| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
y^{\prime \prime }-5 y^{\prime }+4 y&=\left \{\begin {array}{cc} 1 & 0\le t <5 \\ 0 & 5\le t \end {array}\right . \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
3.455 |
|
| \begin{align*}
y^{\prime \prime }+5 y^{\prime }+6 y&=\left \{\begin {array}{cc} 0 & 0\le t <1 \\ 6 & 1\le t <3 \\ 0 & 3\le t \end {array}\right . \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
4.647 |
|
| \begin{align*}
y^{\prime \prime }+9 y&=\operatorname {Heaviside}\left (t -2 \pi \right ) \sin \left (t \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.771 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }+y&=\operatorname {Heaviside}\left (-3+t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
2.105 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }+y&=\left \{\begin {array}{cc} {\mathrm e}^{-t} & 0\le t <4 \\ 0 & 4\le t \end {array}\right . \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
3.220 |
|
| \begin{align*}
y^{\prime }+2 y&=\delta \left (t -1\right ) \\
y \left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.168 |
|
| \begin{align*}
y^{\prime }-3 y&=3+\delta \left (t -2\right ) \\
y \left (0\right ) &= -1 \\
\end{align*}
Using Laplace transform method. |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.185 |
|
| \begin{align*}
y^{\prime }-4 y&=\delta \left (-4+t \right ) \\
y \left (0\right ) &= 2 \\
\end{align*}
Using Laplace transform method. |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.520 |
|
| \begin{align*}
y+y^{\prime }&=\delta \left (t -1\right )-\delta \left (-3+t \right ) \\
y \left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.000 |
|
| \begin{align*}
y^{\prime \prime }+4 y&=\delta \left (t -\pi \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.572 |
|
| \begin{align*}
y^{\prime \prime }-y&=\delta \left (t -1\right )-\delta \left (t -2\right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
3.064 |
|
| \begin{align*}
y^{\prime \prime }+4 y^{\prime }+3 y&=2 \delta \left (t -2\right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= -1 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
3.358 |
|
| \begin{align*}
y^{\prime \prime }+4 y&=\delta \left (t -\pi \right )-\delta \left (t -2 \pi \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.991 |
|
| \begin{align*}
y^{\prime \prime }+4 y^{\prime }+4 y&=3 \delta \left (t -1\right ) \\
y \left (0\right ) &= -1 \\
y^{\prime }\left (0\right ) &= 3 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.941 |
|
| \begin{align*}
y^{\prime \prime }+4 y^{\prime }+5 y&=3 \delta \left (t -\pi \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
2.267 |
|
| \begin{align*}
y^{\prime }-3 y&=\operatorname {Heaviside}\left (t -2\right ) \\
y \left (0\right ) &= 2 \\
\end{align*}
Using Laplace transform method. |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.223 |
|
| \begin{align*}
y^{\prime }+4 y&=\delta \left (-3+t \right ) \\
y \left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.496 |
|
| \begin{align*}
y^{\prime \prime }-y&=\delta \left (t -1\right )-\delta \left (t -2\right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.246 |
|
| \begin{align*}
y^{\prime \prime }-6 y^{\prime }+9 y&=\delta \left (-3+t \right ) \\
y \left (0\right ) &= -1 \\
y^{\prime }\left (0\right ) &= -3 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.901 |
|
| \begin{align*}
