| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
x y^{\prime \prime }+\left (x +1\right ) y^{\prime }+2 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.628 |
|
| \begin{align*}
x \left (x -1\right ) y^{\prime \prime }+3 x y^{\prime }+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
3.639 |
|
| \begin{align*}
x^{2} \left (x^{2}-2 x +1\right ) y^{\prime \prime }-x \left (x +3\right ) y^{\prime }+\left (x +4\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.720 |
|
| \begin{align*}
2 x^{2} \left (x +2\right ) y^{\prime \prime }+5 x^{2} y^{\prime }+\left (x +1\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.687 |
|
| \begin{align*}
2 x^{2} y^{\prime \prime }+x y^{\prime }+\left (x -5\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.910 |
|
| \begin{align*}
2 x^{2} y^{\prime \prime }+2 x y^{\prime }-y x&=\sin \left (x \right ) \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.842 |
|
| \begin{align*}
2 x^{2} y^{\prime \prime }+2 x y^{\prime }-y x&=x \sin \left (x \right ) \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.796 |
|
| \begin{align*}
2 x^{2} y^{\prime \prime }+2 x y^{\prime }-y x&=\sin \left (x \right ) \cos \left (x \right ) \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.851 |
|
| \begin{align*}
2 x^{2} y^{\prime \prime }+2 x y^{\prime }-y x&=x^{3}+x \sin \left (x \right ) \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.843 |
|
| \begin{align*}
\cos \left (x \right ) y^{\prime \prime }+2 x y^{\prime }-y x&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.686 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+4 x y^{\prime }+\left (x^{2}+2\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.666 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+x y^{\prime }-y x&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.596 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.665 |
|
| \begin{align*}
\left (x^{2}-x \right ) y^{\prime \prime }-x y^{\prime }+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
3.661 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+\left (x^{2}+6 x \right ) y^{\prime }+y x&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
0.756 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-x y^{\prime }+\left (x^{2}-8\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
3.588 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-9 x y^{\prime }+25 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.477 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-x y^{\prime }-\left (x^{2}+\frac {5}{4}\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.666 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.656 |
|
| \begin{align*}
x y^{\prime \prime }+\left (2-x \right ) y^{\prime }-y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.750 |
|
| \begin{align*}
2 x^{2} y^{\prime \prime }+3 x y^{\prime }-y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.556 |
|
| \begin{align*}
2 x^{2} y^{\prime \prime }+5 x y^{\prime }+4 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✗ |
0.458 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+3 x y^{\prime }+4 x^{4} y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.628 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-y x&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.740 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }+y^{\prime }+y&=x \,{\mathrm e}^{x} \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.540 |
|
| \begin{align*}
y^{\prime }&=y \left (1-y^{2}\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
3.927 |
|
| \begin{align*}
\frac {x y^{\prime \prime }}{1-x}+y&=\frac {1}{1-x} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
✓ |
✓ |
✗ |
2.050 |
|
| \begin{align*}
\frac {x y^{\prime \prime }}{1-x}+y x&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.773 |
|
| \begin{align*}
\frac {x y^{\prime \prime }}{1-x}+y&=\cos \left (x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
✓ |
✓ |
✗ |
1.850 |
|
| \begin{align*}
\frac {x y^{\prime \prime }}{-x^{2}+1}+y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
✗ |
2.270 |
|
| \begin{align*}
y^{\prime \prime }&=\left (x^{2}+3\right ) y \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.464 |
