| # |
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]] |
✓ |
✓ |
✓ |
✓ |
0.646 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.643 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }-6 y&=\sin \left (t \right )+{\mathrm e}^{2 t} t \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.066 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
2.001 |
|
| \begin{align*}
y^{\prime \prime }-3 y^{\prime }+2 y&={\mathrm e}^{t}+{\mathrm e}^{2 t} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.682 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }&=1+t^{2}+{\mathrm e}^{-2 t} \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.314 |
|
| \begin{align*}
y^{\prime \prime }+y&=\cos \left (t \right ) \cos \left (2 t \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.000 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
1.392 |
|
| \begin{align*}
y^{\prime \prime }-6 y^{\prime }+9 y&=t^{{3}/{2}} {\mathrm e}^{3 t} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.668 |
|
| \begin{align*}
y^{\prime \prime }+t y^{\prime }+y&=0 \\
\end{align*}
Series expansion around \(t=0\). |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.415 |
|
| \begin{align*}
y^{\prime \prime }-y t&=0 \\
\end{align*}
Series expansion around \(t=0\). |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.361 |
|
| \begin{align*}
\left (t^{2}+2\right ) y^{\prime \prime }-t y^{\prime }-3 y&=0 \\
\end{align*}
Series expansion around \(t=0\). |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.520 |
|
| \begin{align*}
y^{\prime \prime }-t^{3} y&=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]] |
✓ |
✓ |
✓ |
✓ |
0.613 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.383 |
|
| \begin{align*}
y^{\prime \prime }-t^{3} y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= -2 \\
\end{align*}
Series expansion around \(t=0\). |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.360 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.579 |
|
| \begin{align*}
y^{\prime \prime }-2 t y^{\prime }+\lambda y&=0 \\
\end{align*}
Series expansion around \(t=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.500 |
|
| \begin{align*}
\left (-t^{2}+1\right ) y^{\prime \prime }-2 t y^{\prime }+\alpha \left (\alpha +1\right ) y&=0 \\
\end{align*}
Series expansion around \(t=0\). |
[_Gegenbauer] |
✓ |
✓ |
✓ |
✓ |
0.671 |
|
| \begin{align*}
\left (-t^{2}+1\right ) y^{\prime \prime }-t y^{\prime }+\alpha ^{2} y&=0 \\
\end{align*}
Series expansion around \(t=0\). |
[_Gegenbauer, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
0.599 |
|
| \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]] |
✓ |
✓ |
✓ |
✗ |
0.572 |
|
| \begin{align*}
\left (1-t \right ) y^{\prime \prime }+t y^{\prime }+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]] |
✓ |
✓ |
✓ |
✓ |
0.515 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }+y t&=0 \\
y \left (0\right ) &= -1 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*}
Series expansion around \(t=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.473 |
|
| \begin{align*}
y^{\prime \prime }+t y^{\prime }+{\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]] |
✓ |
✓ |
✓ |
✓ |
0.620 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.563 |
|
| \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 t y^{\prime }-5 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.211 |
|
| \begin{align*}
2 t^{2} y^{\prime \prime }+3 t y^{\prime }-y&=0 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.302 |
|
| \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)]‘]] |
✓ |
✓ |
✓ |
✓ |
2.668 |
|
| \begin{align*}
t^{2} y^{\prime \prime }+3 t y^{\prime }+y&=0 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.761 |
|
| \begin{align*}
t^{2} y^{\prime \prime }-t y^{\prime }+y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.783 |
|
| \begin{align*}
\left (t -2\right )^{2} y^{\prime \prime }+5 \left (t -2\right ) y^{\prime }+4 y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.572 |
|
| \begin{align*}
t^{2} y^{\prime \prime }+t y^{\prime }+y&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
1.752 |
|
| \begin{align*}
t^{2} y^{\prime \prime }+3 t y^{\prime }+2 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
2.287 |
|
| \begin{align*}
t^{2} y^{\prime \prime }-t y^{\prime }-2 y&=0 \\
y \left (1\right ) &= 0 \\
y^{\prime }\left (1\right ) &= 1 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.397 |
|
| \begin{align*}
t^{2} y^{\prime \prime }-3 t y^{\prime }+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)]‘]] |
✓ |
✓ |
✓ |
✓ |
1.833 |
|
| \begin{align*}
t \left (t -2\right )^{2} y^{\prime \prime }+t y^{\prime }+y&=0 \\
\end{align*}
Series expansion around \(t=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
4.229 |
|
| \begin{align*}
t \left (t -2\right )^{2} y^{\prime \prime }+t y^{\prime }+y&=0 \\
\end{align*}
Series expansion around \(t=2\). |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✓ |
✗ |
0.417 |
|
| \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]] |
✓ |
✓ |
✓ |
✗ |
0.851 |
|
| \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]] |
✓ |
✓ |
✓ |
✗ |
1.233 |
|
| \begin{align*}
\left (-t^{2}+1\right ) y^{\prime \prime }+\frac {y^{\prime }}{\sin \left (t +1\right )}+y&=0 \\
\end{align*}
Series expansion around \(t=-1\). |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✓ |
✗ |
0.372 |
|
| \begin{align*}
t^{3} y^{\prime \prime }+\sin \left (t^{2}\right ) y^{\prime }+y t&=0 \\
\end{align*}
Series expansion around \(t=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.661 |
|
| \begin{align*}
2 t^{2} y^{\prime \prime }+3 t y^{\prime }-\left (t +1\right ) y&=0 \\
\end{align*}
Series expansion around \(t=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.954 |
|
| \begin{align*}
2 t y^{\prime \prime }+\left (1-2 t \right ) y^{\prime }-y&=0 \\
\end{align*}