y^{\prime \prime }+9 y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.343 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime }+y&=0 \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= -3 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.324 |
|
| \begin{align*}
y^{\prime \prime }+4 y^{\prime }+3 y&=0 \\
y \left (0\right ) &= -1 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.226 |
|
| \begin{align*}
y^{\prime \prime \prime }+y^{\prime }&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
y^{\prime \prime }\left (0\right ) &= 4 \\
\end{align*}
Using Laplace transform method. |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.408 |
|
| \begin{align*}
y^{\prime \prime }-y&=0 \\
\end{align*}
Series expansion around \(t=0\). |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.450 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime }+y&=0 \\
\end{align*}
Series expansion around \(t=0\). |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.662 |
|
| \begin{align*}
y^{\prime \prime }+k^{2} y&=0 \\
\end{align*}
Series expansion around \(t=0\). |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.553 |
|
| \begin{align*}
y^{\prime \prime }-3 y^{\prime }+2 y&=0 \\
\end{align*}
Series expansion around \(t=0\). |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.671 |
|
| \begin{align*}
\left (-t^{2}+1\right ) y^{\prime \prime }+2 y&=0 \\
\end{align*}
Series expansion around \(t=0\). |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.555 |
|
| \begin{align*}
\left (-t^{2}+1\right ) y^{\prime \prime }-2 t y^{\prime }+2 y&=0 \\
\end{align*}
Series expansion around \(t=0\). |
[_Gegenbauer] |
✓ |
✓ |
✓ |
✓ |
0.558 |
|
| \begin{align*}
\left (t -1\right ) y^{\prime \prime }-t y^{\prime }+y&=0 \\
\end{align*}
Series expansion around \(t=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.523 |
|
| \begin{align*}
\left (t^{2}+1\right ) y^{\prime \prime }-2 t y^{\prime }+2 y&=0 \\
\end{align*}
Series expansion around \(t=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.465 |
|
| \begin{align*}
\left (t^{2}+1\right ) y^{\prime \prime }-4 t y^{\prime }+6 y&=0 \\
\end{align*}
Series expansion around \(t=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.507 |
|
| \begin{align*}
\left (-t^{2}+1\right ) y^{\prime \prime }-6 t y^{\prime }-4 y&=0 \\
\end{align*}
Series expansion around \(t=0\). |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.658 |
|
| \begin{align*}
y^{\prime \prime }+\frac {t y^{\prime }}{-t^{2}+1}+\frac {y}{t +1}&=0 \\
\end{align*}
Series expansion around \(t=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.754 |
|
| \begin{align*}
y^{\prime \prime }+\frac {\left (1-t \right ) y^{\prime }}{t}+\frac {\left (1-\cos \left (t \right )\right ) y}{t^{3}}&=0 \\
\end{align*}
Series expansion around \(t=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.159 |
|
| \begin{align*}
y^{\prime \prime }+3 t \left (1-t \right ) y^{\prime }+\frac {\left (1-{\mathrm e}^{t}\right ) y}{t}&=0 \\
\end{align*}
Series expansion around \(t=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.258 |
|
| \begin{align*}
y^{\prime \prime }+\frac {y^{\prime }}{t}+\frac {\left (1-t \right ) y}{t^{3}}&=0 \\
\end{align*}
Series expansion around \(t=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✓ |
✗ |
0.243 |
|
| \begin{align*}
t y^{\prime \prime }+\left (1-t \right ) y^{\prime }+4 y t&=0 \\
\end{align*}
Series expansion around \(t=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.007 |
|
| \begin{align*}
2 t y^{\prime \prime }+y^{\prime }+y t&=0 \\
\end{align*}
