| # |
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]] |
✓ |
✓ |
✓ |
✓ |
0.479 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
1.258 |
|
| \begin{align*}
{y^{\prime \prime }}^{2}-2 y^{\prime \prime }+{y^{\prime }}^{2}-2 y^{\prime } x +x^{2}&=0 \\
y \left (0\right ) &= {\frac {1}{2}} \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✗ |
✗ |
6.476 |
|
| \begin{align*}
y^{\prime }-y^{\prime \prime } x +{y^{\prime \prime }}^{2}&=0 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.332 |
|
| \begin{align*}
{y^{\prime \prime }}^{3}&=12 y^{\prime } \left (-2 y^{\prime }+y^{\prime \prime } x \right ) \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✗ |
✗ |
0.660 |
|
| \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]] |
✓ |
✓ |
✓ |
✗ |
3.882 |
|
| \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]] |
✓ |
✓ |
✓ |
✗ |
3.211 |
|
| \begin{align*}
y^{\prime }&=2 y \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.169 |
|
| \begin{align*}
y^{\prime } t&=y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.689 |
|
| \begin{align*}
y^{\prime \prime }+4 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
2.016 |
|
| \begin{align*}
y^{\prime }&=2 y \left (y-1\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.022 |
|
| \begin{align*}
2 y y^{\prime }&=1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.787 |
|
| \begin{align*}
2 y y^{\prime }&=y^{2}+t -1 \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
2.650 |
|
| \begin{align*}
y^{\prime }&=\frac {y^{2}-4 t y+6 t^{2}}{t^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
5.446 |
|
| \begin{align*}
y^{\prime }&=3 y+12 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.697 |
|
| \begin{align*}
y^{\prime }&=-y+3 t \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.460 |
|
| \begin{align*}
y^{\prime }&=y^{2}-y \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.497 |
|
| \begin{align*}
y^{\prime }&=2 t y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.936 |
|
| \begin{align*}
y^{\prime }&=-{\mathrm e}^{y}-1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.378 |
|
| \begin{align*}
\left (1+t \right ) y^{\prime }+y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.767 |
|
| \begin{align*}
y^{\prime }&=y^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.226 |
|
| \begin{align*}
y^{\prime }&=t +3 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.265 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{2 t}-1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.278 |
|
| \begin{align*}
y^{\prime }&=t \,{\mathrm e}^{-t} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.337 |
|
| \begin{align*}
y^{\prime }&=\frac {1+t}{t} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.377 |
|
| \begin{align*}
y^{\prime \prime }&=2 t +1 \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.702 |
|
| \begin{align*}
y^{\prime \prime }&=6 \sin \left (3 t \right ) \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.739 |
|
| \begin{align*}
y^{\prime }&=3 y+12 \\
y \left (0\right ) &= -2 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.313 |
|
| \begin{align*}
y^{\prime }&=-y+3 t \\
y \left (0\right ) &= 0 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.695 |
|
| \begin{align*}
y^{\prime }&=y^{2}-y \\
y \left (0\right ) &= {\frac {1}{2}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.066 |
|
| \begin{align*}
\left (1+t \right ) y^{\prime }+y&=0 \\
y \left (1\right ) &= -9 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.352 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{2 t}-1 \\
y \left (0\right ) &= 4 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.435 |
|
| \begin{align*}
y^{\prime }&=t \,{\mathrm e}^{-t} \\
y \left (0\right ) &= -1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.401 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.998 |
|
| \begin{align*}
y^{\prime }&=t \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.093 |
|
| \begin{align*}
y^{\prime }&=y^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.478 |
|
| \begin{align*}
y^{\prime }&=y \left (y+t \right ) \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
2.007 |
|
| \begin{align*}
y^{\prime }&=1-y^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.232 |
|
| \begin{align*}
y^{\prime }&=y-t \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.411 |
|
| \begin{align*}
y^{\prime }&=-t y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.938 |
|
| \begin{align*}
y^{\prime }&=y-t^{2} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.911 |
|
| \begin{align*}
y^{\prime }&=t y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
11.815 |
|
| \begin{align*}
y^{\prime }&=\frac {t y}{1+y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.700 |
|
| \begin{align*}
y^{\prime }&=y^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.686 |
|
| \begin{align*}
y^{\prime }&=y \left (y+t \right ) \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
1.864 |
|
| \begin{align*}
y^{\prime }&=y-t \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.351 |
|
| \begin{align*}
y^{\prime }&=1-y^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.040 |
|
| \begin{align*}
y^{\prime }&=2 y \left (5-y\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.244 |
|
| \begin{align*}
y y^{\prime }&=1-y \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.905 |
|
| \begin{align*}
t^{2} y^{\prime }&=1-2 t y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.122 |
|
| \begin{align*}
\frac {y^{\prime }}{y}&=y-t \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
2.211 |
|
| \begin{align*}
y^{\prime } t&=y-2 t y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.350 |
|
| \begin{align*}
y^{\prime }&=t y^{2}-y^{2}+t -1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.083 |
