| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
y^{\prime }&=-3 y+4 \cos \left (2 t \right ) \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.112 |
|
| \begin{align*}
y^{\prime }&=2 y+\sin \left (2 t \right ) \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.198 |
|
| \begin{align*}
y^{\prime }&=3 y-4 \,{\mathrm e}^{3 t} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.547 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{2}+4 \,{\mathrm e}^{\frac {t}{2}} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.600 |
|
| \begin{align*}
y^{\prime }+2 y&={\mathrm e}^{\frac {t}{3}} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.049 |
|
| \begin{align*}
-2 y+y^{\prime }&=3 \,{\mathrm e}^{-2 t} \\
y \left (0\right ) &= 10 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.913 |
|
| \begin{align*}
y+y^{\prime }&=\cos \left (2 t \right ) \\
y \left (0\right ) &= 5 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.286 |
|
| \begin{align*}
3 y+y^{\prime }&=\cos \left (2 t \right ) \\
y \left (0\right ) &= -1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.473 |
|
| \begin{align*}
-2 y+y^{\prime }&=7 \,{\mathrm e}^{2 t} \\
y \left (0\right ) &= 3 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.775 |
|
| \begin{align*}
y^{\prime }+2 y&=3 t^{2}+2 t -1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.441 |
|
| \begin{align*}
y^{\prime }+2 y&=t^{2}+2 t +1+{\mathrm e}^{4 t} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.580 |
|
| \begin{align*}
y+y^{\prime }&=t^{3}+\sin \left (3 t \right ) \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.400 |
|
| \begin{align*}
y^{\prime }-3 y&=2 t -{\mathrm e}^{4 t} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.740 |
|
| \begin{align*}
y+y^{\prime }&=\cos \left (2 t \right )+3 \sin \left (2 t \right )+{\mathrm e}^{-t} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.729 |
|
| \begin{align*}
y^{\prime }&=-\frac {y}{t}+2 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.832 |
|
| \begin{align*}
y^{\prime }&=\frac {3 y}{t}+t^{5} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.599 |
|
| \begin{align*}
y^{\prime }&=-\frac {y}{t +1}+t^{2} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.984 |
|
| \begin{align*}
y^{\prime }&=-2 y t +4 \,{\mathrm e}^{-t^{2}} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.707 |
|
| \begin{align*}
y^{\prime }-\frac {2 t y}{t^{2}+1}&=3 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.649 |
|
| \begin{align*}
y^{\prime }-\frac {2 y}{t}&=t^{3} {\mathrm e}^{t} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.891 |
|
| \begin{align*}
y^{\prime }&=-\frac {y}{t +1}+2 \\
y \left (0\right ) &= 3 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.615 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{t +1}+4 t^{2}+4 t \\
y \left (1\right ) &= 10 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.615 |
|
| \begin{align*}
y^{\prime }&=-\frac {y}{t}+2 \\
y \left (1\right ) &= 3 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
6.272 |
|
| \begin{align*}
y^{\prime }&=-2 y t +4 \,{\mathrm e}^{-t^{2}} \\
y \left (0\right ) &= 3 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.934 |
|
| \begin{align*}
y^{\prime }-\frac {2 y}{t}&=2 t^{2} \\
y \left (-2\right ) &= 4 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.424 |
|
| \begin{align*}
y^{\prime }-\frac {3 y}{t}&=2 t^{3} {\mathrm e}^{2 t} \\
y \left (1\right ) &= 0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.873 |
|
| \begin{align*}
y^{\prime }&=\sin \left (t \right ) y+4 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.128 |
|
| \begin{align*}
y^{\prime }&=t^{2} y+4 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.854 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{t^{2}}+4 \cos \left (t \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.336 |
|
| \begin{align*}
y^{\prime }&=y+4 \cos \left (t^{2}\right ) \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.585 |
|
| \begin{align*}
y^{\prime }&=-{\mathrm e}^{-t^{2}} y+\cos \left (t \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.928 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{\sqrt {t^{3}-3}}+t \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
74.306 |
|
| \begin{align*}
y^{\prime }&=a t y+4 \,{\mathrm e}^{-t^{2}} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.970 |
|
| \begin{align*}
y^{\prime }&=t^{r} y+4 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✗ |