Series expansion around \(t=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.971 |
|
| \begin{align*}
t^{2} y^{\prime \prime }+2 t y^{\prime }+t^{2} y&=0 \\
\end{align*}
Series expansion around \(t=0\). |
[_Lienard] |
✓ |
✓ |
✓ |
✓ |
1.017 |
|
| \begin{align*}
t^{2} y^{\prime \prime }+t \,{\mathrm e}^{t} y^{\prime }+4 \left (1-4 t \right ) y&=0 \\
\end{align*}
Series expansion around \(t=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.476 |
|
| \begin{align*}
t y^{\prime \prime }+\left (1-t \right ) y^{\prime }+\lambda y&=0 \\
\end{align*}
Series expansion around \(t=0\). |
[_Laguerre] |
✓ |
✓ |
✓ |
✓ |
1.366 |
|
| \begin{align*}
t^{2} y^{\prime \prime }+3 t \left (1+3 t \right ) y^{\prime }+\left (-t^{2}+1\right ) y&=0 \\
\end{align*}
Series expansion around \(t=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.026 |
|
| \begin{align*}
t^{2} y^{\prime \prime }+5 t y^{\prime }+4 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.182 |
|
| \begin{align*}
t y^{\prime \prime }-2 y^{\prime }+y t&=0 \\
\end{align*}
Series expansion around \(t=0\). |
[_Lienard] |
✓ |
✓ |
✓ |
✓ |
1.036 |
|
| \begin{align*}
2 t^{2} y^{\prime \prime }-t y^{\prime }+\left (t +1\right ) y&=0 \\
\end{align*}
Series expansion around \(t=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.101 |
|
| \begin{align*}
t^{2} y^{\prime \prime }-t \left (t +1\right ) y^{\prime }+y&=0 \\
\end{align*}
Series expansion around \(t=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.904 |
|
| \begin{align*}
2 t^{2} y^{\prime \prime }-t y^{\prime }+\left (1-t \right ) y&=0 \\
\end{align*}
Series expansion around \(t=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.092 |
|
| \begin{align*}
t^{2} y^{\prime \prime }+t^{2} y^{\prime }-2 y&=0 \\
\end{align*}
Series expansion around \(t=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.127 |
|
| \begin{align*}
t^{2} y^{\prime \prime }+2 t y^{\prime }-a \,t^{2} y&=0 \\
\end{align*}
Series expansion around \(t=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.086 |
|
| \begin{align*}
t y^{\prime \prime }+\left (t -1\right ) y^{\prime }-2 y&=0 \\
\end{align*}
Series expansion around \(t=0\). |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
6.049 |
|
| \begin{align*}
t y^{\prime \prime }-4 y&=0 \\
\end{align*}
Series expansion around \(t=0\). |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
4.119 |
|
| \begin{align*}
t^{2} \left (1-t \right ) y^{\prime \prime }+\left (t^{2}+t \right ) y^{\prime }+\left (1-2 t \right ) y&=0 \\
\end{align*}
Series expansion around \(t=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.929 |
|
| \begin{align*}
t^{2} y^{\prime \prime }+t \left (t +1\right ) y^{\prime }-y&=0 \\
\end{align*}
Series expansion around \(t=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.085 |
|
| \begin{align*}
t^{2} y^{\prime \prime }+t \left (1-2 t \right ) y^{\prime }+\left (t^{2}-t +1\right ) y&=0 \\
\end{align*}
Series expansion around \(t=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.898 |
|
| \begin{align*}
t^{2} \left (t +1\right ) y^{\prime \prime }-t \left (2 t +1\right ) y^{\prime }+\left (2 t +1\right ) y&=0 \\
\end{align*}
Series expansion around \(t=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.999 |
|
| \begin{align*}
t y^{\prime \prime }+2 \left (i t -k \right ) y^{\prime }-2 i k y&=0 \\
\end{align*}
Series expansion around \(t=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.546 |
|
| \begin{align*}
y_{1}^{\prime }&=y_{2} \\
y_{2}^{\prime }&=y_{1} y_{2} \\
