| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
y^{\prime \prime }-4 y^{\prime }+4 y&=\frac {{\mathrm e}^{2 t}}{t^{2}} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.555 |
|
| \begin{align*}
y^{\prime \prime }+8 y^{\prime }+16 y&=\frac {{\mathrm e}^{-4 t}}{t^{4}} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.580 |
|
| \begin{align*}
y^{\prime \prime }+6 y^{\prime }+9 y&=\frac {{\mathrm e}^{-3 t}}{t} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.564 |
|
| \begin{align*}
y^{\prime \prime }+6 y^{\prime }+9 y&={\mathrm e}^{-3 t} \ln \left (t \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.582 |
|
| \begin{align*}
y^{\prime \prime }+3 y^{\prime }+2 y&=\cos \left ({\mathrm e}^{t}\right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.620 |
|
| \begin{align*}
y^{\prime \prime }+4 y^{\prime }+4 y&={\mathrm e}^{-2 t} \sqrt {-t^{2}+1} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.658 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime }+y&={\mathrm e}^{t} \sqrt {-t^{2}+1} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.586 |
|
| \begin{align*}
y^{\prime \prime }-10 y^{\prime }+25 y&={\mathrm e}^{5 t} \ln \left (2 t \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.636 |
|
| \begin{align*}
y^{\prime \prime }-4 y^{\prime }+4 y&={\mathrm e}^{2 t} \arctan \left (t \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.638 |
|
| \begin{align*}
y^{\prime \prime }+8 y^{\prime }+16 y&=\frac {{\mathrm e}^{-4 t}}{t^{2}+1} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.524 |
|
| \begin{align*}
y^{\prime \prime }+y&=\sec \left (\frac {t}{2}\right )+\csc \left (\frac {t}{2}\right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.862 |
|
| \begin{align*}
y^{\prime \prime }+9 y&=\tan \left (3 t \right )^{2} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.054 |
|
| \begin{align*}
y^{\prime \prime }+9 y&=\sec \left (3 t \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.628 |
|
| \begin{align*}
y^{\prime \prime }+9 y&=\tan \left (3 t \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.714 |
|
| \begin{align*}
y^{\prime \prime }+4 y&=\tan \left (2 t \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.635 |
|
| \begin{align*}
y^{\prime \prime }+16 y&=\tan \left (2 t \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.618 |
|
| \begin{align*}
y^{\prime \prime }+4 y&=\tan \left (t \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.552 |
|
| \begin{align*}
y^{\prime \prime }+9 y&=\sec \left (3 t \right ) \tan \left (3 t \right ) \\
\end{align*} | [[_2nd_order, _linear, _nonhomogeneous]] | ✓ | ✓ | ✓ | ✓ | 1.027 |
|
| \begin{align*}
y^{\prime \prime }+4 y&=\sec \left (2 t \right ) \tan \left (2 t \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.939 |
|
| \begin{align*}
y^{\prime \prime }+9 y&=\frac {\csc \left (3 t \right )}{2} \\
y \left (\frac {\pi }{4}\right ) &= \sqrt {2} \\
y^{\prime }\left (\frac {\pi }{4}\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.584 |
|
| \begin{align*}
y^{\prime \prime }+4 y&=\sec \left (2 t \right )^{2} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.299 |
|
| \begin{align*}
y^{\prime \prime }-16 y&=16 t \,{\mathrm e}^{-4 t} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.582 |
|
| \begin{align*}
y^{\prime \prime }+y&=\tan \left (t \right )^{2} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.915 |
|
| \begin{align*}
y^{\prime \prime }+4 y&=\sec \left (2 t \right )+\tan \left (2 t \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.240 |
|
| \begin{align*}
y^{\prime \prime }+9 y&=\csc \left (3 t \right ) \\
y \left (\frac {\pi }{12}\right ) &= 0 \\
y^{\prime }\left (\frac {\pi }{12}\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.385 |
|
| \begin{align*}
y^{\prime \prime }+4 y^{\prime }+3 y&=65 \cos \left (2 t \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.417 |
|
| \begin{align*}
t^{2} y^{\prime \prime }+3 t y^{\prime }+y&=\ln \left (t \right ) \\
\end{align*} |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
2.287 |
|
| \begin{align*}
t^{2} y^{\prime \prime }+t y^{\prime }+4 y&=t \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.978 |
|
| \begin{align*}
t^{2} y^{\prime \prime }-4 t y^{\prime }-6 y&=2 \ln \left (t \right ) \\
\end{align*} |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.614 |
|
| \begin{align*}
4 y^{\prime \prime }+4 y^{\prime }+y&={\mathrm e}^{-\frac {t}{2}} \\
y \left (0\right ) &= a \\
y^{\prime }\left (0\right ) &= b \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.606 |
