| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
y^{\prime }&=2-y \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.552 |
|
| \begin{align*}
y^{\prime }&=-2 y+8 \\
y \left (0\right ) &= 6 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.721 |
|
| \begin{align*}
y^{\prime }&=5 \\
y \left (0\right ) &= 2 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.910 |
|
| \begin{align*}
y^{\prime }-9 y&=90 \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.740 |
|
| \begin{align*}
y^{\prime }+9 y&=90 \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.719 |
|
| \begin{align*}
y^{\prime }&=3 y+{\mathrm e}^{3 t} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.044 |
|
| \begin{align*}
y^{\prime }-4 y&=-8 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.451 |
|
| \begin{align*}
y^{\prime }+4 y&=8 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.461 |
|
| \begin{align*}
y^{\prime }+2 y&=6 \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.709 |
|
| \begin{align*}
y^{\prime }+2 y&=-6 \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.644 |
|
| \begin{align*}
y+y^{\prime }&=\operatorname {Heaviside}\left (t -2\right ) \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
0.640 |
|
| \begin{align*}
y+y^{\prime }&=\operatorname {Heaviside}\left (t -10\right ) \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
0.632 |
|
| \begin{align*}
y^{\prime }&=\operatorname {Heaviside}\left (t -T \right ) \\
y \left (0\right ) &= 2 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.544 |
|
| \begin{align*}
y^{\prime }-5 y&=3 \operatorname {Heaviside}\left (t -4\right ) \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
0.667 |
|
| \begin{align*}
y+y^{\prime }&=7 \operatorname {Heaviside}\left (t -4\right ) \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
0.651 |
|
| \begin{align*}
y^{\prime }+2 y&=\operatorname {Heaviside}\left (t -4\right )-\operatorname {Heaviside}\left (t -6\right ) \\
y \left (0\right ) &= 0 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
0.959 |
|
| \begin{align*}
y^{\prime }&=\operatorname {Heaviside}\left (-1+t \right )+\operatorname {Heaviside}\left (t -2\right )+\operatorname {Heaviside}\left (t -3\right ) \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.541 |
|
| \begin{align*}
y^{\prime }&=2 y+\delta \left (t -3\right ) \\
y \left (0\right ) &= 0 \\
\end{align*} | [[_linear, ‘class A‘]] | ✓ | ✓ | ✓ | ✓ | 0.854 |
|
| \begin{align*}
y^{\prime }&=2 y+\delta \left (t -3\right ) \\
y \left (0\right ) &= 1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
0.739 |
|
| \begin{align*}
-y+y^{\prime }&=\delta \left (t -2\right ) \\
y \left (0\right ) &= 2 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
0.899 |
|
| \begin{align*}
y+y^{\prime }&=\delta \left (t -2\right ) \\
y \left (0\right ) &= 2 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
0.825 |
|
| \begin{align*}
y^{\prime }&=\operatorname {Heaviside}\left (-1+t \right )+\delta \left (-1+t \right ) \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.465 |
|
| \begin{align*}
y^{\prime }&=-y+\operatorname {Heaviside}\left (t -3\right )+\delta \left (-1+t \right ) \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
0.830 |
|
| \begin{align*}
-y+y^{\prime }&=8 \,{\mathrm e}^{3 t} \\
y \left (0\right ) &= 2 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.378 |
|
| \begin{align*}
y+y^{\prime }&=8 \,{\mathrm e}^{-3 t} \\
y \left (0\right ) &= 2 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.390 |
|
| \begin{align*}
-2 y+y^{\prime }&={\mathrm e}^{\frac {201 t}{100}} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.400 |
|
| \begin{align*}
-2 y+y^{\prime }&={\mathrm e}^{2 t} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.128 |
|
| \begin{align*}
y^{\prime }+4 y&=8 \,{\mathrm e}^{-4 t}+20 \\
y \left (0\right ) &= 0 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.048 |
|
| \begin{align*}
y^{\prime }-a y&={\mathrm e}^{c t} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.434 |
|
| \begin{align*}
y^{\prime }-a \left (t \right ) y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
1.857 |
|
| \begin{align*}
y^{\prime }-a \left (t \right ) y&=q \left (t \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.669 |
|
| \begin{align*}
