| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
\left (t -1\right ) y^{\prime \prime }-t y^{\prime }+y&=2 t \,{\mathrm e}^{-t} \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
2.109 |
|
| \begin{align*}
\left (t -1\right ) y^{\prime \prime }-t y^{\prime }+y&=2 t \,{\mathrm e}^{-t} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
2.121 |
|
| \begin{align*}
\left (t -1\right ) y^{\prime \prime }-t y^{\prime }+y&=2 t \,{\mathrm e}^{-t} \\
y \left (0\right ) &= a \\
y^{\prime }\left (0\right ) &= b \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
2.085 |
|
| \begin{align*}
t^{2} y^{\prime \prime }-4 t y^{\prime }+6 y&=t^{5} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
3.984 |
|
| \begin{align*}
t^{2} y^{\prime \prime }-4 t y^{\prime }+6 y&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
3.043 |
|
| \begin{align*}
t^{2} y^{\prime \prime }-4 t y^{\prime }+6 y&=t^{5} \\
y \left (1\right ) &= 1 \\
y^{\prime }\left (1\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
3.909 |
|
| \begin{align*}
t^{2} y^{\prime \prime }-4 t y^{\prime }+6 y&=t^{5} \\
y \left (1\right ) &= 0 \\
y^{\prime }\left (1\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
3.875 |
|
| \begin{align*}
t^{2} y^{\prime \prime }-4 t y^{\prime }+6 y&=t^{5} \\
y \left (1\right ) &= -1 \\
y^{\prime }\left (1\right ) &= 3 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
3.891 |
|
| \begin{align*}
t^{2} y^{\prime \prime }-4 t y^{\prime }+6 y&=t^{5} \\
y \left (1\right ) &= a \\
y^{\prime }\left (1\right ) &= b \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
3.853 |
|
| \begin{align*}
t^{2} y^{\prime \prime }+3 t y^{\prime }-4 y&=t^{4} \\
y \left (-1\right ) &= y_{1} \\
y^{\prime }\left (-1\right ) &= y_{1} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
21.434 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime }-2 y&=\frac {t^{2}+1}{-t^{2}+1} \\
y \left (2\right ) &= y_{1} \\
y^{\prime }\left (2\right ) &= y_{1} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
1.419 |
|
| \begin{align*}
\sin \left (t \right ) y^{\prime \prime }+y&=\cos \left (t \right ) \\
y \left (\frac {\pi }{2}\right ) &= y_{1} \\
y^{\prime }\left (\frac {\pi }{2}\right ) &= y_{1} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
✗ |
✗ |
✗ |
20.525 |
|
| \begin{align*}
\left (t^{2}+1\right ) y^{\prime \prime }-t y^{\prime }+t^{2} y&=\cos \left (t \right ) \\
y \left (0\right ) &= y_{1} \\
y^{\prime }\left (0\right ) &= y_{1} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
✓ |
✗ |
✗ |
93.398 |
|
| \begin{align*}
y^{\prime \prime }+\sqrt {t}\, y^{\prime }-\sqrt {-3+t}\, y&=0 \\
y \left (10\right ) &= y_{1} \\
y^{\prime }\left (10\right ) &= y_{1} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
✗ |
60.806 |
|
| \begin{align*}
t \left (t^{2}-4\right ) y^{\prime \prime }+y&={\mathrm e}^{t} \\
y \left (1\right ) &= y_{1} \\
y^{\prime }\left (1\right ) &= y_{1} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
✗ |
✗ |
✗ |
64.867 |
|
| \begin{align*}
t^{2} y^{\prime \prime }-4 t y^{\prime }+6 y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
6.971 |
|
| \begin{align*}
y^{\prime \prime }+a_{1} \left (t \right ) y^{\prime }+a_{0} \left (t \right ) y&=f \left (t \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
✗ |
✗ |
✗ |
69.872 |
|
| \begin{align*}
\left (t -1\right ) y^{\prime \prime }-t y^{\prime }+y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.562 |
|
| \begin{align*}
\left (t^{2}+1\right ) y^{\prime \prime }-2 t y^{\prime }+2 y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.326 |
|
| \begin{align*}
t^{2} y^{\prime \prime }+t y^{\prime }+4 y&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
2.254 |
|
| \begin{align*}
t^{2} y^{\prime \prime }-2 t y^{\prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.646 |
|
| \begin{align*}
t^{2} y^{\prime \prime }+2 t y^{\prime }-2 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.458 |
|
| \begin{align*}
2 t^{2} y^{\prime \prime }-5 t y^{\prime }+3 y&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