|
| \begin{align*}
y^{\prime \prime }+4 y&=f \left (t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.856 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.125 |
|
| \begin{align*}
t^{2} y^{\prime \prime }-4 t y^{\prime }+\left (t^{2}+6\right ) y&=t^{3}+2 t \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
✗ |
1.135 |
|
| \begin{align*}
t y^{\prime \prime }+2 y^{\prime }+t y&=0 \\
\end{align*} |
[_Lienard] |
✓ |
✓ |
✓ |
✓ |
0.113 |
|
| \begin{align*}
t y^{\prime \prime }+2 y^{\prime }+t y&=-t \\
y \left (\pi \right ) &= -1 \\
y^{\prime }\left (\pi \right ) &= -\frac {1}{\pi } \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.010 |
|
| \begin{align*}
4 t^{2} y^{\prime \prime }+4 t y^{\prime }+\left (16 t^{2}-1\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.137 |
|
| \begin{align*}
4 t^{2} y^{\prime \prime }+4 t y^{\prime }+\left (16 t^{2}-1\right ) y&=16 t^{{3}/{2}} \\
y \left (\pi \right ) &= 0 \\
y^{\prime }\left (2 \pi \right ) &= 0 \\
\end{align*} | [[_2nd_order, _linear, _nonhomogeneous]] | ✓ | ✓ | ✓ | ✗ | 1.087 |
|
| \begin{align*}
t^{2} \left (\ln \left (t \right )-1\right ) y^{\prime \prime }-t y^{\prime }+y&=-\frac {3 \left (1+\ln \left (t \right )\right )}{4 \sqrt {t}} \\
y \left (1\right ) &= 0 \\
y^{\prime }\left (1\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.748 |
|
| \begin{align*}
\left (\sin \left (t \right )-t \cos \left (t \right )\right ) y^{\prime \prime }-t \sin \left (t \right ) y^{\prime }+\sin \left (t \right ) y&=t \\
y \left (\frac {\pi }{4}\right ) &= 0 \\
y^{\prime }\left (\frac {\pi }{4}\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
2.017 |
|
| \begin{align*}
y^{\prime \prime \prime }&=0 \\
\end{align*} |
[[_3rd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.037 |
|
| \begin{align*}
y^{\prime \prime \prime }-10 y^{\prime \prime }+25 y^{\prime }&=0 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.060 |
|
| \begin{align*}
8 y^{\prime \prime \prime }+y^{\prime \prime }&=0 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.055 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }+16 y^{\prime \prime }&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.066 |
|
| \begin{align*}
y^{\prime \prime \prime }-2 y^{\prime \prime }-y^{\prime }+2 y&=0 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.065 |
|
| \begin{align*}
3 y^{\prime \prime \prime }-4 y^{\prime \prime }-5 y^{\prime }+2 y&=0 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.062 |
|
| \begin{align*}
6 y^{\prime \prime \prime }-5 y^{\prime \prime }-2 y^{\prime }+y&=0 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.075 |
|
| \begin{align*}
y^{\prime \prime \prime }-5 y^{\prime }+2 y&=0 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.063 |
|
| \begin{align*}
5 y^{\prime \prime \prime }-15 y^{\prime }+11 y&=0 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.095 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }+y^{\prime \prime \prime }&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.046 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-9 y^{\prime \prime }&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.058 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-16 y&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.056 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-6 y^{\prime \prime \prime }-y^{\prime \prime }+54 y^{\prime }-72 y&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.075 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }+7 y^{\prime \prime \prime }+6 y^{\prime \prime }-32 y^{\prime }-32 y&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.076 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }-2 y^{\prime \prime }+8 y&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.076 |
|
| \begin{align*}
y^{\left (5\right )}+4 y^{\prime \prime \prime \prime }&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.063 |
|
| \begin{align*}
y^{\left (5\right )}+4 y^{\prime \prime \prime }&=0 \\
\end{align*} | [[_high_order, _missing_x]] | ✓ | ✓ | ✓ | ✓ | 0.070 |
|
| \begin{align*}
y^{\left (5\right )}+3 y^{\prime \prime \prime \prime }+3 y^{\prime \prime \prime }+y^{\prime \prime }&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.072 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }+2 y^{\prime \prime }+y&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.075 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }+8 y^{\prime \prime }+16 y&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.075 |
