| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
y^{\prime }&=f \left (x \right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.238 |
|
| \begin{align*}
y^{\prime \prime }&=f \left (x \right ) \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.966 |
|
| \begin{align*}
{y^{\prime }}^{2} x -4 y^{\prime }-12 x^{3}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.303 |
|
| \begin{align*}
y^{\prime }&=5-y \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.902 |
|
| \begin{align*}
y^{\prime }&=4+y^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
4.160 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-20 y^{\prime \prime \prime }+158 y^{\prime \prime }-580 y^{\prime }+841 y&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.086 |
|
| \begin{align*}
x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }+20 x y^{\prime }-78 y&=0 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.175 |
|
| \begin{align*}
y^{\prime }&=y-y^{2} \\
y \left (0\right ) &= -{\frac {1}{3}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✗ |
✓ |
1.856 |
|
| \begin{align*}
y^{\prime }&=y-y^{2} \\
y \left (-1\right ) &= 2 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✗ |
✓ |
1.680 |
|
| \begin{align*}
y^{\prime }+2 x y^{2}&=0 \\
y \left (2\right ) &= {\frac {1}{3}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.339 |
|
| \begin{align*}
y^{\prime }+2 x y^{2}&=0 \\
y \left (-2\right ) &= {\frac {1}{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.128 |
|
| \begin{align*}
y^{\prime }+2 x y^{2}&=0 \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.925 |
|
| \begin{align*}
y^{\prime }+2 x y^{2}&=0 \\
y \left (\frac {1}{2}\right ) &= -4 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.251 |
|
| \begin{align*}
x^{\prime \prime }+x&=0 \\
x \left (0\right ) &= -1 \\
x^{\prime }\left (0\right ) &= 8 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
2.050 |
|
| \begin{align*}
x^{\prime \prime }+x&=0 \\
x \left (\frac {\pi }{2}\right ) &= 0 \\
x^{\prime }\left (\frac {\pi }{2}\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
1.295 |
|
| \begin{align*}
x^{\prime \prime }+x&=0 \\
x \left (\frac {\pi }{6}\right ) &= {\frac {1}{2}} \\
x^{\prime }\left (\frac {\pi }{6}\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
1.844 |
|
| \begin{align*}
x^{\prime \prime }+x&=0 \\
x \left (\frac {\pi }{4}\right ) &= \sqrt {2} \\
x^{\prime }\left (\frac {\pi }{4}\right ) &= 2 \sqrt {2} \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
1.694 |
|
| \begin{align*}
y^{\prime \prime }-y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
2.103 |
|
| \begin{align*}
y^{\prime \prime }-y&=0 \\
y \left (1\right ) &= 0 \\
y^{\prime }\left (1\right ) &= {\mathrm e} \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
1.136 |
|
| \begin{align*}
y^{\prime \prime }-y&=0 \\
y \left (-1\right ) &= 5 \\
y^{\prime }\left (-1\right ) &= -5 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
1.300 |
|
| \begin{align*}
y^{\prime \prime }-y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
1.171 |
|
| \begin{align*}
y^{\prime }&=3 y^{{2}/{3}} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
10.707 |
|
| \begin{align*}
x y^{\prime }&=2 y \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
4.459 |
|
| \begin{align*}
y^{\prime }&=y^{{2}/{3}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
3.019 |
|
| \begin{align*}
y^{\prime }&=\sqrt {y x} \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✓ |
19.694 |
|
| \begin{align*}
x y^{\prime }&=y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.971 |
|
| \begin{align*}
y^{\prime }-y&=x \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.579 |
|
| \begin{align*}
\left (4-y^{2}\right ) y^{\prime }&=x^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.642 |
|
| \begin{align*}
\left (y^{3}+1\right ) y^{\prime }&=x^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.557 |
|
| \begin{align*}
\left (x^{2}+y^{2}\right ) y^{\prime }&=y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
12.765 |
|
| \begin{align*}
\left (-x +y\right ) y^{\prime }&=x +y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
20.824 |
|
| \begin{align*}
y^{\prime }&=\sqrt {y^{2}-9} \\
y \left (1\right ) &= 4 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
53.152 |
|
| \begin{align*}
y^{\prime }&=\sqrt {y^{2}-9} \\
y \left (5\right ) &= 3 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