2.925 |
|
| \begin{align*}
9 t^{2} y^{\prime \prime }+3 t y^{\prime }+y&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
2.143 |
|
| \begin{align*}
t^{2} y^{\prime \prime }+t y^{\prime }-2 y&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
2.240 |
|
| \begin{align*}
4 t^{2} y^{\prime \prime }+y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.398 |
|
| \begin{align*}
t^{2} y^{\prime \prime }-3 t y^{\prime }-21 y&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
1.247 |
|
| \begin{align*}
t^{2} y^{\prime \prime }+7 t y^{\prime }+9 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
2.096 |
|
| \begin{align*}
t^{2} y^{\prime \prime }+y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.522 |
|
| \begin{align*}
t^{2} y^{\prime \prime }+t y^{\prime }-4 y&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
2.073 |
|
| \begin{align*}
t^{2} y^{\prime \prime }+t y^{\prime }+4 y&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
2.148 |
|
| \begin{align*}
t^{2} y^{\prime \prime }-3 t y^{\prime }+13 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
2.931 |
|
| \begin{align*}
t^{2} y^{\prime \prime }+2 t y^{\prime }-2 y&=0 \\
y \left (1\right ) &= 0 \\
y^{\prime }\left (1\right ) &= 1 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.747 |
|
| \begin{align*}
4 t^{2} y^{\prime \prime }+y&=0 \\
y \left (1\right ) &= 2 \\
y^{\prime }\left (1\right ) &= 0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.526 |
|
| \begin{align*}
t^{2} y^{\prime \prime }+t y^{\prime }+4 y&=0 \\
y \left (1\right ) &= -3 \\
y^{\prime }\left (1\right ) &= 4 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
2.881 |
|
| \begin{align*}
t^{2} y^{\prime \prime }-4 t y^{\prime }+6 y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= -1 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✗ |
✗ |
✗ |
✗ |
43.649 |
|
| \begin{align*}
t y^{\prime \prime }+\left (t -1\right ) y^{\prime }-y&=0 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.504 |
|
| \begin{align*}
t y^{\prime \prime }+\left (t +1\right ) y^{\prime }+y&=0 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.382 |
|
| \begin{align*}
t y^{\prime \prime }+\left (2+4 t \right ) y^{\prime }+\left (4+4 t \right ) y&=0 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.504 |
|
| \begin{align*}
t y^{\prime \prime }-2 y^{\prime }+y t&=0 \\
\end{align*}
Using Laplace transform method. |
[_Lienard] |
✓ |
✓ |
✓ |
✓ |
0.475 |
|
| \begin{align*}
t y^{\prime \prime }-4 y^{\prime }+y t&=0 \\
y \left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[_Lienard] |
✓ |
✓ |
✓ |
✗ |
0.422 |
|
| \begin{align*}
t y^{\prime \prime }+\left (2 t +2\right ) y^{\prime }+\left (t +2\right ) y&=0 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.449 |
|
| \begin{align*}
-t y^{\prime \prime }+\left (t -2\right ) y^{\prime }+y&=0 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.744 |
|
| \begin{align*}
-t y^{\prime \prime }-2 y^{\prime }+y t&=0 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.557 |
|
| \begin{align*}
t y^{\prime \prime }+\left (2-5 t \right ) y^{\prime }+\left (6 t -5\right ) y&=0 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.763 |
|
| \begin{align*}
t y^{\prime \prime }+2 y^{\prime }+9 y t&=0 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.005 |
|
| \begin{align*}
t y^{\prime \prime \prime }+3 y^{\prime \prime }+t y^{\prime }+y&=0 \\
\end{align*}
Using Laplace transform method. |
[[_3rd_order, _exact, _linear, _homogeneous]] |
✗ |
✓ |
✓ |
✗ |
0.035 |
|
| \begin{align*}
t y^{\prime \prime }+\left (t +2\right ) y^{\prime }+y&=0 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.739 |
|
| \begin{align*}
t^{2} y^{\prime \prime }-3 t y^{\prime }+4 y&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
0.177 |
|
| \begin{align*}
t^{2} y^{\prime \prime }+2 t y^{\prime }-2 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.159 |
|
| \begin{align*}
4 t^{2} y^{\prime \prime }+y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.160 |
