓ | ✓ | ✓ | ✗ | 2.743 |
|
| \begin{align*}
y^{\prime }&=f \left (x \right )+g \left (x \right ) y+a y^{2} \\
\end{align*} |
[_Riccati] |
✗ |
✗ |
✗ |
✗ |
3.822 |
|
| \begin{align*}
y^{\prime }&=x y \left (3+y\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.095 |
|
| \begin{align*}
y^{\prime }&=1-x -x^{3}+\left (2 x^{2}+1\right ) y-x y^{2} \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✓ |
✓ |
4.540 |
|
| \begin{align*}
y^{\prime }&=x \left (2+x^{2} y-y^{2}\right ) \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✓ |
✓ |
3.150 |
|
| \begin{align*}
y^{\prime }&=x +\left (1-2 x \right ) y-\left (1-x \right ) y^{2} \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✓ |
✓ |
4.359 |
|
| \begin{align*}
y^{\prime }&=a x y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.980 |
|
| \begin{align*}
y^{\prime }&=x^{n} \left (a +b y^{2}\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.339 |
|
| \begin{align*}
y^{\prime }&=a \,x^{m}+b \,x^{n} y^{2} \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✓ |
✗ |
44.997 |
|
| \begin{align*}
y^{\prime }&=\left (a +b y \cos \left (k x \right )\right ) y \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.106 |
|
| \begin{align*}
y^{\prime }&=\sin \left (x \right ) \left (2 \sec \left (x \right )^{2}-y^{2}\right ) \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✓ |
✗ |
0.703 |
|
| \begin{align*}
y^{\prime }+4 \csc \left (x \right )&=\left (3-\cot \left (x \right )\right ) y+\sin \left (x \right ) y^{2} \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✓ |
✗ |
0.648 |
|
| \begin{align*}
y^{\prime }&=y \sec \left (x \right )+\left (\sin \left (x \right )-1\right )^{2} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.672 |
|
| \begin{align*}
y^{\prime }+\tan \left (x \right ) \left (1-y^{2}\right )&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.808 |
|
| \begin{align*}
y^{\prime }&=f \left (x \right )+g \left (x \right ) y+h \left (x \right ) y^{2} \\
\end{align*} |
[_Riccati] |
✗ |
✗ |
✗ |
✗ |
9.201 |
|
| \begin{align*}
y^{\prime }&=\left (a +b y+c y^{2}\right ) f \left (x \right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.622 |
|
| \begin{align*}
y^{\prime }+\left (a x +y\right ) y^{2}&=0 \\
\end{align*} |
[_Abel] |
✗ |
✓ |
✓ |
✗ |
4.003 |
|
| \begin{align*}
y^{\prime }&=\left (a \,{\mathrm e}^{x}+y\right ) y^{2} \\
\end{align*} |
[_Abel] |
✗ |
✓ |
✓ |
✗ |
4.217 |
|
| \begin{align*}
y^{\prime }+3 a \left (2 x +y\right ) y^{2}&=0 \\
\end{align*} |
[_Abel] |
✗ |
✓ |
✓ |
✗ |
4.151 |
|
| \begin{align*}
y^{\prime }&=y \left (a +b y^{2}\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
6.595 |
|
| \begin{align*}
y^{\prime }&=a_{0} +a_{1} y+a_{2} y^{2}+a_{3} y^{3} \\
\end{align*} | [_quadrature] | ✓ | ✓ | ✓ | ✓ | 8.028 |
|
| \begin{align*}
y^{\prime }&=x y^{3} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.518 |
|
| \begin{align*}
y^{\prime }+y \left (1-x y^{2}\right )&=0 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
2.473 |
|
| \begin{align*}
y^{\prime }&=\left (a +b x y\right ) y^{2} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _Abel] |
✓ |
✓ |
✓ |
✓ |
4.759 |
|
| \begin{align*}
y^{\prime }+2 x y \left (1+a \,x^{2} y^{2}\right )&=0 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
1.465 |
|
| \begin{align*}
y^{\prime }+2 x y \left (1-a \,x^{2} y^{2}\right )&=0 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
1.455 |
|
| \begin{align*}
y^{\prime }+\left (\tan \left (x \right )+y^{2} \sec \left (x \right )\right ) y&=0 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
2.329 |
|