\end{align*} |
system_of_ODEs |
✗ |
✓ |
✓ |
✗ |
0.039 |
|
| \begin{align*}
y_{1}^{\prime }&=y_{1}+y_{2}+t^{2} \\
y_{2}^{\prime }&=-y_{1}+y_{2}+1 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.941 |
|
| \begin{align*}
y_{1}^{\prime }&=\sin \left (t \right ) y_{1} \\
y_{2}^{\prime }&=y_{1}+\cos \left (t \right ) y_{2} \\
\end{align*} |
system_of_ODEs |
✗ |
✓ |
✓ |
✓ |
0.043 |
|
| \begin{align*}
y_{1}^{\prime }&=t \sin \left (y_{1}\right )-y_{2} \\
y_{2}^{\prime }&=y_{1}+t \cos \left (y_{2}\right ) \\
\end{align*} |
system_of_ODEs |
✗ |
✓ |
✗ |
✗ |
0.053 |
|
| \begin{align*}
y_{1}^{\prime }&=y_{1} \\
y_{2}^{\prime }&=2 y_{1}+y_{4} \\
y_{3}^{\prime }&=y_{4} \\
y_{4}^{\prime }&=y_{2}+2 y_{3} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.573 |
|
| \begin{align*}
y_{1}^{\prime }&=\frac {y_{1}}{2}-y_{2}+5 \\
y_{2}^{\prime }&=-y_{1}+\frac {y_{2}}{2}-5 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.767 |
|
| \begin{align*}
y_{1}^{\prime }&=5 y_{1}-2 y_{2} \\
y_{2}^{\prime }&=4 y_{1}-y_{2} \\
\end{align*}
With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 0 \\
y_{2} \left (0\right ) &= 1 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.589 |
|
| \begin{align*}
y_{1}^{\prime }&=3 y_{1}-y_{2} \\
y_{2}^{\prime }&=4 y_{1}-y_{2} \\
\end{align*}
With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 1 \\
y_{2} \left (0\right ) &= 0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.513 |
|
| \begin{align*}
y_{1}^{\prime }&=2 y_{1}-y_{2} \\
y_{2}^{\prime }&=3 y_{1}-2 y_{2} \\
\end{align*}
With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 1 \\
y_{2} \left (0\right ) &= 3 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.582 |
|
| \begin{align*}
y_{1}^{\prime }&=y_{2}+t \\
y_{2}^{\prime }&=-y_{1}-t \\
\end{align*}
With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 1 \\
y_{2} \left (0\right ) &= 1 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.816 |
|
| \begin{align*}
y_{1}^{\prime }&=-y_{1} \\
y_{2}^{\prime }&=3 y_{2} \\
\end{align*}
With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 1 \\
y_{2} \left (0\right ) &= -2 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.444 |
|
| \begin{align*}
y_{1}^{\prime }&=y_{2} \\
y_{2}^{\prime }&=-2 y_{1} \\
\end{align*}
With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 1 \\
y_{2} \left (0\right ) &= -1 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.670 |
|
| \begin{align*}
y_{1}^{\prime }&=2 y_{1}+y_{2} \\
y_{2}^{\prime }&=2 y_{2} \\
\end{align*}
With initial conditions \begin{align*}
y_{1} \left (0\right ) &= -1 \\
y_{2} \left (0\right ) &= 2 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.424 |
|
| \begin{align*}
y_{1}^{\prime }&=-y_{1}+2 y_{2} \\
y_{2}^{\prime }&=-2 y_{1}-y_{2} \\
\end{align*}
With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 1 \\
y_{2} \left (0\right ) &= 0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.595 |
|
| \begin{align*}
y_{1}^{\prime }&=2 y_{1}-y_{2} \\
y_{2}^{\prime }&=3 y_{1}-2 y_{2} \\
\end{align*}
With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 1 \\
y_{2} \left (0\right ) &= 3 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.561 |
|
| \begin{align*}
y_{1}^{\prime }&=2 y_{1}-5 y_{2} \\
y_{2}^{\prime }&=y_{1}-2 y_{2} \\
\end{align*}
With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 1 \\
y_{2} \left (0\right ) &= -1 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.605 |
|
| \begin{align*}
y_{1}^{\prime }&=3 y_{1}-4 y_{2} \\
y_{2}^{\prime }&=y_{1}-y_{2} \\
