| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
y^{\prime \prime }-2 y^{\prime }+5 y&=2 \cos \left (t \right )^{2} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.563 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime }+5 y&=2 \cos \left (t \right )^{2} {\mathrm e}^{t} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.537 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }-6 y&=\sin \left (t \right )+{\mathrm e}^{2 t} t \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.007 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }+4 y&=t^{2}+\left (2 t +3\right ) \left (1+\cos \left (t \right )\right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.921 |
|
| \begin{align*}
y^{\prime \prime }-3 y^{\prime }+2 y&={\mathrm e}^{t}+{\mathrm e}^{2 t} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.594 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }&=1+t^{2}+{\mathrm e}^{-2 t} \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.083 |
|
| \begin{align*}
y^{\prime \prime }+y&=\cos \left (2 t \right ) \cos \left (t \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.941 |
|
| \begin{align*}
y^{\prime \prime }+y&=\cos \left (t \right ) \cos \left (2 t \right ) \cos \left (3 t \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.322 |
|
| \begin{align*}
y^{\prime \prime }-6 y^{\prime }+9 y&=t^{{3}/{2}} {\mathrm e}^{3 t} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.513 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime } t +y&=0 \\
\end{align*} Series expansion around \(t=0\). |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.420 |
|
| \begin{align*}
y^{\prime \prime }-t y&=0 \\
\end{align*} Series expansion around \(t=0\). |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.399 |
|
| \begin{align*}
\left (t^{2}+2\right ) y^{\prime \prime }-y^{\prime } t -3 y&=0 \\
\end{align*} Series expansion around \(t=0\). |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.530 |
|
| \begin{align*}
y^{\prime \prime }-y t^{3}&=0 \\
\end{align*} Series expansion around \(t=0\). |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.391 |
|
| \begin{align*}
t \left (2-t \right ) y^{\prime \prime }-6 \left (t -1\right ) y^{\prime }-4 y&=0 \\
y \left (1\right ) &= 1 \\
y^{\prime }\left (1\right ) &= 0 \\
\end{align*} Series expansion around \(t=1\). |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.716 |
|
| \begin{align*}
y^{\prime \prime }+t^{2} y&=0 \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= -1 \\
\end{align*} Series expansion around \(t=0\). |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.420 |
|
| \begin{align*}
y^{\prime \prime }-y t^{3}&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= -2 \\
\end{align*} Series expansion around \(t=0\). |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.390 |
|
| \begin{align*}
y^{\prime \prime }+\left (t^{2}+2 t +1\right ) y^{\prime }-\left (4+4 t \right ) y&=0 \\
y \left (-1\right ) &= 0 \\
y^{\prime }\left (-1\right ) &= 1 \\
\end{align*} Series expansion around \(t=-1\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.611 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime } t +\lambda y&=0 \\
\end{align*} Series expansion around \(t=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.553 |
|
| \begin{align*}
\left (-t^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } t +\alpha \left (\alpha +1\right ) y&=0 \\
\end{align*} Series expansion around \(t=0\). |
[_Gegenbauer] |
✓ |
✓ |
✓ |
✓ |
0.718 |
|
| \begin{align*}
\left (-t^{2}+1\right ) y^{\prime \prime }-y^{\prime } t +\alpha ^{2} y&=0 \\
\end{align*} Series expansion around \(t=0\). |
[_Gegenbauer, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
0.638 |
|
| \begin{align*}
y^{\prime \prime }+t^{3} y^{\prime }+3 t^{2} y&={\mathrm e}^{t} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Series expansion around \(t=0\). |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.619 |
|
| \begin{align*}
\left (1-t \right ) y^{\prime \prime }+y^{\prime } t +y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Series expansion around \(t=0\). |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.544 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }+t y&=0 \\
y \left (0\right ) &= -1 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*} Series expansion around \(t=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.502 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime } t +{\mathrm e}^{t} y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Series expansion around \(t=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.623 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }+{\mathrm e}^{t} y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= -1 \\
