| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
x^{4} y^{\prime \prime }&=y^{\prime } \left (y^{\prime }+x^{3}\right ) \\
y \left (1\right ) &= 2 \\
y^{\prime }\left (1\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.637 |
|
| \begin{align*}
y^{\prime \prime }&=2 x +\left (x^{2}-y^{\prime }\right )^{2} \\
\end{align*} |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✓ |
1.839 |
|
| \begin{align*}
{y^{\prime \prime }}^{2}-2 y^{\prime \prime }+{y^{\prime }}^{2}-2 x y^{\prime }+x^{2}&=0 \\
y \left (0\right ) &= {\frac {1}{2}} \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✗ |
✗ |
9.776 |
|
| \begin{align*}
y^{\prime }-x y^{\prime \prime }+{y^{\prime \prime }}^{2}&=0 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.533 |
|
| \begin{align*}
{y^{\prime \prime }}^{3}&=12 y^{\prime } \left (-2 y^{\prime }+x y^{\prime \prime }\right ) \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✗ |
✗ |
0.979 |
|
| \begin{align*}
3 y y^{\prime } y^{\prime \prime }&=-1+{y^{\prime }}^{3} \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
✓ |
✗ |
5.719 |
|
| \begin{align*}
4 y {y^{\prime }}^{2} y^{\prime \prime }&=3+{y^{\prime }}^{4} \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
✓ |
✗ |
5.044 |
|
| \begin{align*}
y^{\prime }&=2 y \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.875 |
|
| \begin{align*}
t y^{\prime }&=y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.743 |
|
| \begin{align*}
y^{\prime \prime }+4 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
2.687 |
|
| \begin{align*}
y^{\prime }&=2 y \left (-1+y\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.717 |
|
| \begin{align*}
2 y y^{\prime }&=1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.798 |
|
| \begin{align*}
2 y y^{\prime }&=y^{2}+t -1 \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.770 |
|
| \begin{align*}
y^{\prime }&=\frac {y^{2}-4 y t +6 t^{2}}{t^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
8.174 |
|
| \begin{align*}
y^{\prime }&=3 y+12 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.072 |
|
| \begin{align*}
y^{\prime }&=-y+3 t \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.128 |
|
| \begin{align*}
y^{\prime }&=y^{2}-y \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.016 |
|
| \begin{align*}
y^{\prime }&=2 y t \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.427 |
|
| \begin{align*}
y^{\prime }&=-{\mathrm e}^{y}-1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
3.108 |
|
| \begin{align*}
\left (t +1\right ) y^{\prime }+y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.821 |
|
| \begin{align*}
y^{\prime }&=y^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
3.332 |
|
| \begin{align*}
y^{\prime }&=t +3 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.394 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{2 t}-1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.401 |
|
| \begin{align*}
y^{\prime }&=t \,{\mathrm e}^{-t} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.425 |
|
| \begin{align*}
y^{\prime }&=\frac {t +1}{t} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.480 |
|
| \begin{align*}
y^{\prime \prime }&=2 t +1 \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
1.075 |
|
| \begin{align*}
y^{\prime \prime }&=6 \sin \left (3 t \right ) \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
1.091 |
|
| \begin{align*}
y^{\prime }&=3 y+12 \\
y \left (0\right ) &= -2 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.921 |
|
| \begin{align*}
y^{\prime }&=-y+3 t \\
y \left (0\right ) &= 0 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.204 |
|
| \begin{align*}
y^{\prime }&=y^{2}-y \\
y \left (0\right ) &= {\frac {1}{2}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.793 |
|
| \begin{align*}
\left (t +1\right ) y^{\prime }+y&=0 \\
y \left (1\right ) &= -9 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.217 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{2 t}-1 \\
y \left (0\right ) &= 4 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.505 |
|
| \begin{align*}
y^{\prime }&=t \,{\mathrm e}^{-t} \\
y \left (0\right ) &= -1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.518 |
|
| \begin{align*}
y^{\prime \prime }&=6 \sin \left (3 t \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
1.434 |
|
| \begin{align*}
y^{\prime }&=t \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.442 |
|
| \begin{align*}
y^{\prime }&=y^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.243 |
|
| \begin{align*}
y^{\prime }&=y \left (t +y\right ) \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
2.796 |
|
| \begin{align*}
y^{\prime }&=1-y^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
3.411 |
|
| \begin{align*}
y^{\prime }&=y-t \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.009 |
|
| \begin{align*}
y^{\prime }&=-y t \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.408 |
|
| \begin{align*}
y^{\prime }&=y-t^{2} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.634 |
|
| \begin{align*}
y^{\prime }&=t y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
10.025 |
|
| \begin{align*}
y^{\prime }&=\frac {t y}{1+y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.971 |
|
| \begin{align*}
y^{\prime }&=y^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.691 |
|
| \begin{align*}
y^{\prime }&=y \left (t +y\right ) \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
2.592 |
|
| \begin{align*}
y^{\prime }&=y-t \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.978 |
|
| \begin{align*}
y^{\prime }&=1-y^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.769 |
|
| \begin{align*}
y^{\prime }&=2 y \left (5-y\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.859 |
|
| \begin{align*}
y y^{\prime }&=1-y \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.329 |
|
| \begin{align*}
t^{2} y^{\prime }&=1-2 y t \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.717 |
|
| \begin{align*}
\frac {y^{\prime }}{y}&=y-t \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
