| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
y^{\prime \prime }+100 y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 10 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
2.737 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime }+y&=0 \\
y \left (0\right ) &= 4 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.598 |
|
| \begin{align*}
y^{\prime \prime }+4 y^{\prime }+4 y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 3 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.595 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }+5 y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.570 |
|
| \begin{align*}
y^{\prime \prime }+4 y^{\prime }+20 y&=0 \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.563 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }-y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.532 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }+y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.593 |
|
| \begin{align*}
y^{\prime \prime }-y^{\prime }+y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.602 |
|
| \begin{align*}
y^{\prime \prime }-y^{\prime }-y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.557 |
|
| \begin{align*}
6 y^{\prime \prime }+5 y^{\prime }+y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.342 |
|
| \begin{align*}
9 y^{\prime \prime }+6 y^{\prime }+y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.451 |
|
| \begin{align*}
y^{\prime \prime }+4 y^{\prime }+20 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.339 |
|
| \begin{align*}
3 t^{2} y^{\prime \prime }-2 t y^{\prime }+2 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
3.329 |
|
| \begin{align*}
t^{2} y^{\prime \prime }-t y^{\prime }+y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
2.413 |
|
| \begin{align*}
a y^{\prime \prime }+2 b y^{\prime }+c y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
1.783 |
|
| \begin{align*}
y^{\prime \prime }+6 y^{\prime }+2 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.387 |
|
| \begin{align*}
y^{\prime \prime }-5 y^{\prime }+6 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.340 |
|
| \begin{align*}
y^{\prime \prime }-6 y^{\prime }-16 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.339 |
|
| \begin{align*}
y^{\prime \prime }-16 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
2.823 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }+5 y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (\frac {\pi }{2}\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.378 |
|
| \begin{align*}
{y^{\prime \prime }}^{2}-5 y^{\prime \prime } y^{\prime }+4 y^{2}&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✗ |
✓ |
✗ |
✗ |
0.109 |
|
| \begin{align*}
{y^{\prime \prime }}^{2}-2 y^{\prime \prime } y^{\prime }+y^{2}&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✗ |
✓ |
✗ |
✗ |
0.043 |
|
| \begin{align*}
y^{\prime \prime }+4 y^{\prime }+3 y&=0 \\
y \left (0\right ) &= a \\
y^{\prime }\left (0\right ) &= b \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.427 |
|
| \begin{align*}
y^{\prime \prime }+y&=8 \,{\mathrm e}^{2 t} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.559 |
|
| \begin{align*}
y^{\prime \prime }-4 y^{\prime }+3 y&=-{\mathrm e}^{-9 t} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.544 |
|
| \begin{align*}
y^{\prime \prime }-4 y^{\prime }+3 y&=2 \,{\mathrm e}^{3 t} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.632 |
|
| \begin{align*}
y^{\prime \prime }-y&=2 t -4 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.516 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime }+y&=t^{2} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.658 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }&=3-4 t \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.352 |
|
| \begin{align*}
y^{\prime \prime }+y&=\cos \left (2 t \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.602 |
|
| \begin{align*}
y^{\prime \prime }+4 y&=4 \cos \left (t \right )-\sin \left (t \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.807 |
|
| \begin{align*}
y^{\prime \prime }+4 y&=\cos \left (2 t \right )+t \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.919 |
|
| \begin{align*}
y^{\prime \prime }+4 y&=3 t \,{\mathrm e}^{-t} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.566 |
|
| \begin{align*}
y^{\prime \prime }&=3 t^{4}-2 t \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
1.273 |
|
| \begin{align*}
y^{\prime \prime }-4 y^{\prime }+13 y&=2 t \,{\mathrm e}^{-2 t} \sin \left (3 t \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.975 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }-2 y&=-1 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.503 |
|
| \begin{align*}
