| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
y^{\prime \prime }-2 y^{\prime }+4 y&=0 \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.412 |
|
| \begin{align*}
y^{\prime \prime }+4 y^{\prime }+29 y&={\mathrm e}^{-2 t} \sin \left (5 t \right ) \\
y \left (0\right ) &= 5 \\
y^{\prime }\left (0\right ) &= -2 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.553 |
|
| \begin{align*}
y^{\prime \prime }+w^{2} y&=\cos \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]] |
✓ |
✓ |
✓ |
✓ |
0.582 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime }+2 y&=\cos \left (t \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.499 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime }+2 y&={\mathrm e}^{-t} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.451 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }+y&=18 \,{\mathrm e}^{-t} \\
y \left (0\right ) &= 7 \\
y^{\prime }\left (0\right ) &= -2 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.436 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+6 y^{\prime \prime }-4 y^{\prime }+y&=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*}
Using Laplace transform method. |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.457 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
y^{\prime \prime }\left (0\right ) &= 1 \\
y^{\prime \prime \prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.402 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-9 y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
y^{\prime \prime }\left (0\right ) &= -3 \\
y^{\prime \prime \prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.414 |
|
| \begin{align*}
y_{1}^{\prime }&=-5 y_{1}+y_{2} \\
y_{2}^{\prime }&=-9 y_{1}+5 y_{2} \\
\end{align*}
With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 1 \\
y_{2} \left (0\right ) &= 0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.614 |
|
| \begin{align*}
y_{1}^{\prime }&=5 y_{1}-2 y_{2} \\
y_{2}^{\prime }&=6 y_{1}-2 y_{2} \\
\end{align*}
With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 1 \\
y_{2} \left (0\right ) &= 0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.569 |
|
| \begin{align*}
y_{1}^{\prime }&=4 y_{1}-4 y_{2} \\
y_{2}^{\prime }&=5 y_{1}-4 y_{2} \\
\end{align*}
With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 1 \\
y_{2} \left (0\right ) &= 0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.580 |
|
| \begin{align*}
y_{1}^{\prime }&=6 y_{2} \\
y_{2}^{\prime }&=-6 y_{1} \\
\end{align*}
With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 5 \\
y_{2} \left (0\right ) &= 4 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.576 |
|
| \begin{align*}
y_{1}^{\prime }&=-4 y_{1}-y_{2} \\
y_{2}^{\prime }&=y_{1}-2 y_{2} \\
\end{align*}
With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 1 \\
y_{2} \left (0\right ) &= 0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.556 |
|
| \begin{align*}
y_{1}^{\prime }&=2 y_{1}-64 y_{2} \\
y_{2}^{\prime }&=y_{1}-14 y_{2} \\
\end{align*}
With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 0 \\
y_{2} \left (0\right ) &= 1 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.553 |
|
| \begin{align*}
y_{1}^{\prime }&=-4 y_{1}-y_{2}+2 \,{\mathrm e}^{t} \\
y_{2}^{\prime }&=y_{1}-2 y_{2}+\sin \left (2 t \right ) \\
\end{align*}
With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 1 \\
y_{2} \left (0\right ) &= 2 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.681 |
|
| \begin{align*}
y_{1}^{\prime }&=5 y_{1}-y_{2}+{\mathrm e}^{-t} \\