2.988 |
|
| \begin{align*}
t y^{\prime }&=y-2 y t \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.249 |
|
| \begin{align*}
y^{\prime }&=t y^{2}-y^{2}+t -1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.442 |
|
| \begin{align*}
\left (t^{2}+3 y^{2}\right ) y^{\prime }&=-2 y t \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
13.181 |
|
| \begin{align*}
y^{\prime }&=t^{2}+y^{2} \\
\end{align*} |
[[_Riccati, _special]] |
✓ |
✓ |
✓ |
✗ |
9.967 |
|
| \begin{align*}
{\mathrm e}^{t} y^{\prime }&=y^{3}-y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
9.739 |
|
| \begin{align*}
y y^{\prime }&=t \\
y \left (2\right ) &= -1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
17.621 |
|
| \begin{align*}
1-y^{2}-t y y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
19.438 |
|
| \begin{align*}
y^{3} y^{\prime }&=t \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.586 |
|
| \begin{align*}
y^{4} y^{\prime }&=t +2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.258 |
|
| \begin{align*}
y^{\prime }&=t y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.888 |
|
| \begin{align*}
\tan \left (t \right ) y+y^{\prime }&=\tan \left (t \right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.625 |
|
| \begin{align*}
y^{\prime }&=t^{m} y^{n} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
45.994 |
|
| \begin{align*}
y^{\prime }&=4 y-y^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.915 |
|
| \begin{align*}
y y^{\prime }&=1+y^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.656 |
|
| \begin{align*}
y^{\prime }&=1+y^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
4.045 |
|
| \begin{align*}
t y y^{\prime }+t^{2}+1&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.097 |
|
| \begin{align*}
y+1+\left (-1+y\right ) \left (t^{2}+1\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.473 |
|
| \begin{align*}
2 y y^{\prime }&={\mathrm e}^{t} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.184 |
|
| \begin{align*}
\left (1-t \right ) y^{\prime }&=y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.830 |
|
| \begin{align*}
-y+y^{\prime }&=y^{2} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
7.153 |
|
| \begin{align*}
y^{\prime }&=4 t y^{2} \\
y \left (1\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
23.362 |
|
| \begin{align*}
y^{\prime }&=\frac {y x +2 y}{x} \\
y \left (1\right ) &= {\mathrm e} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.879 |
|
| \begin{align*}
2 y t +y^{\prime }&=0 \\
y \left (0\right ) &= 4 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.499 |
|
| \begin{align*}
y^{\prime }&=\frac {\cot \left (y\right )}{t} \\
y \left (1\right ) &= \frac {\pi }{4} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
9.899 |
|
| \begin{align*}
\frac {\left (u^{2}+1\right ) y^{\prime }}{y}&=u \\
y \left (0\right ) &= 2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
5.239 |
|
| \begin{align*}
y t -\left (t +2\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.262 |
|
| \begin{align*}
y^{\prime }&=\frac {1+y^{2}}{t} \\
y \left (1\right ) &= \sqrt {3} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.843 |
|
| \begin{align*}
3 y+y^{\prime }&={\mathrm e}^{t} \\
y \left (0\right ) &= -2 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.694 |
|
| \begin{align*}
\cos \left (t \right ) y^{\prime }+\sin \left (t \right ) y&=1 \\
y \left (0\right ) &= 5 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.942 |
|
| \begin{align*}
-2 y+y^{\prime }&={\mathrm e}^{2 t} \\
y \left (0\right ) &= 4 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.323 |
|
| \begin{align*}
t y^{\prime }+y&={\mathrm e}^{t} \\
y \left (1\right ) &= 0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.758 |
|
| \begin{align*}
t y^{\prime }+m y&=t \ln \left (t \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.923 |
|
| \begin{align*}
y^{\prime }&=-\frac {y}{t}+\cos \left (t^{2}\right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.559 |
|
| \begin{align*}
y^{\prime }+2 y&=\sin \left (t \right ) \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.608 |
|
| \begin{align*}
y^{\prime }-3 y&=25 \cos \left (4 t \right ) \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.977 |
|
| \begin{align*}
t \left (t +1\right ) y^{\prime }&=y+2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.998 |
|
| \begin{align*}
z^{\prime }&=2 t \left (z-t^{2}\right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.848 |
|
| \begin{align*}
y^{\prime }+a y&=b \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.513 |
|
| \begin{align*}
\cos \left (t \right ) y+y^{\prime }&=\cos \left (t \right ) \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.658 |
|
| \begin{align*}
y^{\prime }-\frac {2 y}{t +1}&=\left (t +1\right )^{2} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.565 |
|
| \begin{align*}
y^{\prime }-\frac {2 y}{t}&=\frac {t +1}{t} \\
y \left (1\right ) &= -3 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.403 |
|
| \begin{align*}
y^{\prime }+a y&={\mathrm e}^{-a t} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.741 |
|
| \begin{align*}
y^{\prime }+a y&={\mathrm e}^{b t} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.476 |
|
| \begin{align*}
y^{\prime }+a y&=t^{n} {\mathrm e}^{-a t} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
5.520 |
|
| \begin{align*}
y^{\prime }&=\tan \left (t \right ) y+\sec \left (t \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.892 |
|
| \begin{align*}
t y^{\prime }+2 \ln \left (t \right ) y&=4 \ln \left (t \right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.638 |
|
| \begin{align*}
y^{\prime }-\frac {n y}{t}&={\mathrm e}^{t} t^{n} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.407 |
|
| \begin{align*}
-y+y^{\prime }&={\mathrm e}^{2 t} t \\
y \left (0\right ) &= a \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.464 |
|
| \begin{align*}
t y^{\prime }+3 y&=t^{2} \\
y \left (-1\right ) &= 2 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
6.023 |
|