5 y^{\prime \prime }+y^{\prime }-4 y&=-3 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.525 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime }-8 y&=32 t \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.533 |
|
| \begin{align*}
16 y^{\prime \prime }-8 y^{\prime }-15 y&=75 t \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.553 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }+26 y&=-338 t \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.603 |
|
| \begin{align*}
y^{\prime \prime }+3 y^{\prime }-4 y&=-32 t^{2} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.546 |
|
| \begin{align*}
8 y^{\prime \prime }+6 y^{\prime }+y&=5 t^{2} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.546 |
|
| \begin{align*}
y^{\prime \prime }-6 y^{\prime }+8 y&=-256 t^{3} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.562 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime }&=52 \sin \left (3 t \right ) \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.415 |
|
| \begin{align*}
y^{\prime \prime }-6 y^{\prime }+13 y&=25 \sin \left (2 t \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.628 |
|
| \begin{align*}
y^{\prime \prime }-9 y&=54 t \sin \left (2 t \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.905 |
|
| \begin{align*}
y^{\prime \prime }-5 y^{\prime }+6 y&=-78 \cos \left (3 t \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.579 |
|
| \begin{align*}
y^{\prime \prime }+4 y^{\prime }+4 y&=-32 t^{2} \cos \left (2 t \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.431 |
|
| \begin{align*}
y^{\prime \prime }-y^{\prime }-20 y&=-2 \,{\mathrm e}^{t} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.552 |
|
| \begin{align*}
y^{\prime \prime }-4 y^{\prime }-5 y&=-648 t^{2} {\mathrm e}^{5 t} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.684 |
|
| \begin{align*}
y^{\prime \prime }-7 y^{\prime }+12 y&=-2 t^{3} {\mathrm e}^{4 t} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.599 |
|
| \begin{align*}
y^{\prime \prime }+4 y^{\prime }&=8 \,{\mathrm e}^{4 t}-4 \,{\mathrm e}^{-4 t} \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✗ |
1.660 |
|
| \begin{align*}
y^{\prime \prime }-3 y^{\prime }&=t^{2}-{\mathrm e}^{3 t} \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.477 |
|
| \begin{align*}
y^{\prime \prime }+4 y^{\prime }&=-24 t -6-4 t \,{\mathrm e}^{-4 t}+{\mathrm e}^{-4 t} \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.512 |
|
| \begin{align*}
y^{\prime \prime }-3 y^{\prime }&=t^{2}-{\mathrm e}^{3 t} \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.366 |
|
| \begin{align*}
y^{\prime \prime }&=t^{2}+{\mathrm e}^{t}+\sin \left (t \right ) \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
1.888 |
|
| \begin{align*}
y^{\prime \prime }+3 y^{\prime }&=18 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 3 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
2.809 |
|
| \begin{align*}
y^{\prime \prime }-y&=4 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
2.743 |
|
| \begin{align*}
y^{\prime \prime }-4 y&=32 t \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 6 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.660 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }-3 y&=-2 \\
y \left (0\right ) &= {\frac {2}{3}} \\
y^{\prime }\left (0\right ) &= 8 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.652 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }-6 y&=3 t \\
y \left (0\right ) &= {\frac {23}{12}} \\
y^{\prime }\left (0\right ) &= -{\frac {3}{2}} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.673 |
|
| \begin{align*}
y^{\prime \prime }+8 y^{\prime }+16 y&=4 \\
y \left (0\right ) &= {\frac {5}{4}} \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.800 |
|
| \begin{align*}
y^{\prime \prime }+7 y^{\prime }+10 y&=t \,{\mathrm e}^{-t} \\
y \left (0\right ) &= -{\frac {5}{16}} \\
y^{\prime }\left (0\right ) &= {\frac {9}{16}} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.701 |
|
| \begin{align*}
y^{\prime \prime }+6 y^{\prime }+25 y&=-1 \\
y \left (0\right ) &= -{\frac {1}{25}} \\
y^{\prime }\left (0\right ) &= 7 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.736 |
|
| \begin{align*}
y^{\prime \prime }-3 y^{\prime }&=-{\mathrm e}^{3 t}-2 t \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= {\frac {8}{9}} \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.782 |
|
| \begin{align*}
y^{\prime \prime }-y^{\prime }&=-3 t -4 \,{\mathrm e}^{2 t} t^{2} \\
y \left (0\right ) &= -{\frac {7}{2}} \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
2.068 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime }&=2 t^{2} \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= {\frac {3}{2}} \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.580 |
|
| \begin{align*}
y^{\prime \prime }+4 y^{\prime }&=-24 t -6-4 t \,{\mathrm e}^{-4 t}+{\mathrm e}^{-4 t} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.750 |