y_{2}^{\prime }&=y_{1}+3 y_{2}+2 \,{\mathrm e}^{t} \\
\end{align*}
With initial conditions \begin{align*}
y_{1} \left (0\right ) &= -3 \\
y_{2} \left (0\right ) &= 2 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.601 |
|
| \begin{align*}
y_{1}^{\prime }&=-y_{1}-5 y_{2}+3 \\
y_{2}^{\prime }&=y_{1}+3 y_{2}+5 \cos \left (t \right ) \\
\end{align*}
With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 1 \\
y_{2} \left (0\right ) &= -1 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.634 |
|
| \begin{align*}
y_{1}^{\prime }&=-2 y_{1}+y_{2} \\
y_{2}^{\prime }&=y_{1}-2 y_{2}+\sin \left (t \right ) \\
\end{align*}
With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 0 \\
y_{2} \left (0\right ) &= 0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.596 |
|
| \begin{align*}
y_{1}^{\prime }&=y_{2}-y_{3} \\
y_{2}^{\prime }&=y_{1}+y_{3}-{\mathrm e}^{-t} \\
y_{3}^{\prime }&=y_{1}+y_{2}+{\mathrm e}^{t} \\
\end{align*}
With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 1 \\
y_{2} \left (0\right ) &= 2 \\
y_{3} \left (0\right ) &= 3 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.810 |
|
| \begin{align*}
y^{\prime \prime }+y&=\left \{\begin {array}{cc} 1 & 0\le t <\frac {\pi }{2} \\ 0 & \frac {\pi }{2}\le t \end {array}\right . \\
y \left (0\right ) &= 5 \\
y^{\prime }\left (0\right ) &= 3 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
2.425 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }+2 y&=\left \{\begin {array}{cc} 0 & 0\le t <\pi \\ 1 & \pi \le t \le 2 \pi \\ 0 & t \le 2 \pi \end {array}\right . \\
y \left (0\right ) &= 5 \\
y^{\prime }\left (0\right ) &= 4 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
4.979 |
|
| \begin{align*}
y^{\prime \prime }+4 y&=\sin \left (t \right )-\operatorname {Heaviside}\left (t -2 \pi \right ) \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]] |
✓ |
✓ |
✓ |
✓ |
1.271 |
|
| \begin{align*}
y^{\prime \prime }+4 y&=\sin \left (t \right )-\sin \left (t \right ) \operatorname {Heaviside}\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]] |
✓ |
✓ |
✓ |
✓ |
1.411 |
|
| \begin{align*}
y^{\prime \prime }+3 y^{\prime }+2 y&=\left \{\begin {array}{cc} 1 & 0\le t <10 \\ 0 & 10\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]] |
✓ |
✓ |
✓ |
✗ |
4.030 |
|
| \begin{align*}
y^{\prime \prime }+3 y^{\prime }+2 y&=\operatorname {Heaviside}\left (-2+t \right ) \\
y \left (0\right ) &= 6 \\
y^{\prime }\left (0\right ) &= 6 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
2.167 |
|
| \begin{align*}
y^{\prime \prime }+y&=\operatorname {Heaviside}\left (t -3 \pi \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.815 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }+\frac {5 y}{4}&=t -\operatorname {Heaviside}\left (t -\frac {\pi }{2}\right ) \left (t -\frac {\pi }{2}\right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
4.032 |
|
| \begin{align*}
y^{\prime \prime }+y&=\left \{\begin {array}{cc} \frac {t}{2} & 0\le t <6 \\ 3 & 6\le t \end {array}\right . \\
y \left (0\right ) &= 6 \\
y^{\prime }\left (0\right ) &= 8 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
2.090 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }+\frac {5 y}{4}&=\left \{\begin {array}{cc} \sin \left (t \right ) & 0\le t <\pi \\ 0 & \pi \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]] |
✓ |
✓ |
✓ |
✗ |
4.355 |
|
| \begin{align*}
y^{\prime \prime }+4 y&=\operatorname {Heaviside}\left (t -\pi \right )-\operatorname {Heaviside}\left (t -3 \pi \right ) \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= 7 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
