| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
y^{\prime }&=2-y \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.615 |
|
| \begin{align*}
y^{\prime }&=-2 y+8 \\
y \left (0\right ) &= 6 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.838 |
|
| \begin{align*}
y^{\prime }&=5 \\
y \left (0\right ) &= 2 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
4.108 |
|
| \begin{align*}
y^{\prime }-9 y&=90 \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.898 |
|
| \begin{align*}
y^{\prime }+9 y&=90 \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.872 |
|
| \begin{align*}
y^{\prime }&=3 y+{\mathrm e}^{3 t} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.115 |
|
| \begin{align*}
y^{\prime }-4 y&=-8 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.521 |
|
| \begin{align*}
y^{\prime }+4 y&=8 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.512 |
|
| \begin{align*}
y^{\prime }+2 y&=6 \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.825 |
|
| \begin{align*}
y^{\prime }+2 y&=-6 \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.671 |
|
| \begin{align*}
y+y^{\prime }&=\operatorname {Heaviside}\left (-2+t \right ) \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
0.751 |
|
| \begin{align*}
y+y^{\prime }&=\operatorname {Heaviside}\left (t -10\right ) \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
0.766 |
|
| \begin{align*}
y^{\prime }&=\operatorname {Heaviside}\left (t -T \right ) \\
y \left (0\right ) &= 2 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.713 |
|
| \begin{align*}
y^{\prime }-5 y&=3 \operatorname {Heaviside}\left (t -4\right ) \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
0.791 |
|
| \begin{align*}
y+y^{\prime }&=7 \operatorname {Heaviside}\left (t -4\right ) \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
0.793 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
1.090 |
|
| \begin{align*}
y^{\prime }&=\operatorname {Heaviside}\left (t -1\right )+\operatorname {Heaviside}\left (-2+t \right )+\operatorname {Heaviside}\left (t -3\right ) \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.565 |
|
| \begin{align*}
y^{\prime }&=2 y+\delta \left (t -3\right ) \\
y \left (0\right ) &= 0 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.051 |
|
| \begin{align*}
y^{\prime }&=2 y+\delta \left (t -3\right ) \\
y \left (0\right ) &= 1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
0.928 |
|
| \begin{align*}
-y+y^{\prime }&=\delta \left (-2+t \right ) \\
y \left (0\right ) &= 2 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.074 |
|
| \begin{align*}
y+y^{\prime }&=\delta \left (-2+t \right ) \\
y \left (0\right ) &= 2 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
0.992 |
|
| \begin{align*}
y^{\prime }&=\operatorname {Heaviside}\left (t -1\right )+\delta \left (t -1\right ) \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.536 |
|
| \begin{align*}
y^{\prime }&=-y+\operatorname {Heaviside}\left (t -3\right )+\delta \left (t -1\right ) \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.022 |
|
| \begin{align*}
-y+y^{\prime }&=8 \,{\mathrm e}^{3 t} \\
y \left (0\right ) &= 2 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.526 |
|
| \begin{align*}
y+y^{\prime }&=8 \,{\mathrm e}^{-3 t} \\
y \left (0\right ) &= 2 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.527 |
|
| \begin{align*}
-2 y+y^{\prime }&={\mathrm e}^{\frac {201 t}{100}} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.553 |
|
| \begin{align*}
-2 y+y^{\prime }&={\mathrm e}^{2 t} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.258 |
|
| \begin{align*}
y^{\prime }+4 y&=8 \,{\mathrm e}^{-4 t}+20 \\
y \left (0\right ) &= 0 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.148 |
|
| \begin{align*}
y^{\prime }-a y&={\mathrm e}^{c t} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.750 |
|
| \begin{align*}
y^{\prime }-a \left (t \right ) y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.444 |
|
| \begin{align*}
y^{\prime }-a \left (t \right ) y&=q \left (t \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.680 |
|
| \begin{align*}
y^{\prime }-a \left (t \right ) y&=q \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.437 |
|
| \begin{align*}
y^{\prime }-a \left (t \right ) y&=\operatorname {Heaviside}\left (t \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
0.662 |
|
| \begin{align*}
y^{\prime }-a \left (t \right ) y&=\delta \left (t \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
0.599 |
|
| \begin{align*}
y^{\prime }-a \left (t \right ) y&={\mathrm e}^{c t} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.766 |
|
| \begin{align*}
y^{\prime }&=a \left (t \right ) y+q \left (t \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.623 |
|
| \begin{align*}
y^{\prime }&=2 y+3 \cos \left (t \right )+4 \sin \left (t \right ) \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.046 |
|
| \begin{align*}
y^{\prime }&=-y-\cos \left (2 t \right ) \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.642 |
|
| \begin{align*}
y^{\prime }&=y+\cos \left (t \right ) \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.575 |
|
| \begin{align*}
y^{\prime }-4 y&=\cos \left (3 t \right )+\sin \left (3 t \right ) \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.000 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
2.527 |
|
| \begin{align*}
y^{\prime }&=A \cos \left (\omega t \right )+B \sin \left (\omega t \right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.364 |
|
| \begin{align*}
y^{\prime }-3 y&=5 \,{\mathrm e}^{2 i t} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
24.271 |
|
| \begin{align*}
y^{\prime }&=2 y-{\mathrm e}^{i t} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
25.641 |
|
| \begin{align*}
z^{\prime }+4 z&={\mathrm e}^{8 i t} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
49.280 |
|
| \begin{align*}
z^{\prime }+4 i z&={\mathrm e}^{8 i t} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
0.905 |
|
| \begin{align*}
z^{\prime }+4 i z&={\mathrm e}^{8 t} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
49.383 |
|
| \begin{align*}
y^{\prime }-a y&=R \cos \left (\omega t -\phi \right ) \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.061 |
|
| \begin{align*}
-2 y+y^{\prime }&=\cos \left (\omega t \right ) \\