2.183 |
|
| \begin{align*}
v^{\prime }+\frac {2 v}{5}&=3 \cos \left (2 t \right ) \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.282 |
|
| \begin{align*}
y^{\prime }&=-2 y t +4 \,{\mathrm e}^{-t^{2}} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.681 |
|
| \begin{align*}
y^{\prime }+2 y&=3 \,{\mathrm e}^{-2 t} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.542 |
|
| \begin{align*}
y^{\prime }&=3 y \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.289 |
|
| \begin{align*}
y^{\prime }&=t^{2} \left (t^{2}+1\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.431 |
|
| \begin{align*}
y^{\prime }&=-\sin \left (y\right )^{5} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
16.146 |
|
| \begin{align*}
y^{\prime }&=\frac {\left (t^{2}-4\right ) \left (1+y\right ) {\mathrm e}^{y}}{\left (t -1\right ) \left (3-y\right )} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.094 |
|
| \begin{align*}
y^{\prime }&=\sin \left (y\right )^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.457 |
|
| \begin{align*}
y^{\prime }&=\left (y-3\right ) \left (\sin \left (y\right ) \sin \left (t \right )+\cos \left (t \right )+1\right ) \\
y \left (0\right ) &= 4 \\
\end{align*} |
[‘x=_G(y,y’)‘] |
✗ |
✗ |
✗ |
✗ |
16.783 |
|
| \begin{align*}
y^{\prime }&=y+{\mathrm e}^{-t} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.737 |
|
| \begin{align*}
y^{\prime }&=3-2 y \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.881 |
|
| \begin{align*}
y^{\prime }&=y t \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.923 |
|
| \begin{align*}
y^{\prime }&=3 y+{\mathrm e}^{7 t} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.791 |
|
| \begin{align*}
y^{\prime }&=\frac {t y}{t^{2}+1} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.677 |
|
| \begin{align*}
y^{\prime }&=-5 y+\sin \left (3 t \right ) \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.171 |
|
| \begin{align*}
y^{\prime }&=t +\frac {2 y}{t +1} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.210 |
|
| \begin{align*}
y^{\prime }&=3+y^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
3.806 |
|
| \begin{align*}
y^{\prime }&=2 y-y^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.576 |
|
| \begin{align*}
y^{\prime }&=-3 y+{\mathrm e}^{-2 t}+t^{2} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.186 |
|
| \begin{align*}
x^{\prime }&=-x t \\
x \left (0\right ) &= {\mathrm e} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.967 |
|
| \begin{align*}
y^{\prime }&=2 y+\cos \left (4 t \right ) \\
y \left (0\right ) &= 1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.622 |
|
| \begin{align*}
y^{\prime }&=3 y+2 \,{\mathrm e}^{3 t} \\
y \left (0\right ) &= -1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.775 |
|
| \begin{align*}
y^{\prime }&=t^{2} y^{3}+y^{3} \\
y \left (0\right ) &= -{\frac {1}{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.494 |
|
| \begin{align*}
y^{\prime }+5 y&=3 \,{\mathrm e}^{-5 t} \\
y \left (0\right ) &= -2 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.793 |
|
| \begin{align*}
y^{\prime }&=2 y t +3 t \,{\mathrm e}^{t^{2}} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.101 |
|
| \begin{align*}
y^{\prime }&=\frac {\left (t +1\right )^{2}}{\left (1+y\right )^{2}} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
9.852 |
|
| \begin{align*}
y^{\prime }&=2 t y^{2}+3 y^{2} t^{2} \\
y \left (1\right ) &= -1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.355 |
|
| \begin{align*}
y^{\prime }&=1-y^{2} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
4.732 |
|
| \begin{align*}
y^{\prime }&=\frac {t^{2}}{y+t^{3} y} \\
y \left (0\right ) &= -2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.862 |
|
| \begin{align*}
y^{\prime }&=y^{2}-2 y+1 \\
y \left (0\right ) &= 2 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.614 |
|
| \begin{align*}
y^{\prime }&=\left (-2+y\right ) \left (y+1-\cos \left (t \right )\right ) \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✓ |
✓ |
6.006 |
|
| \begin{align*}
y^{\prime }&=\left (-1+y\right ) \left (-2+y\right ) \left (y-{\mathrm e}^{\frac {t}{2}}\right ) \\
\end{align*} |
[_Abel] |
✗ |
✗ |
✗ |
✗ |
12.544 |
|
| \begin{align*}
y^{\prime }&=t^{2} y+1+y+t^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.158 |
|
| \begin{align*}
y^{\prime }&=\frac {2 y+1}{t} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.130 |
|
| \begin{align*}
y^{\prime }&=3-y^{2} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✗ |