\end{align*} Series expansion around \(t=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.586 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }+{\mathrm e}^{-t} y&=0 \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= 5 \\
\end{align*} Series expansion around \(t=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.776 |
|
| \begin{align*}
t^{2} y^{\prime \prime }+5 y^{\prime } t -5 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.182 |
|
| \begin{align*}
2 t^{2} y^{\prime \prime }+3 y^{\prime } t -y&=0 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.254 |
|
| \begin{align*}
\left (t -1\right )^{2} y^{\prime \prime }-2 \left (t -1\right ) y^{\prime }+2 y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
2.829 |
|
| \begin{align*}
t^{2} y^{\prime \prime }+3 y^{\prime } t +y&=0 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.818 |
|
| \begin{align*}
t^{2} y^{\prime \prime }-y^{\prime } t +y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.880 |
|
| \begin{align*}
\left (-2+t \right )^{2} y^{\prime \prime }+5 \left (-2+t \right ) y^{\prime }+4 y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.610 |
|
| \begin{align*}
t^{2} y^{\prime \prime }+y^{\prime } t +y&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
1.734 |
|
| \begin{align*}
t^{2} y^{\prime \prime }+3 y^{\prime } t +2 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
2.356 |
|
| \begin{align*}
t^{2} y^{\prime \prime }-y^{\prime } t -2 y&=0 \\
y \left (1\right ) &= 0 \\
y^{\prime }\left (1\right ) &= 1 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.325 |
|
| \begin{align*}
t^{2} y^{\prime \prime }-3 y^{\prime } t +4 y&=0 \\
y \left (1\right ) &= 1 \\
y^{\prime }\left (1\right ) &= 0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
1.803 |
|
| \begin{align*}
t \left (-2+t \right )^{2} y^{\prime \prime }+y^{\prime } t +y&=0 \\
\end{align*} Series expansion around \(t=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
4.437 |
|
| \begin{align*}
t \left (-2+t \right )^{2} y^{\prime \prime }+y^{\prime } t +y&=0 \\
\end{align*} Series expansion around \(t=2\). |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✓ |
✗ |
0.443 |
|
| \begin{align*}
\sin \left (t \right ) y^{\prime \prime }+\cos \left (t \right ) y^{\prime }+\frac {y}{t}&=0 \\
\end{align*} Series expansion around \(t=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.885 |
|
| \begin{align*}
\left ({\mathrm e}^{t}-1\right ) y^{\prime \prime }+{\mathrm e}^{t} y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(t=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.200 |
|
| \begin{align*}
\left (-t^{2}+1\right ) y^{\prime \prime }+\frac {y^{\prime }}{\sin \left (1+t \right )}+y&=0 \\
\end{align*} Series expansion around \(t=-1\). |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✓ |
✗ |
0.477 |
|
| \begin{align*}
t^{3} y^{\prime \prime }+\sin \left (t^{2}\right ) y^{\prime }+t y&=0 \\
\end{align*} Series expansion around \(t=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.663 |
|
| \begin{align*}
2 t^{2} y^{\prime \prime }+3 y^{\prime } t -\left (1+t \right ) y&=0 \\
\end{align*} Series expansion around \(t=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.933 |
|
| \begin{align*}
2 t y^{\prime \prime }+\left (1-2 t \right ) y^{\prime }-y&=0 \\
\end{align*} Series expansion around \(t=0\). |
[_Laguerre] |
✓ |
✓ |
✓ |
✓ |
1.021 |
|
| \begin{align*}
2 t y^{\prime \prime }+\left (1+t \right ) y^{\prime }-2 y&=0 \\
\end{align*} Series expansion around \(t=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.057 |
|
| \begin{align*}
2 t^{2} y^{\prime \prime }-y^{\prime } t +\left (1+t \right ) y&=0 \\
\end{align*} Series expansion around \(t=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.924 |
|
| \begin{align*}
4 t y^{\prime \prime }+3 y^{\prime }-3 y&=0 \\
\end{align*} Series expansion around \(t=0\). |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.067 |
|
| \begin{align*}
2 t^{2} y^{\prime \prime }+\left (t^{2}-t \right ) y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(t=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.920 |
|
| \begin{align*}
t^{2} y^{\prime \prime }-y^{\prime } t -\left (t^{2}+\frac {5}{4}\right ) y&=0 \\
\end{align*} Series expansion around \(t=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.858 |
|
| \begin{align*}