y \left (0\right ) &= 0 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.852 |
|
| \begin{align*}
-y+y^{\prime }&=\sin \left (\omega t \right )+\cos \left (\omega t \right ) \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.046 |
|
| \begin{align*}
y^{\prime }-\sqrt {3}\, y&=\sin \left (t \right )+\cos \left (t \right ) \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.250 |
|
| \begin{align*}
y^{\prime }-a y&=A \cos \left (\omega t \right )+B \sin \left (\omega t \right ) \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.058 |
|
| \begin{align*}
y^{\prime }&=1+y \\
y \left (0\right ) &= 4 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.610 |
|
| \begin{align*}
y^{\prime }&=y-1 \\
y \left (0\right ) &= {\frac {1}{2}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.611 |
|
| \begin{align*}
y^{\prime }&=t^{2}+y \\
y \left (0\right ) &= 1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.711 |
|
| \begin{align*}
y^{\prime }&=y+{\mathrm e}^{t} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.226 |
|
| \begin{align*}
y^{\prime }&=y-t^{2} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.625 |
|
| \begin{align*}
y^{\prime }&=-{\mathrm e}^{t}+y \\
y \left (0\right ) &= 1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.234 |
|
| \begin{align*}
y^{\prime }&=y-{\mathrm e}^{2 t} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.468 |
|
| \begin{align*}
y^{\prime }&=y+2 t \\
y \left (0\right ) &= 0 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.054 |
|
| \begin{align*}
y^{\prime }&=t +2 y \\
y \left (0\right ) &= 0 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.141 |
|
| \begin{align*}
y^{\prime }&=2 y+{\mathrm e}^{t} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.294 |
|
| \begin{align*}
y^{\prime }&=y+{\mathrm e}^{2 t} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.817 |
|
| \begin{align*}
y^{\prime }&=a \left (t \right ) y+\delta \left (-t +s \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
0.608 |
|
| \begin{align*}
y^{\prime }&=\sin \left (t \right ) y+Q \sin \left (t \right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.647 |
|
| \begin{align*}
y^{\prime }&=\sin \left (t \right ) y \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.947 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{1+t}+10 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.240 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{1+t} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.497 |
|
| \begin{align*}
y^{\prime }&=a y-b y^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
5.348 |
|
| \begin{align*}
m y^{\prime \prime }+k y&=F \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
5.336 |
|
| \begin{align*}
y^{\prime }&=1+y \\
y \left (0\right ) &= -1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.385 |
|
| \begin{align*}
y^{\prime }&=1+y \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.544 |
|
| \begin{align*}
y^{\prime }&=y^{2}+y \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.182 |
|
| \begin{align*}
y^{\prime }&=a y-b y^{n} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.571 |
|
| \begin{align*}
y^{\prime }&=-y^{2}+y \\
y \left (0\right ) &= {\frac {1}{2}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.131 |
|
| \begin{align*}
y^{\prime }&=-y^{2}+y \\
y \left (0\right ) &= 2 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.380 |
|
| \begin{align*}
y^{\prime }&=-y^{2}+y \\
y \left (0\right ) &= -1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.068 |
|
| \begin{align*}
y^{\prime }&=y-y^{2}-\frac {1}{4} \\
y \left (0\right ) &= {\frac {1}{2}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
0.588 |
|
| \begin{align*}
y^{\prime }&=y \left (1-y\right ) \left (2-y\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.527 |
|
| \begin{align*}
y^{\prime }&=y \left (1-\ln \left (y\right )\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.259 |
|
| \begin{align*}
y^{\prime }&=2 \left (1-y\right ) \left (1-{\mathrm e}^{y}\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.060 |
|
| \begin{align*}
y^{\prime }&=\left (1-y^{2}\right ) \left (4-y^{2}\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
0.786 |
|
| \begin{align*}
y^{\prime }&=k \left (m^{4}-y^{4}\right ) \\
y \left (0\right ) &= \frac {m}{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
9.362 |
|
| \begin{align*}
y^{\prime }&=a y-y^{3} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
7.270 |
|
| \begin{align*}
y^{\prime }&=\sin \left (y\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
26.512 |
|
| \begin{align*}
y^{\prime }&=\sin \left (y\right )^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.694 |
|
| \begin{align*}
y^{\prime }&=y^{2}-y^{4} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.841 |
|
| \begin{align*}
y^{\prime }&=y^{2} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
3.155 |
|
| \begin{align*}
y^{\prime }&=y^{2} \\
y \left (0\right ) &= y_{0} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
3.915 |
|
| \begin{align*}
y^{\prime }&=a \left (t \right ) y \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.591 |
|
| \begin{align*}
y^{\prime }&=t y \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.248 |
|
| \begin{align*}
y^{\prime }&=t^{m} y^{n} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✗ |
✗ |
138.339 |
|
| \begin{align*}
y^{\prime }&=a \left (t \right ) y^{2} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.446 |
|
| \begin{align*}
y^{\prime }&=y+t \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.086 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{t} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.180 |
|
| \begin{align*}
y^{\prime }&=\frac {c t -a y}{A t +b y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
58.061 |
|
| \begin{align*}
y^{\prime }&=\frac {y^{2}}{t^{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.347 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{y+t} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.100 |
|
| \begin{align*}
y^{\prime }&=t y+t +y+1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.567 |
|
| \begin{align*}
y^{\prime }&=\left (y+4\right ) \cos \left (t \right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.662 |
|