y^{\prime }-a \left (t \right ) y&=q \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.329 |
|
| \begin{align*}
y^{\prime }-a \left (t \right ) y&=\operatorname {Heaviside}\left (t \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
0.732 |
|
| \begin{align*}
y^{\prime }-a \left (t \right ) y&=\delta \left (t \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
0.446 |
|
| \begin{align*}
y^{\prime }-a \left (t \right ) y&={\mathrm e}^{c t} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.695 |
|
| \begin{align*}
y^{\prime }&=a \left (t \right ) y+q \left (t \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.515 |
|
| \begin{align*}
y^{\prime }&=2 y+3 \cos \left (t \right )+4 \sin \left (t \right ) \\
\end{align*} | [[_linear, ‘class A‘]] | ✓ | ✓ | ✓ | ✓ | 2.027 |
|
| \begin{align*}
y^{\prime }&=-y-\cos \left (2 t \right ) \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.610 |
|
| \begin{align*}
y^{\prime }&=y+\cos \left (t \right ) \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.536 |
|
| \begin{align*}
y^{\prime }-4 y&=\cos \left (3 t \right )+\sin \left (3 t \right ) \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.969 |
|
| \begin{align*}
y^{\prime }-a y&=A \cos \left (\omega t \right )+B \sin \left (\omega t \right ) \\
y \left (0\right ) &= 0 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.340 |
|
| \begin{align*}
y^{\prime }&=A \cos \left (\omega t \right )+B \sin \left (\omega t \right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.408 |
|
| \begin{align*}
y^{\prime }-3 y&=5 \,{\mathrm e}^{2 i t} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
23.757 |
|
| \begin{align*}
y^{\prime }&=2 y-{\mathrm e}^{i t} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
24.916 |
|
| \begin{align*}
z^{\prime }+4 z&={\mathrm e}^{8 i t} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
51.434 |
|
| \begin{align*}
z^{\prime }+4 i z&={\mathrm e}^{8 i t} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
0.868 |
|
| \begin{align*}
z^{\prime }+4 i z&={\mathrm e}^{8 t} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
51.465 |
|
| \begin{align*}
y^{\prime }-a y&=R \cos \left (\omega t -\phi \right ) \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.034 |
|
| \begin{align*}
-2 y+y^{\prime }&=\cos \left (\omega t \right ) \\
y \left (0\right ) &= 0 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.770 |
|
| \begin{align*}
-y+y^{\prime }&=\sin \left (\omega t \right )+\cos \left (\omega t \right ) \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.012 |
|
| \begin{align*}
y^{\prime }-\sqrt {3}\, y&=\sin \left (t \right )+\cos \left (t \right ) \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.157 |
|
| \begin{align*}
y^{\prime }-a y&=A \cos \left (\omega t \right )+B \sin \left (\omega t \right ) \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.976 |
|
| \begin{align*}
y^{\prime }&=1+y \\
y \left (0\right ) &= 4 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.554 |
|
| \begin{align*}
y^{\prime }&=y-1 \\
y \left (0\right ) &= {\frac {1}{2}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.557 |
|
| \begin{align*}
y^{\prime }&=t^{2}+y \\
y \left (0\right ) &= 1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.623 |
|
| \begin{align*}
y^{\prime }&=y+{\mathrm e}^{t} \\
y \left (0\right ) &= 1 \\
\end{align*} | [[_linear, ‘class A‘]] | ✓ | ✓ | ✓ | ✓ | 1.169 |
|
| \begin{align*}
y^{\prime }&=y-t^{2} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.533 |
|
| \begin{align*}
y^{\prime }&=-{\mathrm e}^{t}+y \\
y \left (0\right ) &= 1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.162 |
|
| \begin{align*}
y^{\prime }&=y-{\mathrm e}^{2 t} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.331 |
|
| \begin{align*}
y^{\prime }&=y+2 t \\
y \left (0\right ) &= 0 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
0.915 |
|
| \begin{align*}
y^{\prime }&=t +2 y \\
y \left (0\right ) &= 0 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.005 |
|
| \begin{align*}
y^{\prime }&=2 y+{\mathrm e}^{t} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.211 |
|
| \begin{align*}
y^{\prime }&=y+{\mathrm e}^{2 t} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.991 |
|
| \begin{align*}
y^{\prime }&=a \left (t \right ) y+\delta \left (-t +s \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