|
| \begin{align*}
t^{2} y^{\prime \prime }+2 t y^{\prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.151 |
|
| \begin{align*}
t^{2} y^{\prime \prime }-t \left (t +2\right ) y^{\prime }+\left (t +2\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.172 |
|
| \begin{align*}
t^{2} y^{\prime \prime }-4 t y^{\prime }+\left (t^{2}+6\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.171 |
|
| \begin{align*}
t y^{\prime \prime }-y^{\prime }+4 t^{3} y&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
0.183 |
|
| \begin{align*}
t y^{\prime \prime }-2 \left (t +1\right ) y^{\prime }+4 y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.178 |
|
| \begin{align*}
y^{\prime \prime }-2 \sec \left (t \right )^{2} y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.189 |
|
| \begin{align*}
t y^{\prime \prime }+\left (t -1\right ) y^{\prime }-y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.164 |
|
| \begin{align*}
y^{\prime \prime }-\tan \left (t \right ) y^{\prime }-\sec \left (t \right )^{2} y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
0.188 |
|
| \begin{align*}
\left (t^{2}+1\right ) y^{\prime \prime }-2 t y^{\prime }+2 y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.162 |
|
| \begin{align*}
\left (1+\cos \left (2 t \right )\right ) y^{\prime \prime }-4 y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
1.361 |
|
| \begin{align*}
t^{2} y^{\prime \prime }-2 t y^{\prime }+\left (t^{2}+2\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.166 |
|
| \begin{align*}
\left (-t^{2}+1\right ) y^{\prime \prime }+2 y&=0 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.178 |
|
| \begin{align*}
\left (-t^{2}+1\right ) y^{\prime \prime }-2 t y^{\prime }+2 y&=0 \\
\end{align*} |
[_Gegenbauer] |
✓ |
✓ |
✓ |
✗ |
0.176 |
|
| \begin{align*}
y^{\prime \prime }+y&=\sin \left (t \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.625 |
|
| \begin{align*}
y^{\prime \prime }-4 y&={\mathrm e}^{2 t} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.616 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime }+5 y&={\mathrm e}^{t} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.588 |
|
| \begin{align*}
y^{\prime \prime }+3 y^{\prime }&={\mathrm e}^{-3 t} \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.207 |
|
| \begin{align*}
y^{\prime \prime }-3 y^{\prime }+2 y&={\mathrm e}^{3 t} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.519 |
|
| \begin{align*}
y^{\prime \prime }+y&=\tan \left (t \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.655 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime }+y&=\frac {{\mathrm e}^{t}}{t} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.711 |
|
| \begin{align*}
y^{\prime \prime }+y&=\sec \left (t \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.648 |
|
| \begin{align*}
t^{2} y^{\prime \prime }-2 t y^{\prime }+2 y&=t^{4} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
4.125 |
|
| \begin{align*}
t y^{\prime \prime }-y^{\prime }&=3 t^{2}-1 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.438 |
|
| \begin{align*}
t^{2} y^{\prime \prime }-t y^{\prime }+y&=t \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
11.980 |
|
| \begin{align*}
y^{\prime \prime }-4 y^{\prime }+4 y&=\frac {{\mathrm e}^{2 t}}{t^{2}+1} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.724 |
|
| \begin{align*}
y^{\prime \prime }-\tan \left (t \right ) y^{\prime }-\sec \left (t \right )^{2} y&=t \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
12.079 |
|
| \begin{align*}
t y^{\prime \prime }+\left (t -1\right ) y^{\prime }-y&={\mathrm e}^{-t} t^{2} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.362 |
|
| \begin{align*}
t y^{\prime \prime }-y^{\prime }+4 t^{3} y&=4 t^{5} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
3.854 |
|
| \begin{align*}
y^{\prime \prime }-y&=\frac {1}{1+{\mathrm e}^{-t}} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.646 |
|
| \begin{align*}