|
| \begin{align*}
y^{\prime \prime }-3 y^{\prime }&={\mathrm e}^{-3 t}-{\mathrm e}^{3 t} \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✗ |
1.744 |
|
| \begin{align*}
y^{\prime \prime }+9 y&=\left \{\begin {array}{cc} 2 t & 0\le t <\pi \\ 0 & \pi \le t \end {array}\right . \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
4.155 |
|
| \begin{align*}
y^{\prime \prime }+9 \pi ^{2} y&=\left \{\begin {array}{cc} 2 t & 0\le t <\pi \\ 2 t -2 \pi & \pi \le t <2 \pi \\ 0 & 2 \pi \le t \end {array}\right . \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
17.358 |
|
| \begin{align*}
y^{\prime \prime }+4 y&=\left \{\begin {array}{cc} 0 & 0\le t <\pi \\ 10 & \pi \le t <2 \pi \\ 0 & 2 \pi \le t \end {array}\right . \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
4.532 |
|
| \begin{align*}
y^{\prime }-4 y&=t^{2} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.580 |
|
| \begin{align*}
y+y^{\prime }&=\cos \left (2 t \right ) \\
y \left (0\right ) &= 0 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.975 |
|
| \begin{align*}
-y+y^{\prime }&={\mathrm e}^{4 t} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.007 |
|
| \begin{align*}
y^{\prime }+4 y&={\mathrm e}^{-4 t} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.532 |
|
| \begin{align*}
y^{\prime }+4 y&=t \,{\mathrm e}^{-4 t} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
4.636 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }-2 y&=f \left (t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= a \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.139 |
|
| \begin{align*}
x^{\prime \prime }+9 x&=\sin \left (3 t \right ) \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.839 |
|
| \begin{align*}
4 y^{\prime \prime }+4 y^{\prime }+37 y&=\cos \left (3 t \right ) \\
y \left (0\right ) &= a \\
y^{\prime }\left (\pi \right ) &= a \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.849 |
|
| \begin{align*}
y^{\prime \prime }+4 y&=1 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
3.638 |
|
| \begin{align*}
y^{\prime \prime }+16 y^{\prime }&=t \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.319 |
|
| \begin{align*}
y^{\prime \prime }-7 y^{\prime }+10 y&={\mathrm e}^{3 t} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.523 |
|
| \begin{align*}
y^{\prime \prime }+16 y&=2 \cos \left (4 t \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.640 |
|
| \begin{align*}
y^{\prime \prime }+4 y^{\prime }+20 y&=2 t \,{\mathrm e}^{-2 t} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.572 |
|
| \begin{align*}
y^{\prime \prime }+\frac {y}{4}&=\sec \left (\frac {t}{2}\right )+\csc \left (\frac {t}{2}\right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.995 |
|
| \begin{align*}
y^{\prime \prime }+16 y&=\csc \left (4 t \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.180 |
|
| \begin{align*}
y^{\prime \prime }+16 y&=\cot \left (4 t \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.344 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }+50 y&={\mathrm e}^{-t} \csc \left (7 t \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.013 |
|
| \begin{align*}
y^{\prime \prime }+6 y^{\prime }+25 y&={\mathrm e}^{-3 t} \left (\sec \left (4 t \right )+\csc \left (4 t \right )\right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.980 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime }+26 y&={\mathrm e}^{t} \left (\sec \left (5 t \right )+\csc \left (5 t \right )\right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.194 |
|
| \begin{align*}
y^{\prime \prime }+12 y^{\prime }+37 y&={\mathrm e}^{-6 t} \csc \left (t \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.126 |
|
| \begin{align*}
y^{\prime \prime }-6 y^{\prime }+34 y&={\mathrm e}^{3 t} \tan \left (5 t \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.148 |
|
| \begin{align*}
y^{\prime \prime }-10 y^{\prime }+34 y&={\mathrm e}^{5 t} \cot \left (3 t \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.975 |
|
| \begin{align*}
y^{\prime \prime }-12 y^{\prime }+37 y&={\mathrm e}^{6 t} \sec \left (t \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.080 |
|
| \begin{align*}
y^{\prime \prime }-8 y^{\prime }+17 y&={\mathrm e}^{4 t} \sec \left (t \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.132 |
|
| \begin{align*}
y^{\prime \prime }-9 y&=\frac {1}{1+{\mathrm e}^{3 t}} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.688 |
|
| \begin{align*}
y^{\prime \prime }-25 y&=\frac {1}{1-{\mathrm e}^{5 t}} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.742 |
|
| \begin{align*}
y^{\prime \prime }-y&=2 \sinh \left (t \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.714 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime }+y&=\frac {{\mathrm e}^{t}}{t} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.684 |
|