0.482 |
|
| \begin{align*}
y^{\prime }&=\sin \left (t \right ) y+Q \sin \left (t \right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.329 |
|
| \begin{align*}
y^{\prime }&=\sin \left (t \right ) y \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.441 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{t +1}+10 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.947 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{t +1} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.036 |
|
| \begin{align*}
y^{\prime }&=a y-b y^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
3.797 |
|
| \begin{align*}
m y^{\prime \prime }+k y&=F \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
2.354 |
|
| \begin{align*}
y^{\prime }&=1+y \\
y \left (0\right ) &= -1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.410 |
|
| \begin{align*}
y^{\prime }&=1+y \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.504 |
|
| \begin{align*}
y^{\prime }&=y^{2}+y \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.906 |
|
| \begin{align*}
y^{\prime }&=a y-b y^{n} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.931 |
|
| \begin{align*}
y^{\prime }&=-y^{2}+y \\
y \left (0\right ) &= {\frac {1}{2}} \\
\end{align*} | [_quadrature] | ✓ | ✓ | ✓ | ✓ | 0.863 |
|
| \begin{align*}
y^{\prime }&=-y^{2}+y \\
y \left (0\right ) &= 2 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.049 |
|
| \begin{align*}
y^{\prime }&=-y^{2}+y \\
y \left (0\right ) &= -1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.832 |
|
| \begin{align*}
y^{\prime }&=y-y^{2}-\frac {1}{4} \\
y \left (0\right ) &= {\frac {1}{2}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
0.514 |
|
| \begin{align*}
y^{\prime }&=y \left (1-y\right ) \left (2-y\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.133 |
|
| \begin{align*}
y^{\prime }&=y \left (1-\ln \left (y\right )\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.877 |
|
| \begin{align*}
y^{\prime }&=2 \left (1-y\right ) \left (1-{\mathrm e}^{y}\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.026 |
|
| \begin{align*}
y^{\prime }&=\left (1-y^{2}\right ) \left (4-y^{2}\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
0.611 |
|
| \begin{align*}
y^{\prime }&=k \left (m^{4}-y^{4}\right ) \\
y \left (0\right ) &= \frac {m}{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
8.320 |
|
| \begin{align*}
y^{\prime }&=a y-y^{3} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
5.449 |
|
| \begin{align*}
y^{\prime }&=\sin \left (y\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
25.374 |
|
| \begin{align*}
y^{\prime }&=\sin \left (y\right )^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.524 |
|
| \begin{align*}
y^{\prime }&=y^{2}-y^{4} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.633 |
|
| \begin{align*}
y^{\prime }&=y^{2} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.375 |
|
| \begin{align*}
y^{\prime }&=y^{2} \\
y \left (0\right ) &= y_{0} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.879 |
|
| \begin{align*}
y^{\prime }&=a \left (t \right ) y \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.132 |
|
| \begin{align*}
y^{\prime }&=t y \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
1.886 |
|
| \begin{align*}
y^{\prime }&=t^{m} y^{n} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✗ |
✗ |
113.811 |
|
| \begin{align*}
y^{\prime }&=a \left (t \right ) y^{2} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.929 |
|
| \begin{align*}
y^{\prime }&=t +y \\
\end{align*} | [[_linear, ‘class A‘]] | ✓ | ✓ | ✓ | ✓ | 0.909 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{t} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
1.835 |
|
| \begin{align*}
y^{\prime }&=\frac {c t -a y}{A t +b y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
47.760 |
|
| \begin{align*}
y^{\prime }&=\frac {y^{2}}{t^{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.409 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{t +y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
1.850 |
|
| \begin{align*}
y^{\prime }&=t y+t +y+1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.207 |
|
| \begin{align*}
y^{\prime }&=\left (y+4\right ) \cos \left (t \right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.375 |
|