12.765 |
|
| \begin{align*}
y^{\prime }&=\sqrt {y^{2}-9} \\
y \left (2\right ) &= -3 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
11.066 |
|
| \begin{align*}
y^{\prime }&=\sqrt {y^{2}-9} \\
y \left (-1\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
12.550 |
|
| \begin{align*}
x y^{\prime }&=y \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
3.210 |
|
| \begin{align*}
y^{\prime }&=1+y^{2} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✗ |
✓ |
2.997 |
|
| \begin{align*}
y^{\prime }&=y^{2} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
3.476 |
|
| \begin{align*}
y^{\prime }&=y^{2} \\
y \left (0\right ) &= -1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.247 |
|
| \begin{align*}
y^{\prime }&=y^{2} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
5.576 |
|
| \begin{align*}
y^{\prime }&=y^{2} \\
y \left (1\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
3.359 |
|
| \begin{align*}
y^{\prime }&=y^{2} \\
y \left (3\right ) &= -1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.487 |
|
| \begin{align*}
y y^{\prime }&=3 x \\
y \left (-2\right ) &= 3 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
10.086 |
|
| \begin{align*}
y y^{\prime }&=3 x \\
y \left (2\right ) &= -4 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
9.181 |
|
| \begin{align*}
y y^{\prime }&=3 x \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
19.594 |
|
| \begin{align*}
4 y+y^{\prime \prime }&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (\frac {\pi }{4}\right ) &= 3 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✗ |
✗ |
✗ |
5.563 |
|
| \begin{align*}
4 y+y^{\prime \prime }&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (\pi \right ) &= 0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
1.174 |
|
| \begin{align*}
4 y+y^{\prime \prime }&=0 \\
y^{\prime }\left (0\right ) &= 0 \\
y^{\prime }\left (\frac {\pi }{6}\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
1.411 |
|
| \begin{align*}
4 y+y^{\prime \prime }&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (\pi \right ) &= 5 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
1.619 |
|
| \begin{align*}
4 y+y^{\prime \prime }&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (\pi \right ) &= 2 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
1.116 |
|
| \begin{align*}
4 y+y^{\prime \prime }&=0 \\
y^{\prime }\left (\frac {\pi }{2}\right ) &= 1 \\
y^{\prime }\left (\pi \right ) &= 0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✗ |
✗ |
✗ |
✗ |
4.220 |
|
| \begin{align*}
y^{\prime }&=x -2 y \\
y \left (0\right ) &= {\frac {1}{2}} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.994 |
|
| \begin{align*}
y^{\prime }&=x^{2}+y^{2} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[[_Riccati, _special]] |
✗ |
✓ |
✓ |
✗ |
11.805 |
|
| \begin{align*}
2 y^{\prime \prime }-3 y^{2}&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
✗ |
✗ |
1.360 |
|
| \begin{align*}
2 y+y^{\prime }&=3 x -6 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.787 |
|
| \begin{align*}
y^{\prime }&=x \sqrt {y} \\
y \left (2\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
12.375 |
|
| \begin{align*}
x y^{\prime }&=2 x \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.095 |
|
| \begin{align*}
y^{\prime }&=2 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.842 |
|
| \begin{align*}
y^{\prime }&=2 y-4 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.006 |
|
| \begin{align*}
x y^{\prime }&=y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.107 |
|
| \begin{align*}
y^{\prime \prime }+9 y&=18 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
2.555 |
|
| \begin{align*}
-y^{\prime }+x y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.912 |
|
| \begin{align*}
y^{\prime \prime }&=y^{\prime } \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
1.077 |
|
| \begin{align*}
y^{\prime }&=y \left (-3+y\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.584 |
|
| \begin{align*}
3 x y^{\prime }-2 y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.749 |
|
| \begin{align*}
\left (-2+2 y\right ) y^{\prime }&=2 x -1 \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
10.430 |
|
| \begin{align*}
x y^{\prime }+y&=2 x \\
y \left (x_{0} \right ) &= 1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
7.647 |
|
| \begin{align*}
y^{\prime }&=x^{2}+y^{2} \\
y \left (1\right ) &= -1 \\