|
| \begin{align*}
y^{\prime \prime }+\left (x -1\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.348 |
|
| \begin{align*}
x^{\prime }&=x+2 y+2 t +1 \\
y^{\prime }&=5 x+y+3 t -1 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.920 |
|
| \begin{align*}
y^{\prime \prime }+20 y^{\prime }+500 y&=100000 \cos \left (100 x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.514 |
|
| \begin{align*}
y^{\prime \prime } \sin \left (2 x \right )^{2}+y^{\prime } \sin \left (4 x \right )-4 y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
4.521 |
|
| \begin{align*}
y^{\prime \prime }&=A y^{{2}/{3}} \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
✓ |
✓ |
2.682 |
|
| \begin{align*}
y^{\prime \prime }+2 x y^{\prime }+\left (x^{2}+1\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.472 |
|
| \begin{align*}
y^{\prime \prime }+2 \cot \left (x \right ) y^{\prime }-y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.691 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.701 |
|
| \begin{align*}
4 x^{2} y^{\prime \prime }+\left (-8 x^{2}+4 x \right ) y^{\prime }+\left (4 x^{2}-4 x -1\right ) y&=4 \sqrt {x}\, {\mathrm e}^{x} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.760 |
|
| \begin{align*}
x y^{\prime \prime }-\left (2 x +2\right ) y^{\prime }+\left (x +2\right ) y&=6 \,{\mathrm e}^{x} x^{3} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.459 |
|
| \begin{align*}
y^{\prime }+y&=\frac {1}{x} \\
\end{align*}
Series expansion around \(x=0\). |
[[_linear, ‘class A‘]] |
✗ |
✗ |
✓ |
✗ |
0.234 |
|
| \begin{align*}
y^{\prime }+y&=\frac {1}{x^{2}} \\
\end{align*}
Series expansion around \(x=0\). |
[[_linear, ‘class A‘]] |
✗ |
✗ |
✓ |
✗ |
0.270 |
|
| \begin{align*}
x y^{\prime }+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[_separable] |
✓ |
✓ |
✓ |
✗ |
0.266 |
|
| \begin{align*}
y^{\prime }&=\frac {1}{x} \\
\end{align*}
Series expansion around \(x=0\). |
[_quadrature] |
✗ |
✗ |
✓ |
✗ |
0.133 |
|
| \begin{align*}
y^{\prime \prime }&=\frac {1}{x} \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _quadrature]] |
✗ |
✗ |
✓ |
✗ |
0.501 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }&=\frac {1}{x} \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _missing_y]] |
✗ |
✗ |
✓ |
✗ |
0.687 |
|
| \begin{align*}
y^{\prime \prime }+y&=\frac {1}{x} \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
✗ |
✓ |
✗ |
0.594 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }+y&=\frac {1}{x} \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
✗ |
✓ |
✗ |
0.654 |
|
| \begin{align*}
h^{2}+\frac {2 a h}{\sqrt {1+{h^{\prime }}^{2}}}&=b^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
2.788 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }-24 y&=16-\left (x +2\right ) {\mathrm e}^{4 x} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.562 |
|
| \begin{align*}
y^{\prime \prime }+3 y^{\prime }-4 y&=6 \,{\mathrm e}^{2 t -2} \\
y \left (1\right ) &= 4 \\
y^{\prime }\left (1\right ) &= 5 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.336 |
|
| \begin{align*}
y^{\prime \prime }+y&={\mathrm e}^{a \cos \left (x \right )} \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.971 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{2 \ln \left (y\right ) y+y-x} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
4.767 |
|
| \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]] |
✓ |
✓ |
✓ |
✗ |
0.352 |
|
| \begin{align*}
x^{2} y^{\prime }+{\mathrm e}^{-y}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.288 |
|
| \begin{align*}
y^{\prime \prime }+{\mathrm e}^{y}&=0 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
✓ |
✓ |
8.628 |
|
| \begin{align*}
y^{\prime }&=\frac {y x +3 x -2 y+6}{y x -3 x -2 y+6} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
✗ |
11.898 |
|
| \begin{align*}
y^{\prime }&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.374 |
|
| \begin{align*}
y^{\prime }&=a \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.678 |
|
| \begin{align*}
y^{\prime }&=x \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.950 |
|
| \begin{align*}
y^{\prime }&=1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.780 |
