| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
\left (2 x +3\right )^{3} y^{\prime \prime \prime }+3 \left (2 x +3\right ) y^{\prime }-6 y&=0 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
0.037 |
|
| \begin{align*}
\left (2 x +1\right ) y^{\prime \prime }+4 x y^{\prime }-4 y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.757 |
|
| \begin{align*}
x^{2} \left (x +1\right ) y^{\prime \prime }-2 y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.100 |
|
| \begin{align*}
x y^{\prime \prime }-\left (2 x +1\right ) y^{\prime }+\left (x +1\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.466 |
|
| \begin{align*}
x y^{\prime \prime }+2 y^{\prime }-y x&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.105 |
|
| \begin{align*}
x y^{\prime \prime }-2 \left (1+\tan \left (x \right )^{2}\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
✗ |
0.758 |
|
| \begin{align*}
x \left (x -1\right ) y^{\prime \prime }-x y^{\prime }+y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
0.662 |
|
| \begin{align*}
y^{\prime \prime } \left (1+{\mathrm e}^{x}\right )-2 y^{\prime }-y \,{\mathrm e}^{x}&=0 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.268 |
|
| \begin{align*}
x^{2} \ln \left (x \right ) y^{\prime \prime }-x y^{\prime }+y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.489 |
|
| \begin{align*}
y^{\prime \prime }-\tan \left (x \right ) y^{\prime }+2 y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.131 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime \prime }+5 x y^{\prime }+4 y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.165 |
|
| \begin{align*}
x y^{\prime \prime }-\left (x +1\right ) y^{\prime }-2 \left (x -1\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.371 |
|
| \begin{align*}
y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}+2\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.394 |
|
| \begin{align*}
x y^{\prime \prime }-\left (2 x +1\right ) y^{\prime }+2 y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.490 |
|
| \begin{align*}
\left (2 x +1\right ) x y^{\prime \prime }+2 \left (x +1\right ) y^{\prime }-2 y&=0 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.892 |
|
| \begin{align*}
x \left (x +4\right ) y^{\prime \prime }-\left (2 x +4\right ) y^{\prime }+2 y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.668 |
|
| \begin{align*}
x \left (x^{2}+6\right ) y^{\prime \prime }-4 \left (x^{2}+3\right ) y^{\prime }+6 y x&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.615 |
|
| \begin{align*}
-2 y+\left (x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.506 |
|
| \begin{align*}
2 x \left (x +2\right ) y^{\prime \prime }+\left (2-x \right ) y^{\prime }+y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.655 |
|
| \begin{align*}
y-x y^{\prime }-y^{\prime \prime }+x y^{\prime \prime \prime }&=0 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
0.054 |
|
| \begin{align*}
x^{2} \left (2 x -1\right ) y^{\prime \prime \prime }+\left (4 x -3\right ) x y^{\prime \prime }-2 x y^{\prime }+2 y&=0 \\
\end{align*} |
[[_3rd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.463 |
|
| \begin{align*}
\left (x^{2}-2 x +3\right ) y^{\prime \prime \prime }-\left (x^{2}+1\right ) y^{\prime \prime }+2 x y^{\prime }-2 y&=0 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
0.056 |
|
| \begin{align*}
x \left (x +1\right ) y^{\prime \prime }+\left (x +2\right ) y^{\prime }-y&=x +\frac {1}{x} \\
\end{align*} |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
1.265 |
|
| \begin{align*}
\left (2 x +1\right ) y^{\prime \prime }+\left (2 x -1\right ) y^{\prime }-2 y&=x^{2}+x \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.744 |
|
| \begin{align*}
\left (x^{2}-1\right ) y^{\prime \prime }+4 x y^{\prime }+2 y&=6 x \\
\end{align*} |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.848 |
|
| \begin{align*}
\left (3 x^{3}+x \right ) y^{\prime \prime }+2 y^{\prime }-6 y x&=-12 x^{2}+4 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.948 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-2 x y^{\prime }+\left (x^{2}+2\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.487 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-4 x y^{\prime }+\left (-x^{2}+6\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.424 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime \prime }+4 x y^{\prime }+2 y&=0 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.556 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+2 x^{2} y^{\prime }+\left (x^{2}-1\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.338 |