\end{align*}
With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 1 \\
y_{2} \left (0\right ) &= 1 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.490 |
|
| \begin{align*}
y_{1}^{\prime }&=-y_{1}+3 y_{3} \\
y_{2}^{\prime }&=2 y_{2} \\
y_{3}^{\prime }&=y_{3} \\
\end{align*}
With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 1 \\
y_{2} \left (0\right ) &= 1 \\
y_{3} \left (0\right ) &= 2 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.780 |
|
| \begin{align*}
y_{1}^{\prime }&=4 y_{2} \\
y_{2}^{\prime }&=-y_{1} \\
y_{3}^{\prime }&=y_{1}+4 y_{2}-y_{3} \\
\end{align*}
With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 2 \\
y_{2} \left (0\right ) &= 1 \\
y_{3} \left (0\right ) &= 2 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.014 |
|
| \begin{align*}
y_{1}^{\prime }&=2 y_{1}-y_{2}+{\mathrm e}^{t} \\
y_{2}^{\prime }&=3 y_{1}-2 y_{2}+{\mathrm e}^{t} \\
\end{align*}
With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 1 \\
y_{2} \left (0\right ) &= 3 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✗ |
0.839 |
|
| \begin{align*}
y_{1}^{\prime }&=-y_{1}+2 y_{2}+5 \\
y_{2}^{\prime }&=-2 y_{1}-y_{2} \\
\end{align*}
With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 1 \\
y_{2} \left (0\right ) &= 0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.855 |
|
| \begin{align*}
y_{1}^{\prime }&=2 y_{1}-5 y_{2}+2 \cos \left (t \right ) \\
y_{2}^{\prime }&=y_{1}-2 y_{2}+\cos \left (t \right ) \\
\end{align*}
With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 1 \\
y_{2} \left (0\right ) &= -1 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.082 |
|
| \begin{align*}
y_{1}^{\prime }&=-y_{1}-4 y_{2}+4 \\
y_{2}^{\prime }&=y_{1}-y_{2}+1 \\
\end{align*}
With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 2 \\
y_{2} \left (0\right ) &= -1 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.871 |
|
| \begin{align*}
y_{1}^{\prime }&=2 y_{1}+y_{2}+{\mathrm e}^{t} \\
y_{2}^{\prime }&=y_{1}+2 y_{2}-{\mathrm e}^{t} \\
\end{align*}
With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 1 \\
y_{2} \left (0\right ) &= 1 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✗ |
0.750 |
|
| \begin{align*}
y_{1}^{\prime }&=5 y_{1}+2 y_{2}+t \\
y_{2}^{\prime }&=-8 y_{1}-3 y_{2}-2 t \\
\end{align*}
With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 0 \\
y_{2} \left (0\right ) &= 1 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.780 |
|
| \begin{align*}
y_{1}^{\prime }&=-2 y_{1}+2 y_{2}+y_{3}+{\mathrm e}^{-2 t} \\
y_{2}^{\prime }&=-y_{2} \\
y_{3}^{\prime }&=2 y_{1}-2 y_{2}-y_{3}-{\mathrm e}^{-2 t} \\
\end{align*}
With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 2 \\
y_{2} \left (0\right ) &= 1 \\
y_{3} \left (0\right ) &= 1 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.170 |
|
| \begin{align*}
y_{1}^{\prime }&=y_{2}+y_{3}+{\mathrm e}^{2 t} \\
y_{2}^{\prime }&=y_{1}+y_{2}-y_{3}+{\mathrm e}^{2 t} \\
y_{3}^{\prime }&=-2 y_{1}+y_{2}+3 y_{3}-{\mathrm e}^{2 t} \\
\end{align*}
With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 0 \\
y_{2} \left (0\right ) &= 0 \\
y_{3} \left (0\right ) &= 0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.112 |
|
| \begin{align*}
y_{1}^{\prime }&=-2 y_{1}+y_{2} \\
y_{2}^{\prime }&=-4 y_{1}+3 y_{2} \\
\end{align*}
With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 1 \\
y_{2} \left (0\right ) &= -2 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.595 |
|
| \begin{align*}
y_{1}^{\prime }&=5 y_{1}-3 y_{2} \\