|
| \begin{align*}
y^{\prime }&=a x \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.759 |
|
| \begin{align*}
y^{\prime }&=a x y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.480 |
|
| \begin{align*}
y^{\prime }&=a x +y \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.046 |
|
| \begin{align*}
y^{\prime }&=a x +b y \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.322 |
|
| \begin{align*}
y^{\prime }&=y \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.931 |
|
| \begin{align*}
y^{\prime }&=b y \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.971 |
|
| \begin{align*}
y^{\prime }&=a x +b y^{2} \\
\end{align*} |
[[_Riccati, _special]] |
✓ |
✓ |
✓ |
✗ |
29.630 |
|
| \begin{align*}
c y^{\prime }&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.411 |
|
| \begin{align*}
c y^{\prime }&=a \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.862 |
|
| \begin{align*}
c y^{\prime }&=a x \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.823 |
|
| \begin{align*}
c y^{\prime }&=a x +y \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.238 |
|
| \begin{align*}
c y^{\prime }&=a x +b y \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.358 |
|
| \begin{align*}
c y^{\prime }&=y \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.157 |
|
| \begin{align*}
c y^{\prime }&=b y \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.260 |
|
| \begin{align*}
c y^{\prime }&=a x +b y^{2} \\
\end{align*} |
[[_Riccati, _special]] |
✓ |
✓ |
✓ |
✗ |
28.050 |
|
| \begin{align*}
c y^{\prime }&=\frac {a x +b y^{2}}{r} \\
\end{align*} |
[[_Riccati, _special]] |
✓ |
✓ |
✓ |
✗ |
4.136 |
|
| \begin{align*}
c y^{\prime }&=\frac {a x +b y^{2}}{r x} \\
\end{align*} |
[_rational, _Riccati] |
✓ |
✓ |
✓ |
✗ |
6.220 |
|
| \begin{align*}
c y^{\prime }&=\frac {a x +b y^{2}}{r \,x^{2}} \\
\end{align*} |
[_rational, _Riccati] |
✓ |
✓ |
✓ |
✗ |
8.192 |
|
| \begin{align*}
c y^{\prime }&=\frac {a x +b y^{2}}{y} \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
2.965 |
|
| \begin{align*}
a \sin \left (x \right ) y x y^{\prime }&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.165 |
|
| \begin{align*}
f \left (x \right ) \sin \left (x \right ) y x y^{\prime } \pi &=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.172 |
|
| \begin{align*}
y^{\prime }&=\sin \left (x \right )+y \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.891 |
|
| \begin{align*}
y^{\prime }&=\sin \left (x \right )+y^{2} \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✓ |
✗ |
9.043 |
|
| \begin{align*}
y^{\prime }&=\cos \left (x \right )+\frac {y}{x} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.250 |
|
| \begin{align*}
y^{\prime }&=\cos \left (x \right )+\frac {y^{2}}{x} \\
\end{align*} |
[_Riccati] |
✗ |
✗ |
✗ |
✗ |
5.302 |
|
| \begin{align*}
y^{\prime }&=x +y+b y^{2} \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✓ |
✗ |
48.596 |
|
| \begin{align*}
x y^{\prime }&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.412 |
|
| \begin{align*}
5 y^{\prime }&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.403 |
|
| \begin{align*}
{\mathrm e} y^{\prime }&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.436 |
|
| \begin{align*}
\pi y^{\prime }&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.431 |
|
| \begin{align*}
\sin \left (x \right ) y^{\prime }&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.476 |
|
| \begin{align*}
f \left (x \right ) y^{\prime }&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.493 |
|
| \begin{align*}
x y^{\prime }&=1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.611 |
|
| \begin{align*}
x y^{\prime }&=\sin \left (x \right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.471 |
|
| \begin{align*}
\left (x -1\right ) y^{\prime }&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.418 |
|
| \begin{align*}
y y^{\prime }&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.145 |
|
| \begin{align*}
x y y^{\prime }&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.155 |
|
| \begin{align*}
x y \sin \left (x \right ) y^{\prime }&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.158 |
|