|
| \begin{align*}
\left (t^{2}+3 y^{2}\right ) y^{\prime }&=-2 t y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
14.139 |
|
| \begin{align*}
y^{\prime }&=t^{2}+y^{2} \\
\end{align*} |
[[_Riccati, _special]] |
✓ |
✓ |
✓ |
✗ |
8.934 |
|
| \begin{align*}
{\mathrm e}^{t} y^{\prime }&=y^{3}-y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.406 |
|
| \begin{align*}
y y^{\prime }&=t \\
y \left (2\right ) &= -1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
15.133 |
|
| \begin{align*}
1-y^{2}-t y y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
11.175 |
|
| \begin{align*}
y^{3} y^{\prime }&=t \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.822 |
|
| \begin{align*}
y^{4} y^{\prime }&=t +2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.503 |
|
| \begin{align*}
y^{\prime }&=t y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.425 |
|
| \begin{align*}
\tan \left (t \right ) y+y^{\prime }&=\tan \left (t \right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.167 |
|
| \begin{align*}
y^{\prime }&=t^{m} y^{n} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
40.952 |
|
| \begin{align*}
y^{\prime }&=4 y-y^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.322 |
|
| \begin{align*}
y y^{\prime }&=1+y^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.851 |
|
| \begin{align*}
y^{\prime }&=1+y^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.904 |
|
| \begin{align*}
t y y^{\prime }+t^{2}+1&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.982 |
|
| \begin{align*}
y+1+\left (y-1\right ) \left (t^{2}+1\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.504 |
|
| \begin{align*}
2 y y^{\prime }&={\mathrm e}^{t} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.108 |
|
| \begin{align*}
\left (1-t \right ) y^{\prime }&=y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.890 |
|
| \begin{align*}
-y+y^{\prime }&=y^{2} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
5.055 |
|
| \begin{align*}
y^{\prime }&=4 t y^{2} \\
y \left (1\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
19.088 |
|
| \begin{align*}
y^{\prime }&=\frac {y x +2 y}{x} \\
y \left (1\right ) &= {\mathrm e} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.690 |
|
| \begin{align*}
2 t y+y^{\prime }&=0 \\
y \left (0\right ) &= 4 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.337 |
|
| \begin{align*}
y^{\prime }&=\frac {\cot \left (y\right )}{t} \\
y \left (1\right ) &= \frac {\pi }{4} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.640 |
|
| \begin{align*}
\frac {\left (u^{2}+1\right ) y^{\prime }}{y}&=u \\
y \left (0\right ) &= 2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
3.841 |
|
| \begin{align*}
t y-\left (t +2\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.791 |
|
| \begin{align*}
y^{\prime }&=\frac {1+y^{2}}{t} \\
y \left (1\right ) &= \sqrt {3} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.581 |
|
| \begin{align*}
3 y+y^{\prime }&={\mathrm e}^{t} \\
y \left (0\right ) &= -2 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.103 |
|
| \begin{align*}
\cos \left (t \right ) y^{\prime }+\sin \left (t \right ) y&=1 \\
y \left (0\right ) &= 5 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.239 |
|
| \begin{align*}
-2 y+y^{\prime }&={\mathrm e}^{2 t} \\
y \left (0\right ) &= 4 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.876 |
|
| \begin{align*}
y^{\prime } t +y&={\mathrm e}^{t} \\
y \left (1\right ) &= 0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.316 |
|
| \begin{align*}
y^{\prime } t +m y&=t \ln \left (t \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.243 |
|
| \begin{align*}
y^{\prime }&=-\frac {y}{t}+\cos \left (t^{2}\right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.231 |
|
| \begin{align*}
y^{\prime }+2 y&=\sin \left (t \right ) \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.176 |
|
| \begin{align*}
y^{\prime }-3 y&=25 \cos \left (4 t \right ) \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.571 |
|
| \begin{align*}
t \left (1+t \right ) y^{\prime }&=2+y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.041 |
|
| \begin{align*}
z^{\prime }&=2 t \left (z-t^{2}\right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.947 |
|
| \begin{align*}
y^{\prime }+a y&=b \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.016 |
|
| \begin{align*}
y \cos \left (t \right )+y^{\prime }&=\cos \left (t \right ) \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.860 |
|
| \begin{align*}
y^{\prime }-\frac {2 y}{1+t}&=\left (1+t \right )^{2} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.768 |
|
| \begin{align*}
y^{\prime }-\frac {2 y}{t}&=\frac {1+t}{t} \\
y \left (1\right ) &= -3 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.259 |
|
| \begin{align*}
y^{\prime }+a y&={\mathrm e}^{-a t} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.448 |
|
| \begin{align*}
y^{\prime }+a y&={\mathrm e}^{b t} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.456 |
|
| \begin{align*}
y^{\prime }+a y&=t^{n} {\mathrm e}^{-a t} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
4.439 |
|
| \begin{align*}
y^{\prime }&=\tan \left (t \right ) y+\sec \left (t \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.259 |
|
| \begin{align*}
y^{\prime } t +2 y \ln \left (t \right )&=4 \ln \left (t \right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.823 |
|
| \begin{align*}
y^{\prime }-\frac {n y}{t}&={\mathrm e}^{t} t^{n} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.761 |
|
| \begin{align*}
-y+y^{\prime }&={\mathrm e}^{2 t} t \\
y \left (0\right ) &= a \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.095 |
|
| \begin{align*}
y^{\prime } t +3 y&=t^{2} \\
y \left (-1\right ) &= 2 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.858 |
|