3.201 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-y&=\operatorname {Heaviside}\left (t -1\right )-\operatorname {Heaviside}\left (-2+t \right ) \\
y \left (0\right ) &= 12 \\
y^{\prime }\left (0\right ) &= 7 \\
y^{\prime \prime }\left (0\right ) &= 2 \\
y^{\prime \prime \prime }\left (0\right ) &= -9 \\
\end{align*}
Using Laplace transform method. |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
6.461 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }+5 y^{\prime \prime }+4 y&=1-\operatorname {Heaviside}\left (t -\pi \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
y^{\prime \prime }\left (0\right ) &= 0 \\
y^{\prime \prime \prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
2.334 |
|
| \begin{align*}
u^{\prime \prime }+\frac {u^{\prime }}{4}+u&=\frac {\left (\left \{\begin {array}{cc} 1 & \frac {3}{2}\le t <\frac {5}{2} \\ 0 & \operatorname {otherwise} \end {array}\right .\right )}{2} \\
u \left (0\right ) &= 0 \\
u^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
21.529 |
|
| \begin{align*}
u^{\prime \prime }+\frac {u^{\prime }}{4}+u&=\left \{\begin {array}{cc} 1 & \frac {3}{2}\le t <\frac {5}{2} \\ 0 & \operatorname {otherwise} \end {array}\right . \\
u \left (0\right ) &= 0 \\
u^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
10.011 |
|
| \begin{align*}
u^{\prime \prime }+\frac {u^{\prime }}{4}+u&=2 \left (\left \{\begin {array}{cc} 1 & \frac {3}{2}\le t <\frac {5}{2} \\ 0 & \operatorname {otherwise} \end {array}\right .\right ) \\
u \left (0\right ) &= 0 \\
u^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
10.455 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }+2 y&=\delta \left (t -\pi \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
2.090 |
|
| \begin{align*}
y^{\prime \prime }+4 y&=\delta \left (t -\pi \right )-\delta \left (t -2 \pi \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.315 |
|
| \begin{align*}
y^{\prime \prime }+3 y^{\prime }+2 y&=\delta \left (t -\pi \right )+\operatorname {Heaviside}\left (t -10\right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= {\frac {1}{2}} \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
5.450 |
|
| \begin{align*}
y^{\prime \prime }-y&=-20 \delta \left (t -3\right ) \\
y \left (0\right ) &= 4 \\
y^{\prime }\left (0\right ) &= 3 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
2.099 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }+3 y&=\sin \left (t \right )+\delta \left (t -3 \pi \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
5.239 |
|
| \begin{align*}
y^{\prime \prime }+4 y&=\delta \left (t -4 \pi \right ) \\
y \left (0\right ) &= {\frac {1}{2}} \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.409 |
|
| \begin{align*}
y^{\prime \prime }+y&=\delta \left (t -2 \pi \right ) \cos \left (t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.191 |
|
| \begin{align*}
y^{\prime \prime }+4 y&=2 \delta \left (t -\frac {\pi }{4}\right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.198 |
|
| \begin{align*}
y^{\prime \prime }+y&=\operatorname {Heaviside}\left (t -\frac {\pi }{2}\right )+3 \delta \left (t -\frac {3 \pi }{2}\right )-\operatorname {Heaviside}\left (t -2 \pi \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
3.704 |
|
| \begin{align*}
2 y^{\prime \prime }+y^{\prime }+6 y&=\delta \left (t -\frac {\pi }{6}\right ) \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]] |
✓ |
✓ |
✓ |
✓ |