t^{2} y^{\prime \prime }+\left (-t^{2}+t \right ) y^{\prime }-y&=0 \\
\end{align*} Series expansion around \(t=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.925 |
|
| \begin{align*}
t y^{\prime \prime }-\left (t^{2}+2\right ) y^{\prime }+t y&=0 \\
\end{align*} Series expansion around \(t=0\). |
[_Lienard] |
✓ |
✓ |
✓ |
✓ |
0.970 |
|
| \begin{align*}
t^{2} y^{\prime \prime }+\left (-t^{2}+3 t \right ) y^{\prime }-t y&=0 \\
\end{align*} Series expansion around \(t=0\). |
[_Laguerre, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
1.070 |
|
| \begin{align*}
t^{2} y^{\prime \prime }+t \left (1+t \right ) y^{\prime }-y&=0 \\
\end{align*} Series expansion around \(t=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.935 |
|
| \begin{align*}
t y^{\prime \prime }-\left (t +4\right ) y^{\prime }+2 y&=0 \\
\end{align*} Series expansion around \(t=0\). |
[_Laguerre] |
✓ |
✓ |
✓ |
✗ |
1.135 |
|
| \begin{align*}
t^{2} y^{\prime \prime }+\left (t^{2}-3 t \right ) y^{\prime }+3 y&=0 \\
\end{align*} Series expansion around \(t=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
4.059 |
|
| \begin{align*}
t^{2} y^{\prime \prime }+y^{\prime } t -\left (1+t \right ) y&=0 \\
\end{align*} Series expansion around \(t=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
3.958 |
|
| \begin{align*}
t y^{\prime \prime }+y^{\prime } t +2 y&=0 \\
\end{align*} Series expansion around \(t=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
3.223 |
|
| \begin{align*}
t^{2} y^{\prime \prime }+\left (-t^{2}+1\right ) y^{\prime }+4 t y&=0 \\
\end{align*} Series expansion around \(t=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✓ |
✗ |
0.113 |
|
| \begin{align*}
t^{2} y^{\prime \prime }+y^{\prime } t +t^{2} y&=0 \\
\end{align*} Series expansion around \(t=0\). |
[_Lienard] |
✓ |
✓ |
✓ |
✓ |
0.729 |
|
| \begin{align*}
t^{2} y^{\prime \prime }+y^{\prime } t +\left (t^{2}-v^{2}\right ) y&=0 \\
\end{align*} Series expansion around \(t=0\). |
[_Bessel] |
✓ |
✓ |
✓ |
✗ |
0.929 |
|
| \begin{align*}
t y^{\prime \prime }+\left (1-t \right ) y^{\prime }+\lambda y&=0 \\
\end{align*} Series expansion around \(t=0\). |
[_Laguerre] |
✓ |
✓ |
✓ |
✓ |
1.187 |
|
| \begin{align*}
t \left (1-t \right ) y^{\prime \prime }+\left (\gamma -\left (\alpha +\beta +1\right ) t \right ) y^{\prime }-\alpha \beta y&=0 \\
\end{align*} Series expansion around \(t=0\). |
[_Jacobi] |
✓ |
✓ |
✓ |
✗ |
1.532 |
|
| \begin{align*}
2 \sin \left (t \right ) y^{\prime \prime }+\left (1-t \right ) y^{\prime }-2 y&=0 \\
\end{align*} Series expansion around \(t=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.153 |
|
| \begin{align*}
t^{2} y^{\prime \prime }+y^{\prime } t +\left (1+t \right ) y&=0 \\
\end{align*} Series expansion around \(t=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.783 |
|
| \begin{align*}
t y^{\prime \prime }+y^{\prime }-4 y&=0 \\
\end{align*} Series expansion around \(t=0\). |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.874 |
|
| \begin{align*}
t^{2} y^{\prime \prime }-t \left (1+t \right ) y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(t=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.773 |
|
| \begin{align*}
t^{2} y^{\prime \prime }+y^{\prime } t +\left (t^{2}-1\right ) y&=0 \\
\end{align*} Series expansion around \(t=0\). |
[_Bessel] |
✓ |
✓ |
✓ |
✓ |
3.882 |
|
| \begin{align*}
t y^{\prime \prime }+3 y^{\prime }-3 y&=0 \\
\end{align*} Series expansion around \(t=0\). |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
3.240 |
|
| \begin{align*}
t^{2} y^{\prime \prime }+t p \left (t \right ) y^{\prime }+q \left (t \right ) y&=0 \\
\end{align*} Series expansion around \(t=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
31.826 |
|
| \begin{align*}
y^{\prime \prime }-5 y^{\prime }+4 y&={\mathrm e}^{2 t} \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= -1 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.465 |
|
| \begin{align*}
2 y^{\prime \prime }+y^{\prime }-y&={\mathrm e}^{3 t} \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.393 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }+y&={\mathrm e}^{-t} \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 3 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.375 |
|
| \begin{align*}
y^{\prime \prime }+y&=t^{2} \sin \left (t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.596 |
|
| \begin{align*}
y^{\prime \prime }+3 y^{\prime }+7 y&=\cos \left (t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.512 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }+y&=t^{3} \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.519 |