\end{align*} |
[[_Riccati, _special]] |
✓ |
✓ |
✓ |
✗ |
10.951 |
|
| \begin{align*}
{y^{\prime }}^{2}&=4 x^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.330 |
|
| \begin{align*}
y^{\prime }&=6 \sqrt {y}+5 x^{3} \\
y \left (-1\right ) &= 4 \\
\end{align*} |
[_Chini] |
✗ |
✗ |
✗ |
✗ |
3.691 |
|
| \begin{align*}
y^{\prime \prime }+y&=2 \cos \left (x \right )-2 \sin \left (x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.700 |
|
| \begin{align*}
y^{\prime \prime }+y&=\sec \left (x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.559 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+x y^{\prime }+y&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
1.755 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+x y^{\prime }+y&=\sec \left (\ln \left (x \right )\right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
8.349 |
|
| \begin{align*}
y^{\prime }+y \sin \left (x \right )&=x \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.464 |
|
| \begin{align*}
y^{\prime }-2 y x&={\mathrm e}^{x} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.286 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+\left (x^{2}-x \right ) y^{\prime }+\left (1-x \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.955 |
|
| \begin{align*}
y^{\prime \prime }+y&={\mathrm e}^{x^{2}} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.778 |
|
| \begin{align*}
x y^{\prime }+y&=\frac {1}{y^{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.951 |
|
| \begin{align*}
1+{y^{\prime }}^{2}&=\frac {1}{y^{2}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.063 |
|
| \begin{align*}
y^{\prime \prime }&=2 y {y^{\prime }}^{3} \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
✓ |
✓ |
✗ |
0.538 |
|
| \begin{align*}
\left (-y x +1\right ) y^{\prime }&=y^{2} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
42.400 |
|
| \begin{align*}
y^{\prime \prime }+9 y&=5 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
2.647 |
|
| \begin{align*}
2 y+y^{\prime }&=3 x \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.832 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime }-3 y&=6 x +4 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.633 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime }-3 y&=6 x +4 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= -3 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.611 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime }-3 y&=6 x +4 \\
y \left (1\right ) &= 4 \\
y^{\prime }\left (1\right ) &= -2 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.598 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime }-3 y&=6 x +4 \\
y \left (-1\right ) &= 0 \\
y^{\prime }\left (-1\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.627 |
|
| \begin{align*}
y^{\prime }&=x^{2}-y^{2} \\
y \left (-2\right ) &= 1 \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✓ |
✗ |
8.598 |
|
| \begin{align*}
y^{\prime }&=x^{2}-y^{2} \\
y \left (3\right ) &= 0 \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✓ |
✗ |
7.500 |
|
| \begin{align*}
y^{\prime }&=x^{2}-y^{2} \\
y \left (0\right ) &= 2 \\
\end{align*} |
[_Riccati] |
✗ |
✓ |
✓ |
✗ |
7.348 |
|
| \begin{align*}
y^{\prime }&=x^{2}-y^{2} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✓ |
✗ |
6.140 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{-\frac {x y^{2}}{100}} \\
y \left (-6\right ) &= 0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
✗ |
1.714 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{-\frac {x y^{2}}{100}} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
✗ |
0.971 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{-\frac {x y^{2}}{100}} \\
y \left (0\right ) &= -4 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
✗ |
0.980 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{-\frac {x y^{2}}{100}} \\
y \left (8\right ) &= -4 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
✗ |
0.984 |
|
| \begin{align*}
y^{\prime }&=-y x +1 \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.035 |
|
| \begin{align*}
y^{\prime }&=-y x +1 \\
y \left (-1\right ) &= 0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.022 |
|
| \begin{align*}
y^{\prime }&=-y x +1 \\
y \left (2\right ) &= 2 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.061 |
|
| \begin{align*}
y^{\prime }&=-y x +1 \\
y \left (0\right ) &= -4 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.918 |
|