|
| \begin{align*}
x y^{\prime \prime }+y^{\prime }+y x&=0 \\
\end{align*} |
[_Lienard] |
✓ |
✓ |
✓ |
✓ |
0.314 |
|
| \begin{align*}
x y^{\prime \prime }-y^{\prime }-4 x^{3} y&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
1.247 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime \prime }+x y^{\prime }+y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
1.340 |
|
| \begin{align*}
x^{2} \left (-x^{2}+1\right ) y^{\prime \prime }+2 \left (-x^{3}+x \right ) y^{\prime }-2 y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.386 |
|
| \begin{align*}
y^{\prime \prime }-y^{\prime }+{\mathrm e}^{4 x} y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.185 |
|
| \begin{align*}
2 x y^{\prime \prime }+y^{\prime }+y x&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.331 |
|
| \begin{align*}
y^{\prime \prime }+2 y x&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.232 |
|
| \begin{align*}
x y^{\prime \prime }+y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.186 |
|
| \begin{align*}
y^{\prime \prime }-2 x y^{\prime }+\left (x +1\right )^{2} y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
2.961 |
|
| \begin{align*}
y^{\prime \prime }-2 \,{\mathrm e}^{x} y^{\prime }+y \,{\mathrm e}^{2 x}&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
2.773 |
|
| \begin{align*}
y^{\prime \prime }+y x&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.215 |
|
| \begin{align*}
y^{\prime \prime }+x^{2} y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✗ |
0.309 |
|
| \begin{align*}
y^{\prime \prime }+y \,{\mathrm e}^{2 x}&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.150 |
|
| \begin{align*}
x y^{\prime \prime }-y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.199 |
|
| \begin{align*}
y^{\prime \prime }-y x&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.221 |
|
| \begin{align*}
x y^{\prime \prime }+2 y^{\prime }+y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.208 |
|
| \begin{align*}
y^{\prime \prime }-2 \left (x -1\right ) y^{\prime }+x^{2} y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
2.731 |
|
| \begin{align*}
y^{\prime \prime }+\left (x^{4}+1\right ) y&=0 \\
\end{align*} |
[_Titchmarsh] |
✗ |
✓ |
✓ |
✗ |
1.807 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime \prime }-y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✗ |
✓ |
✓ |
✓ |
2.015 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+\ln \left (x \right )^{2} y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
✗ |
1.496 |
|
| \begin{align*}
y^{\prime \prime }-4 x^{2} y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✗ |
0.313 |
|
| \begin{align*}
x y^{\prime \prime }+y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.182 |
|
| \begin{align*}
y^{\prime }&=y^{2}-x \\
y \left (0\right ) &= 1 \\
\end{align*}
Series expansion around \(x=0\). |
[[_Riccati, _special]] |
✓ |
✓ |
✓ |
✓ |
0.370 |
|
| \begin{align*}
y^{\prime }&=x +\frac {1}{y} \\
y \left (0\right ) &= 1 \\
\end{align*}
Series expansion around \(x=0\). |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
0.256 |
|
| \begin{align*}
y^{\prime }&=y+x \,{\mathrm e}^{y} \\
y \left (0\right ) &= 0 \\
\end{align*}
Series expansion around \(x=0\). |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✓ |
✓ |
0.442 |
|
| \begin{align*}
y^{\prime }&=2 x +\cos \left (y\right ) \\
y \left (0\right ) &= 0 \\
\end{align*}
Series expansion around \(x=0\). |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✓ |
✓ |
0.617 |
|
| \begin{align*}
y^{\prime }&=x^{2}+y^{3} \\
y \left (1\right ) &= 1 \\
\end{align*}
Series expansion around \(x=1\). |
[_Abel] |
✓ |
✓ |
✓ |
✓ |
0.336 |
|
| \begin{align*}
y^{\prime \prime }&=x y^{\prime }-y^{2} \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*}
Series expansion around \(x=0\). |
[[_Emden, _modified]] |
✓ |
✓ |
✓ |
✗ |
0.174 |
|
| \begin{align*}
y^{\prime \prime }&={y^{\prime }}^{2}+y x \\
y \left (0\right ) &= 4 \\
y^{\prime }\left (0\right ) &= -2 \\