|
| \begin{align*}
y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y&={\mathrm e}^{4 t} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
y^{\prime \prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.516 |
|
| \begin{align*}
y^{\prime \prime }-3 y^{\prime }+2 y&={\mathrm e}^{-t} \\
y \left (t_{0} \right ) &= 1 \\
y^{\prime }\left (t_{0} \right ) &= 0 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.459 |
|
| \begin{align*}
y^{\prime \prime }+y&=\sin \left (t \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.436 |
|
| \begin{align*}
y^{\prime \prime }+y&=t \sin \left (t \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.500 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime }+y&={\mathrm e}^{t} t \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.436 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime }+7 y&=\sin \left (t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.491 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }+y&=1+{\mathrm e}^{-t} \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= -5 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.473 |
|
| \begin{align*}
y^{\prime \prime }+y&=\left \{\begin {array}{cc} 2 & 0\le t \le 3 \\ 3 t -7 & 3<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]] |
✓ |
✓ |
✓ |
✓ |
3.549 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }+y&=2 \left (t -3\right ) \operatorname {Heaviside}\left (t -3\right ) \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
2.531 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }+y&=\operatorname {Heaviside}\left (t -\pi \right )-\operatorname {Heaviside}\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]] |
✓ |
✓ |
✓ |
✓ |
23.185 |
|
| \begin{align*}
y^{\prime \prime }+4 y&=\left \{\begin {array}{cc} 1 & 0\le t <4 \\ 0 & 4<t \end {array}\right . \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= -2 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
2.392 |
|
| \begin{align*}
y^{\prime \prime }+y&=\left \{\begin {array}{cc} \sin \left (t \right ) & 0\le t <\pi \\ \cos \left (t \right ) & \pi \le t \end {array}\right . \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
3.119 |
|
| \begin{align*}
y^{\prime \prime }+y&=\left \{\begin {array}{cc} \cos \left (t \right ) & 0\le t <\frac {\pi }{2} \\ 0 & \frac {\pi }{2}\le t \end {array}\right . \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= -1 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
2.129 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }+y&=\left \{\begin {array}{cc} \sin \left (2 t \right ) & 0\le t <\frac {\pi }{2} \\ 0 & \frac {\pi }{2}\le t \end {array}\right . \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
5.108 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }+7 y&=\left \{\begin {array}{cc} t & 0\le t <2 \\ 0 & 2\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]] |
✓ |
✓ |
✓ |
✗ |
11.376 |
|
| \begin{align*}
y^{\prime \prime }+y&=\left \{\begin {array}{cc} t^{2} & 0\le t <1 \\ 0 & 1\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]] |
✓ |
✓ |
✓ |
✓ |
2.576 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime }+y&=\left \{\begin {array}{cc} 0 & 0\le t <1 \\ t & 1\le t <2 \\ 0 & 2\le t \end {array}\right . \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
5.286 |
|
| \begin{align*}
y^{\prime \prime }+4 y^{\prime }+5 y&=\delta \left (t -1\right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.891 |
|
| \begin{align*}
y^{\prime \prime }+4 y&=\sin \left (t \right )+\delta \left (t -\pi \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.602 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }+y&=2 \delta \left (t -1\right )-\delta \left (-2+t \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
7.123 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }+y&={\mathrm e}^{-t}+3 \delta \left (t -3\right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 3 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.454 |
|
| \begin{align*}
x^{\prime }&=6 x-3 y \\
y^{\prime }&=2 x+y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.569 |
|
| \begin{align*}
x^{\prime }&=-2 x+y+t \\
y^{\prime }&=-4 x+3 y-1 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.851 |
|
| \begin{align*}
x^{\prime }&=6 x-3 y \\
y^{\prime }&=2 x+y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.496 |
|
| \begin{align*}
x^{\prime }&=x+y+{\mathrm e}^{t} \\
y^{\prime }&=x-y-{\mathrm e}^{t} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.227 |
|