✗ |
3.143 |
|
| \begin{align*}
x^{\prime }&=x-y \\
y^{\prime }&=x-y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.292 |
|
| \begin{align*}
x^{\prime }&=2 x-y \\
y^{\prime }&=0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.345 |
|
| \begin{align*}
x^{\prime }&=x \\
y^{\prime }&=2 x+y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.281 |
|
| \begin{align*}
x^{\prime }&=-x+2 y \\
y^{\prime }&=2 x-y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.372 |
|
| \begin{align*}
x^{\prime }&=2 x+y \\
y^{\prime }&=x+y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.584 |
|
| \begin{align*}
x^{\prime }&=3 y \\
y^{\prime }&=3 \pi y-\frac {x}{3} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.770 |
|
| \begin{align*}
p^{\prime }&=3 p-2 q-7 r \\
q^{\prime }&=-2 p+6 r \\
r^{\prime }&=\frac {73 q}{100}+2 r \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
49.921 |
|
| \begin{align*}
x^{\prime }&=-3 x+2 \pi y \\
y^{\prime }&=4 x-y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.727 |
|
| \begin{align*}
x^{\prime }&=\beta y \\
y^{\prime }&=\gamma x-y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.727 |
|
| \begin{align*}
x^{\prime }&=2 y \\
y^{\prime }&=x+y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= -2 \\
y \left (0\right ) &= -1 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.444 |
|
| \begin{align*}
x^{\prime }&=x-y \\
y^{\prime }&=x+3 y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 2 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.375 |
|
| \begin{align*}
x^{\prime }&=-2 x-y \\
y^{\prime }&=2 x-5 y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 2 \\
y \left (0\right ) &= 3 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.456 |
|
| \begin{align*}
x^{\prime }&=-2 x-3 y \\
y^{\prime }&=3 x-2 y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 2 \\
y \left (0\right ) &= 3 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.477 |
|
| \begin{align*}
x^{\prime }&=2 x+3 y \\
y^{\prime }&=x \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 2 \\
y \left (0\right ) &= 3 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.448 |
|
| \begin{align*}
x^{\prime }&=1 \\
y^{\prime }&=x \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.435 |
|
| \begin{align*}
x^{\prime }&=3 x \\
y^{\prime }&=-2 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.311 |
|
| \begin{align*}
x^{\prime }&=-4 x-2 y \\
y^{\prime }&=-x-3 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.433 |
|
| \begin{align*}
x^{\prime }&=-5 x-2 y \\
y^{\prime }&=-x-4 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.444 |
|
| \begin{align*}
x^{\prime }&=2 x+y \\
y^{\prime }&=-x+4 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.335 |
|
| \begin{align*}
x^{\prime }&=-\frac {x}{2} \\
y^{\prime }&=x-\frac {y}{2} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.303 |
|
| \begin{align*}
x^{\prime }&=5 x+4 y \\
y^{\prime }&=9 x \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.431 |
|
| \begin{align*}
x^{\prime }&=3 x+4 y \\
y^{\prime }&=x \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.404 |
|
| \begin{align*}
x^{\prime }&=2 x-y \\
y^{\prime }&=-x+y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.558 |
|
| \begin{align*}
x^{\prime }&=2 x+y \\
y^{\prime }&=x+y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.527 |
|
| \begin{align*}
x^{\prime }&=-x-2 y \\
y^{\prime }&=x-4 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.425 |
|
| \begin{align*}
x^{\prime }&=-2 x-2 y \\
y^{\prime }&=-2 x+y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.484 |
|
| \begin{align*}
x^{\prime }&=-2 x-2 y \\
y^{\prime }&=-2 x+y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 1 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.450 |
|
| \begin{align*}
x^{\prime }&=-2 x-2 y \\
y^{\prime }&=-2 x+y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= -2 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.424 |
|
| \begin{align*}
x^{\prime }&=3 x \\
y^{\prime }&=x-2 y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.412 |
|
| \begin{align*}
x^{\prime }&=3 x \\
y^{\prime }&=x-2 y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 1 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.382 |
|
| \begin{align*}
x^{\prime }&=3 x \\
y^{\prime }&=x-2 y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 2 \\
y \left (0\right ) &= 2 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.405 |
|