|
| \begin{align*}
y^{\left (6\right )}+3 y^{\prime \prime \prime \prime }+3 y^{\prime \prime }+y&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.089 |
|
| \begin{align*}
y^{\left (6\right )}+12 y^{\prime \prime \prime \prime }+48 y^{\prime \prime }+64 y&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.095 |
|
| \begin{align*}
y^{\prime \prime \prime }-2 y^{\prime \prime }&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 2 \\
y^{\prime \prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.075 |
|
| \begin{align*}
y^{\prime \prime \prime }-y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
y^{\prime \prime }\left (0\right ) &= 3 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.130 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }+16 y^{\prime \prime \prime }&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
y^{\prime \prime }\left (0\right ) &= 0 \\
y^{\prime \prime \prime }\left (0\right ) &= 1 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.108 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-8 y^{\prime \prime }+16 y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
y^{\prime \prime }\left (0\right ) &= 8 \\
y^{\prime \prime \prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.104 |
|
| \begin{align*}
24 y^{\prime \prime \prime }-26 y^{\prime \prime }+9 y^{\prime }-y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
y^{\prime \prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.112 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-5 y^{\prime \prime }+4 y&=0 \\
y \left (0\right ) &= -1 \\
y^{\prime }\left (0\right ) &= 3 \\
y^{\prime \prime }\left (0\right ) &= -7 \\
y^{\prime \prime \prime }\left (0\right ) &= 15 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.106 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-16 y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 2 \\
y^{\prime \prime }\left (0\right ) &= 4 \\
y^{\prime \prime \prime }\left (0\right ) &= -24 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.101 |
|
| \begin{align*}
8 y^{\left (5\right )}+4 y^{\prime \prime \prime \prime }+66 y^{\prime \prime \prime }-41 y^{\prime \prime }-37 y^{\prime }&=0 \\
y \left (0\right ) &= 4 \\
y^{\prime }\left (0\right ) &= -14 \\
y^{\prime \prime }\left (0\right ) &= -14 \\
y^{\prime \prime \prime }\left (0\right ) &= 139 \\
y^{\prime \prime \prime \prime }\left (0\right ) &= -{\frac {29}{4}} \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.148 |
|
| \begin{align*}
2 y^{\left (5\right )}+7 y^{\prime \prime \prime \prime }+17 y^{\prime \prime \prime }+17 y^{\prime \prime }+5 y^{\prime }&=0 \\
y \left (0\right ) &= -3 \\
y^{\prime }\left (0\right ) &= {\frac {15}{2}} \\
y^{\prime \prime }\left (0\right ) &= {\frac {17}{4}} \\
y^{\prime \prime \prime }\left (0\right ) &= -{\frac {385}{8}} \\
y^{\prime \prime \prime \prime }\left (0\right ) &= {\frac {1217}{16}} \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.124 |
|
| \begin{align*}
y^{\left (5\right )}+8 y^{\prime \prime \prime \prime }&=0 \\
y \left (0\right ) &= 8 \\
y^{\prime }\left (0\right ) &= 4 \\
y^{\prime \prime }\left (0\right ) &= 0 \\
y^{\prime \prime \prime }\left (0\right ) &= 48 \\
y^{\prime \prime \prime \prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.104 |
|
| \begin{align*}
y^{\left (6\right )}-3 y^{\prime \prime \prime \prime }+3 y^{\prime \prime }-y&=0 \\
y \left (0\right ) &= 16 \\
y^{\prime }\left (0\right ) &= 0 \\
y^{\prime \prime }\left (0\right ) &= 0 \\
y^{\prime \prime \prime }\left (0\right ) &= 0 \\
y^{\prime \prime \prime \prime }\left (0\right ) &= 0 \\
y^{\left (5\right )}\left (0\right ) &= 0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.150 |
|
| \begin{align*}
y^{\prime \prime \prime }+9 y^{\prime \prime }+16 y^{\prime }-26 y&=0 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.069 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }+12 y^{\prime \prime \prime }+60 y^{\prime \prime }+124 y^{\prime }+75 y&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.082 |
|
| \begin{align*}
y^{\prime \prime \prime }+3 y^{\prime \prime }+2 y^{\prime }+6 y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
y^{\prime \prime }\left (0\right ) &= -1 \\
\end{align*} | [[_3rd_order, _missing_x]] | ✓ | ✓ | ✓ | ✓ | 0.137 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-8 y^{\prime \prime \prime }+30 y^{\prime \prime }-56 y^{\prime }+49 y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 2 \\