\end{align*}
Series expansion around \(x=0\). |
[NONE] |
✓ |
✓ |
✓ |
✗ |
0.169 |
|
| \begin{align*}
y^{\prime }&=y^{2}-x \\
y \left (0\right ) &= 1 \\
\end{align*}
Series expansion around \(x=0\). |
[[_Riccati, _special]] |
✓ |
✓ |
✓ |
✓ |
0.134 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{y}-x^{2} y \\
y \left (0\right ) &= 0 \\
\end{align*}
Series expansion around \(x=0\). |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✓ |
✓ |
0.322 |
|
| \begin{align*}
y^{\prime \prime }-x^{2} y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.180 |
|
| \begin{align*}
y^{\prime \prime }-x y^{\prime }-2 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[_Hermite] |
✓ |
✓ |
✓ |
✓ |
0.221 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }-4 x y^{\prime }-2 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.308 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime \prime }+5 x y^{\prime }+3 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.283 |
|
| \begin{align*}
\left (1-x \right ) y^{\prime \prime }-2 y^{\prime }+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.304 |
|
| \begin{align*}
\left (x^{2}-x +1\right ) y^{\prime \prime }+\left (4 x -2\right ) y^{\prime }+2 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.348 |
|
| \begin{align*}
y^{\prime \prime }-x y^{\prime }+y x&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.256 |
|
| \begin{align*}
y^{\prime \prime }+y \sin \left (x \right )&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.325 |
|
| \begin{align*}
x y^{\prime \prime }+y \ln \left (1-x \right )&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.410 |
|
| \begin{align*}
y^{\prime \prime \prime }-x y^{\prime \prime }+\left (x -2\right ) y^{\prime }+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_3rd_order, _exact, _linear, _homogeneous]] |
✗ |
✓ |
✓ |
✗ |
0.060 |
|
| \begin{align*}
x y^{\prime \prime }+2 y^{\prime }+y x&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[_Lienard] |
✓ |
✓ |
✓ |
✓ |
0.503 |
|
| \begin{align*}
2 x^{2} y^{\prime \prime }+\left (-2 x^{2}+3 x \right ) y^{\prime }-\left (x +1\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.547 |
|
| \begin{align*}
9 x^{2} y^{\prime \prime }-\left (x^{2}-2\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.423 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-x^{2} y^{\prime }+\left (x -2\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.510 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+2 x y^{\prime }-\left (x^{2}+2 x +2\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.535 |
|
| \begin{align*}
x y^{\prime \prime }-x y^{\prime }-y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.860 |
|
| \begin{align*}
x y^{\prime \prime }+y^{\prime }-y x&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.310 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+x y^{\prime }-\left (x +2\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.617 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+x y^{\prime }+\left (1-x \right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.384 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+\left (x -1\right ) y&=-1 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✗ |
✓ |
✗ |
0.732 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }+y&=\sin \left (x \right ) \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.289 |
|
| \begin{align*}
y^{\prime \prime }-y^{\prime }-y&=\frac {2 \sin \left (x \right )}{5-4 \cos \left (x \right )} \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.954 |
|
| \begin{align*}
y^{\prime }&=4 \mu \left (x +1\right )-y^{2} \\
y \left (0\right ) &= 1 \\
\end{align*}
Series expansion around \(x=0\). |
[_Riccati] |
✓ |
✓ |
✓ |
✓ |
0.136 |
|
| \begin{align*}
y^{\prime }&=\frac {2}{y}-5 \mu x \\
y \left (1\right ) &= 2 \\
\end{align*}
Series expansion around \(x=1\). |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
0.254 |
|
| \begin{align*}
x y^{\prime }&=x^{2} \mu +\ln \left (y\right ) \\
y \left (1\right ) &= 1 \\
\end{align*}
Series expansion around \(x=1\). |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✓ |
✓ |
0.425 |
|
| \begin{align*}
x^{\prime }&=2 x+y \\
y^{\prime }&=3 x+4 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.437 |
|