3.356 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }+2 y&=\cos \left (t \right )+\delta \left (t -\frac {\pi }{2}\right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
3.144 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-y&=\delta \left (t -1\right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
y^{\prime \prime }\left (0\right ) &= 0 \\
y^{\prime \prime \prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.549 |
|
| \begin{align*}
y^{\prime \prime }+\frac {y^{\prime }}{2}+y&=\delta \left (t -1\right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
2.631 |
|
| \begin{align*}
y^{\prime \prime }+\frac {y^{\prime }}{4}+y&=\delta \left (t -1\right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
2.573 |
|
| \begin{align*}
y^{\prime \prime }+y&=\delta \left (t -1\right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.290 |
|
| \begin{align*}
y^{\prime \prime }+\frac {y^{\prime }}{5}+y&=k \delta \left (t -1\right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
2.545 |
|
| \begin{align*}
y^{\prime \prime }+\frac {y^{\prime }}{10}+y&=k \delta \left (t -1\right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
2.550 |
|
| \begin{align*}
y^{\prime \prime }+w^{2} y&=g \left (t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
2.064 |
|
| \begin{align*}
y^{\prime \prime }+6 y^{\prime }+25 y&=\sin \left (\alpha t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.671 |
|
| \begin{align*}
4 y^{\prime \prime }+4 y^{\prime }+17 y&=g \left (t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
2.644 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }+\frac {5 y}{4}&=1-\operatorname {Heaviside}\left (t -\pi \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= -1 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
4.546 |
|
| \begin{align*}
y^{\prime \prime }+4 y^{\prime }+4 y&=g \left (t \right ) \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= -3 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.334 |
|
| \begin{align*}
y^{\prime \prime }+3 y^{\prime }+2 y&=\cos \left (\alpha t \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.520 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-16 y&=g \left (t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
y^{\prime \prime }\left (0\right ) &= 0 \\
y^{\prime \prime \prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
2.913 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }+y^{\prime \prime }+16 y&=g \left (t \right ) \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 0 \\
y^{\prime \prime }\left (0\right ) &= 0 \\
y^{\prime \prime \prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.717 |
|
| \begin{align*}
\frac {7 y^{\prime \prime }}{5}+y&=\operatorname {Heaviside}\left (t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.451 |
|
| \begin{align*}
\frac {8 y^{\prime \prime }}{5}+y&=\operatorname {Heaviside}\left (t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.460 |
|
| \begin{align*}
x_{1}^{\prime }&=x_{1}+x_{2}+x_{3} \\
x_{2}^{\prime }&=2 x_{1}+x_{2}-x_{3} \\
x_{3}^{\prime }&=-x_{2}+x_{3} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.118 |
|
| \begin{align*}
x_{1}^{\prime }&=x_{1}-x_{2}+4 x_{3} \\
x_{2}^{\prime }&=3 x_{1}+2 x_{2}-x_{3} \\
x_{3}^{\prime }&=2 x_{1}+x_{2}-x_{3} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.257 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }+6 y^{\prime \prime \prime }+3 y&=t \\
\end{align*} |
[[_high_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.253 |
|
| \begin{align*}