y^{\prime \prime }\left (0\right ) &= -1 \\
y^{\prime \prime \prime }\left (0\right ) &= -1 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.159 |
|
| \begin{align*}
\frac {31 y^{\prime \prime \prime }}{100}+\frac {56 y^{\prime \prime }}{5}-\frac {49 y^{\prime }}{5}+\frac {53 y}{10}&=0 \\
y \left (0\right ) &= -1 \\
y^{\prime }\left (0\right ) &= -1 \\
y^{\prime \prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✗ |
0.730 |
|
| \begin{align*}
2 y y^{\prime \prime }+y^{2}&={y^{\prime }}^{2} \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✗ |
2.725 |
|
| \begin{align*}
y^{\prime \prime \prime }+y^{\prime \prime }&={\mathrm e}^{t} \\
\end{align*} |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.106 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-16 y&=1 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.119 |
|
| \begin{align*}
y^{\left (5\right )}-y^{\prime \prime \prime \prime }&=1 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.144 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }+9 y^{\prime \prime }&=1 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.141 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }+9 y^{\prime \prime }&=9 \,{\mathrm e}^{3 t} \\
\end{align*} |
[[_high_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.151 |
|
| \begin{align*}
y^{\prime \prime \prime }+10 y^{\prime \prime }+34 y^{\prime }+40 y&=t \,{\mathrm e}^{-4 t}+2 \,{\mathrm e}^{-3 t} \cos \left (t \right ) \\
\end{align*} |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.767 |
|
| \begin{align*}
y^{\prime \prime \prime }+6 y^{\prime \prime }+11 y^{\prime }+6 y&=2 \,{\mathrm e}^{-3 t}-t \,{\mathrm e}^{-t} \\
\end{align*} |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.273 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-6 y^{\prime \prime \prime }+13 y^{\prime \prime }-24 y^{\prime }+36 y&=108 t \\
\end{align*} |
[[_high_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.161 |
|
| \begin{align*}
y^{\prime \prime \prime }+6 y^{\prime \prime }-14 y^{\prime }-104 y&=-111 \,{\mathrm e}^{t} \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.146 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-10 y^{\prime \prime \prime }+38 y^{\prime \prime }-64 y^{\prime }+40 y&=153 \,{\mathrm e}^{-t} \\
\end{align*} |
[[_high_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.167 |
|
| \begin{align*}
y^{\prime \prime \prime }+4 y^{\prime }&=\tan \left (2 t \right ) \\
\end{align*} |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.583 |
|
| \begin{align*}
y^{\prime \prime \prime }+4 y^{\prime }&=\sec \left (2 t \right ) \tan \left (2 t \right ) \\
\end{align*} |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.474 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }+4 y^{\prime \prime }&=\sec \left (2 t \right )^{2} \\
\end{align*} |
[[_high_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.543 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }+4 y^{\prime \prime }&=\tan \left (2 t \right )^{2} \\
\end{align*} |
[[_high_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.569 |
|
| \begin{align*}
y^{\prime \prime \prime }+9 y^{\prime }&=\sec \left (3 t \right ) \\
\end{align*} |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.036 |
|
| \begin{align*}
y^{\prime \prime \prime }+y^{\prime }&=-\sec \left (t \right ) \tan \left (t \right ) \\
\end{align*} | [[_3rd_order, _missing_y]] | ✓ | ✓ | ✓ | ✓ | 0.386 |
|
| \begin{align*}
y^{\prime \prime \prime }+4 y^{\prime }&=\sec \left (2 t \right ) \\
\end{align*} |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.417 |
|
| \begin{align*}
y^{\prime \prime \prime }-2 y^{\prime \prime }&=-\frac {1}{t^{2}}-\frac {2}{t} \\
\end{align*} |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.272 |
|
| \begin{align*}
y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y&=\frac {{\mathrm e}^{t}}{t} \\
\end{align*} |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.283 |
|
| \begin{align*}
y^{\prime \prime \prime }-4 y^{\prime \prime }-11 y^{\prime }+30 y&={\mathrm e}^{4 t} \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.140 |
|
| \begin{align*}
y^{\prime \prime \prime }+3 y^{\prime \prime }-10 y^{\prime }-24 y&={\mathrm e}^{-3 t} \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.135 |
|
| \begin{align*}
y^{\prime \prime \prime }-13 y^{\prime }+12 y&=\cos \left (t \right ) \\
\end{align*} |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.148 |
|