y_{2}^{\prime }&=2 y_{1} \\
\end{align*}
With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 2 \\
y_{2} \left (0\right ) &= 1 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.582 |
|
| \begin{align*}
y_{1}^{\prime }&=y_{2} t \\
y_{2}^{\prime }&=-y_{1} t \\
\end{align*}
With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 1 \\
y_{2} \left (0\right ) &= 0 \\
\end{align*} |
system_of_ODEs |
✗ |
✓ |
✓ |
✓ |
0.046 |
|
| \begin{align*}
y_{1}^{\prime }&=y_{1} t +y_{2} t \\
y_{2}^{\prime }&=-y_{1} t -y_{2} t \\
\end{align*}
With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 4 \\
y_{2} \left (0\right ) &= 0 \\
\end{align*} |
system_of_ODEs |
✗ |
✓ |
✓ |
✓ |
0.050 |
|
| \begin{align*}
y_{1}^{\prime }&=\frac {y_{1}}{t}+y_{2} \\
y_{2}^{\prime }&=-y_{1}+\frac {y_{2}}{t} \\
\end{align*}
With initial conditions \begin{align*}
y_{1} \left (\pi \right ) &= 1 \\
y_{2} \left (\pi \right ) &= -1 \\
\end{align*} |
system_of_ODEs |
✗ |
✓ |
✓ |
✓ |
0.050 |
|
| \begin{align*}
y_{1}^{\prime }&=\left (2 t +1\right ) y_{1}+2 y_{2} t \\
y_{2}^{\prime }&=-2 y_{1} t +\left (1-2 t \right ) y_{2} \\
\end{align*}
With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 1 \\
y_{2} \left (0\right ) &= 0 \\
\end{align*} |
system_of_ODEs |
✗ |
✓ |
✓ |
✓ |
0.053 |
|
| \begin{align*}
y_{1}^{\prime }&=y_{1}+y_{2} \\
y_{2}^{\prime }&=\frac {y_{1}}{t}+\frac {y_{2}}{t} \\
\end{align*}
With initial conditions \begin{align*}
y_{1} \left (1\right ) &= -3 \\
y_{2} \left (1\right ) &= 4 \\
\end{align*} |
system_of_ODEs |
✗ |
✓ |
✓ |
✓ |
0.050 |
|
| \begin{align*}
y_{1}^{\prime }&=\frac {y_{1}}{t}+1 \\
y_{2}^{\prime }&=\frac {y_{2}}{t}+t \\
\end{align*}
With initial conditions \begin{align*}
y_{1} \left (1\right ) &= 1 \\
y_{2} \left (1\right ) &= 2 \\
\end{align*} |
system_of_ODEs |
✗ |
✓ |
✓ |
✗ |
0.046 |
|
| \begin{align*}
y_{1}^{\prime }&=-\frac {y_{2}}{t}+1 \\
y_{2}^{\prime }&=\frac {y_{1}}{t}+\frac {2 y_{2}}{t}-1 \\
\end{align*}
With initial conditions \begin{align*}
y_{1} \left (1\right ) &= 2 \\
y_{2} \left (1\right ) &= 0 \\
\end{align*} |
system_of_ODEs |
✗ |
✓ |
✓ |
✗ |
0.049 |
|
| \begin{align*}
y_{1}^{\prime }&=\frac {4 t y_{1}}{t^{2}+1}+\frac {6 y_{2} t}{t^{2}+1}-3 t \\
y_{2}^{\prime }&=-\frac {2 t y_{1}}{t^{2}+1}-\frac {4 y_{2} t}{t^{2}+1}+t \\
\end{align*}
With initial conditions \begin{align*}
y_{1} \left (1\right ) &= 1 \\
y_{2} \left (1\right ) &= -1 \\
\end{align*} |
system_of_ODEs |
✗ |
✓ |
✓ |
✓ |
0.056 |
|
| \begin{align*}
y_{1}^{\prime }&=3 \sec \left (t \right ) y_{1}+5 \sec \left (t \right ) y_{2} \\
y_{2}^{\prime }&=-\sec \left (t \right ) y_{1}-3 \sec \left (t \right ) y_{2} \\
\end{align*}
With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 2 \\
y_{2} \left (0\right ) &= 1 \\
\end{align*} |
system_of_ODEs |
✗ |
✓ |
✗ |
✓ |
0.055 |
|
| \begin{align*}
y_{1}^{\prime }&=y_{1} t +y_{2} t +4 t \\
y_{2}^{\prime }&=-y_{1} t -y_{2} t +4 t \\
\end{align*}
With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 4 \\
y_{2} \left (0\right ) &= 0 \\
\end{align*} |
system_of_ODEs |
✗ |
✓ |
✓ |
✓ |
0.050 |
|
| \begin{align*}
y^{\prime }&=y \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.831 |
|
| \begin{align*}
y^{\prime }&=a \left (t \right ) y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.296 |
|
| \begin{align*}
y^{\prime }&=2-y \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.214 |
|
| \begin{align*}
y^{\prime }&=2-y \\
y \left (0\right ) &= 4 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.421 |
|