t y^{\prime \prime \prime }+\sin \left (t \right ) y^{\prime \prime }+8 y&=\cos \left (t \right ) \\
\end{align*} |
[[_3rd_order, _linear, _nonhomogeneous]] |
✗ |
✗ |
✗ |
✗ |
0.160 |
|
| \begin{align*}
t \left (t -1\right ) y^{\prime \prime \prime \prime }+{\mathrm e}^{t} y^{\prime \prime }+4 t^{2} y&=0 \\
\end{align*} |
[[_high_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
✗ |
0.191 |
|
| \begin{align*}
y^{\prime \prime \prime }+t y^{\prime \prime }+t^{2} y^{\prime }+t^{2} y&=\ln \left (t \right ) \\
\end{align*} |
[[_3rd_order, _linear, _nonhomogeneous]] |
✗ |
✗ |
✗ |
✗ |
0.185 |
|
| \begin{align*}
\left (x -4\right ) y^{\prime \prime \prime \prime }+\left (x +1\right ) y^{\prime \prime }+\tan \left (x \right ) y&=0 \\
\end{align*} |
[[_high_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
✗ |
0.202 |
|
| \begin{align*}
\left (x^{2}-2\right ) y^{\left (6\right )}+x^{2} y^{\prime \prime }+3 y&=0 \\
\end{align*} |
[[_high_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
✗ |
0.274 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }+5 y^{\prime \prime \prime }+4 y&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.149 |
|
| \begin{align*}
t y^{\prime \prime \prime }+\sin \left (t \right ) y^{\prime \prime }+4 y&=\cos \left (t \right ) \\
\end{align*} |
[[_3rd_order, _linear, _nonhomogeneous]] |
✗ |
✗ |
✗ |
✗ |
0.160 |
|
| \begin{align*}
t \left (t -1\right ) y^{\prime \prime \prime \prime }+{\mathrm e}^{t} y^{\prime \prime }+7 t^{2} y&=0 \\
\end{align*} |
[[_high_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
✗ |
0.217 |
|
| \begin{align*}
y^{\prime \prime \prime }+t y^{\prime \prime }+5 t^{2} y^{\prime }+2 y t^{3}&=\ln \left (t \right ) \\
\end{align*} |
[[_3rd_order, _linear, _nonhomogeneous]] |
✗ |
✗ |
✗ |
✗ |
0.235 |
|
| \begin{align*}
\left (-1+x \right ) y^{\prime \prime \prime \prime }+\left (x +5\right ) y^{\prime \prime }+\tan \left (x \right ) y&=0 \\
\end{align*} |
[[_high_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
✗ |
0.214 |
|
| \begin{align*}
\left (x^{2}-25\right ) y^{\left (6\right )}+x^{2} y^{\prime \prime }+5 y&=0 \\
\end{align*} |
[[_high_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
✗ |
0.260 |
|
| \begin{align*}
x_{1}^{\prime }&=x_{2}+x_{3} \\
x_{2}^{\prime }&=x_{1}+x_{3} \\
x_{3}^{\prime }&=x_{1}+x_{2} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.905 |
|
| \begin{align*}
x_{1}^{\prime }&=3 x_{1}+2 x_{2}+4 x_{3} \\
x_{2}^{\prime }&=2 x_{1}+2 x_{3} \\
x_{3}^{\prime }&=4 x_{1}+2 x_{2}+3 x_{3} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.013 |
|
| \begin{align*}
y^{\prime \prime \prime }+y^{\prime }&=0 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.066 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }+y^{\prime \prime }&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.075 |
|
| \begin{align*}
y^{\prime \prime \prime }+4 y^{\prime \prime }-4 y^{\prime }-16 y&=0 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.092 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }+6 y^{\prime \prime \prime }+9 y^{\prime \prime }&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.096 |
|
| \begin{align*}
x y^{\prime \prime \prime }-y^{\prime \prime }&=0 \\
\end{align*} |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.454 |
|
| \begin{align*}
x^{3} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y&=0 \\
\end{align*} |
[[_3rd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.241 |
|
| \begin{align*}
x_{1}^{\prime }&=-4 x_{1}+x_{2} \\