Series expansion around \(t=0\). |
[_Laguerre] |
✓ |
✓ |
✓ |
✓ |
1.026 |
|
| \begin{align*}
2 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]] |
✓ |
✓ |
✓ |
✓ |
1.076 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.935 |
|
| \begin{align*}
4 t y^{\prime \prime }+3 y^{\prime }-3 y&=0 \\
\end{align*}
Series expansion around \(t=0\). |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.019 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.925 |
|
| \begin{align*}
t^{2} y^{\prime \prime }-t y^{\prime }-\left (t^{2}+\frac {5}{4}\right ) y&=0 \\
\end{align*}
Series expansion around \(t=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.875 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.923 |
|
| \begin{align*}
t y^{\prime \prime }-\left (t^{2}+2\right ) y^{\prime }+y t&=0 \\
\end{align*}
Series expansion around \(t=0\). |
[_Lienard] |
✓ |
✓ |
✓ |
✓ |
0.960 |
|
| \begin{align*}
t^{2} y^{\prime \prime }+\left (-t^{2}+3 t \right ) y^{\prime }-y t&=0 \\
\end{align*}
Series expansion around \(t=0\). |
[_Laguerre, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
1.044 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.934 |
|
| \begin{align*}
t y^{\prime \prime }-\left (t +4\right ) y^{\prime }+2 y&=0 \\
\end{align*}
Series expansion around \(t=0\). |
[_Laguerre] |
✓ |
✓ |
✓ |
✗ |
1.120 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
3.721 |
|
| \begin{align*}
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]] |
✓ |
✓ |
✓ |
✓ |
3.623 |
|
| \begin{align*}
t y^{\prime \prime }+t y^{\prime }+2 y&=0 \\
\end{align*}
Series expansion around \(t=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
3.019 |
|
| \begin{align*}
t^{2} y^{\prime \prime }+\left (-t^{2}+1\right ) y^{\prime }+4 y t&=0 \\
\end{align*}
Series expansion around \(t=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✓ |
✗ |
0.164 |
|
| \begin{align*}
t^{2} y^{\prime \prime }+t y^{\prime }+t^{2} y&=0 \\
\end{align*}
Series expansion around \(t=0\). |
[_Lienard] |
✓ |
✓ |
✓ |
✓ |
0.690 |
|
| \begin{align*}
t^{2} y^{\prime \prime }+t y^{\prime }+\left (t^{2}-v^{2}\right ) y&=0 \\
\end{align*}
Series expansion around \(t=0\). |
[_Bessel] |
✓ |
✓ |
✓ |
✗ |
0.927 |
|
| \begin{align*}
t y^{\prime \prime }+\left (1-t \right ) y^{\prime }+\lambda y&=0 \\
\end{align*}
Series expansion around \(t=0\). |
[_Laguerre] |
✓ |
✓ |
✓ |
✓ |
1.116 |
|
| \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] |
✓ |
✓ |
✓ |
✗ |
1.506 |
|
| \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]] |
✓ |
✓ |
✓ |
✗ |
1.113 |
|
| \begin{align*}
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]] |
✓ |
✓ |
✓ |
✗ |
0.789 |
|
| \begin{align*}
t y^{\prime \prime }+y^{\prime }-4 y&=0 \\
\end{align*}
Series expansion around \(t=0\). |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.861 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.785 |
|
| \begin{align*}
t^{2} y^{\prime \prime }+t y^{\prime }+\left (t^{2}-1\right ) y&=0 \\
\end{align*}
Series expansion around \(t=0\). |
[_Bessel] |
✓ |
✓ |
✓ |
✓ |
3.662 |
|
| \begin{align*}
t y^{\prime \prime }+3 y^{\prime }-3 y&=0 \\
\end{align*}
Series expansion around \(t=0\). |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
3.016 |
|
| \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]] |
✓ |
✓ |
✓ |
✗ |
30.034 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.399 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.319 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.299 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.496 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.447 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.440 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.388 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.363 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.345 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.408 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.214 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.418 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.390 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
3.011 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }+y&=2 \left (-3+t \right ) \operatorname {Heaviside}\left (-3+t \right ) \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.755 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
21.807 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
2.113 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
2.781 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
1.890 |
|
| \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]] |
✓ |
✓ |
✓ |
✗ |
4.611 |
|
| \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]] |
✓ |
✓ |
✓ |
✗ |
10.104 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
2.255 |
|
| \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]] |
✓ |
✓ |
✓ |
✗ |
4.628 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
1.702 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
1.464 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }+y&=2 \delta \left (t -1\right )-\delta \left (t -2\right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
6.388 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }+y&={\mathrm e}^{-t}+3 \delta \left (-3+t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 3 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.279 |
|
| \begin{align*}
x^{\prime }&=6 x-3 y \\
y^{\prime }&=2 x+y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.488 |
|
| \begin{align*}
x^{\prime }&=-2 x+y+t \\
y^{\prime }&=-4 x+3 y-1 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.768 |
|
| \begin{align*}
x^{\prime }&=6 x-3 y \\
y^{\prime }&=2 x+y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.465 |
|
| \begin{align*}
x^{\prime }&=x+y+{\mathrm e}^{t} \\
y^{\prime }&=x-y-{\mathrm e}^{t} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.998 |
|