y^{\prime \prime }+a^{2} y&=f \left (t \right ) \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
2.257 |
|
| \begin{align*}
y^{\prime \prime }-a^{2} y&=f \left (t \right ) \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
2.201 |
|
| \begin{align*}
y^{\prime \prime }-2 a y^{\prime }+a^{2} y&=f \left (t \right ) \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.475 |
|
| \begin{align*}
y^{\prime \prime }-\left (a +b \right ) y^{\prime }+a b y&=f \left (t \right ) \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.644 |
|
| \begin{align*}
y^{\prime \prime }+4 y&=\left \{\begin {array}{cc} 4 & 0\le t <2 \\ 8 t & 2\le t <\infty \end {array}\right . \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✗ |
✓ |
✓ |
4.565 |
|
| \begin{align*}
y^{\prime \prime }-3 y^{\prime }+2 y&=\left \{\begin {array}{cc} {\mathrm e}^{t} & 0\le t <1 \\ {\mathrm e}^{2 t} & 1\le t <\infty \end {array}\right . \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✗ |
✓ |
✓ |
0.584 |
|
| \begin{align*}
-y+y^{\prime }&=\left \{\begin {array}{cc} 1 & 0\le t <2 \\ -1 & 2\le t <4 \\ 0 & 4\le t <\infty \end {array}\right . \\
y \left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
2.798 |
|
| \begin{align*}
3 y+y^{\prime }&=\left \{\begin {array}{cc} t & 0\le t <1 \\ 1 & 1\le t <\infty \end {array}\right . \\
y \left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[[_linear, ‘class A‘]] |
✓ |
✗ |
✓ |
✗ |
3.018 |
|
| \begin{align*}
-y+y^{\prime }&=\left \{\begin {array}{cc} 0 & 0\le t <1 \\ t -1 & 1\le t <2 \\ 3-t & 2\le t <3 \\ 0 & 3\le t <\infty \end {array}\right . \\
y \left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
2.819 |
|
| \begin{align*}
y+y^{\prime }&=\left \{\begin {array}{cc} \sin \left (t \right ) & 0\le t <\pi \\ 0 & \pi \le t <\infty \end {array}\right . \\
y \left (\pi \right ) &= -1 \\
\end{align*}
Using Laplace transform method. |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.921 |
|
| \begin{align*}
y^{\prime \prime }-y&=\left \{\begin {array}{cc} t & 0\le t <1 \\ 0 & 1\le t <\infty \end {array}\right . \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
2.704 |
|
| \begin{align*}
y^{\prime \prime }-4 y^{\prime }+4 y&=\left \{\begin {array}{cc} 0 & 0\le t <2 \\ 4 & 2\le t <\infty \end {array}\right . \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✗ |
✓ |
✗ |
2.322 |
|
| \begin{align*}
y^{\prime }&=\left \{\begin {array}{cc} 0 & t =0 \\ \sin \left (\frac {1}{t}\right ) & \operatorname {otherwise} \end {array}\right . \\
\end{align*}
Using Laplace transform method. |
[_quadrature] |
✓ |
✗ |
✓ |
✓ |
2.079 |
|
| \begin{align*}
y^{\prime }+2 y&=\left \{\begin {array}{cc} 0 & 0\le t <1 \\ -3 & 1\le t \end {array}\right . \\
y \left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
1.283 |
|
| \begin{align*}
y^{\prime }+5 y&=\left \{\begin {array}{cc} -5 & 0\le t <1 \\ 5 & 1\le t \end {array}\right . \\
y \left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
2.187 |
|
| \begin{align*}
y^{\prime }-3 y&=\left \{\begin {array}{cc} 0 & 0\le t <2 \\ 2 & 2\le t <3 \\ 0 & 3\le t \end {array}\right . \\
y \left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
3.664 |
|
| \begin{align*}
y^{\prime }+2 y&=\left \{\begin {array}{cc} t & 0\le t <1 \\ 0 & 1\le t \end {array}\right . \\
y \left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
2.319 |
|
| \begin{align*}
y^{\prime }-4 y&=\left \{\begin {array}{cc} 12 \,{\mathrm e}^{t} & 0\le t <1 \\ 12 \,{\mathrm e} & 1\le t \end {array}\right . \\
y \left (0\right ) &= 2 \\
\end{align*}
Using Laplace transform method. |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
6.450 |
|
| \begin{align*}
3 y+y^{\prime }&=\left \{\begin {array}{cc} 10 \sin \left (t \right ) & 0\le t <\pi \\ 0 & \pi \le t \end {array}\right . \\
y \left (0\right ) &= -1 \\
\end{align*}
Using Laplace transform method. |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
3.830 |
|
| \begin{align*}
y^{\prime \prime }+9 y&=\operatorname {Heaviside}\left (-3+t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.843 |
|