x_{2}^{\prime }&=x_{1}-5 x_{2}+x_{3} \\
x_{3}^{\prime }&=x_{2}-4 x_{3} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.108 |
|
| \begin{align*}
x_{1}^{\prime }&=x_{1}+4 x_{2}+4 x_{3} \\
x_{2}^{\prime }&=3 x_{2}+2 x_{3} \\
x_{3}^{\prime }&=2 x_{2}+3 x_{3} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.868 |
|
| \begin{align*}
x_{1}^{\prime }&=2 x_{1}-4 x_{2}+2 x_{3} \\
x_{2}^{\prime }&=-4 x_{1}+2 x_{2}-2 x_{3} \\
x_{3}^{\prime }&=2 x_{1}-2 x_{2}-x_{3} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.081 |
|
| \begin{align*}
x_{1}^{\prime }&=-2 x_{1}+2 x_{2}-x_{3} \\
x_{2}^{\prime }&=-2 x_{1}+3 x_{2}-2 x_{3} \\
x_{3}^{\prime }&=-2 x_{1}+4 x_{2}-3 x_{3} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.006 |
|
| \begin{align*}
x_{1}^{\prime }&=x_{1}+x_{2}+6 x_{3} \\
x_{2}^{\prime }&=x_{1}+6 x_{2}+x_{3} \\
x_{3}^{\prime }&=6 x_{1}+x_{2}+x_{3} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.121 |
|
| \begin{align*}
x_{1}^{\prime }&=3 x_{1}+2 x_{2}+4 x_{3} \\
x_{2}^{\prime }&=2 x_{1}+2 x_{3} \\
x_{3}^{\prime }&=4 x_{1}+2 x_{2}+3 x_{3} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.957 |
|
| \begin{align*}
x_{1}^{\prime }&=x_{1}+x_{2}+x_{3} \\
x_{2}^{\prime }&=2 x_{1}+x_{2}-x_{3} \\
x_{3}^{\prime }&=-8 x_{1}-5 x_{2}-3 x_{3} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.344 |
|
| \begin{align*}
x_{1}^{\prime }&=x_{1}-x_{2}+4 x_{3} \\
x_{2}^{\prime }&=3 x_{1}+2 x_{2}-x_{3} \\
x_{3}^{\prime }&=2 x_{1}+x_{2}-x_{3} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.160 |
|
| \begin{align*}
x_{1}^{\prime }&=x_{1}+x_{2}+2 x_{3} \\
x_{2}^{\prime }&=2 x_{2}+2 x_{3} \\
x_{3}^{\prime }&=-x_{1}+x_{2}+3 x_{3} \\
\end{align*}
With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 11 \\
x_{2} \left (0\right ) &= 1 \\
x_{3} \left (0\right ) &= 5 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.123 |
|
| \begin{align*}
x_{1}^{\prime }&=-x_{3} \\
x_{2}^{\prime }&=2 x_{1} \\
x_{3}^{\prime }&=-x_{1}+2 x_{2}+4 x_{3} \\
\end{align*}
With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 7 \\
x_{2} \left (0\right ) &= 5 \\
x_{3} \left (0\right ) &= 5 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.241 |
|
| \begin{align*}
x_{1}^{\prime }&=x_{1}+3 x_{3} \\
x_{2}^{\prime }&=-2 x_{2} \\
x_{3}^{\prime }&=3 x_{1}-x_{3} \\
\end{align*}
With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 2 \\
x_{2} \left (0\right ) &= -1 \\
x_{3} \left (0\right ) &= -2 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.293 |
|
| \begin{align*}
x_{1}^{\prime }&=\frac {x_{1}}{2}-x_{2}-\frac {3 x_{3}}{2} \\
x_{2}^{\prime }&=\frac {3 x_{1}}{2}-2 x_{2}-\frac {3 x_{3}}{2} \\
x_{3}^{\prime }&=-2 x_{1}+2 x_{2}+x_{3} \\
\end{align*}
With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 2 \\
x_{2} \left (0\right ) &= 1 \\
x_{3} \left (0\right ) &= 1 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.128 |
|
| \begin{align*}
x_{1}^{\prime }&=x_{1}+5 x_{2}+3 x_{3}-5 x_{4} \\
x_{2}^{\prime }&=2 x_{1}+3 x_{2}+2 x_{3}-4 x_{4} \\
x_{3}^{\prime }&=-x_{2}-2 x_{3}+x_{4} \\
x_{4}^{\prime }&=2 x_{1}+4 x_{2}+2 x_{3}-5 x_{4} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.754 |
|
| \begin{align*}
x_{1}^{\prime }&=-5 x_{1}+x_{2}-4 x_{3}-x_{4} \\
x_{2}^{\prime }&=-3 x_{2} \\
x_{3}^{\prime }&=x_{1}-x_{2}+x_{4} \\
x_{4}^{\prime }&=2 x_{1}-x_{2}+2 x_{3}-2 x_{4} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.990 |
|
| \begin{align*}
x_{1}^{\prime }&=2 x_{1}+2 x_{2}-x_{4} \\
x_{2}^{\prime }&=2 x_{1}-x_{2}+2 x_{4} \\
x_{3}^{\prime }&=3 x_{3} \\
x_{4}^{\prime }&=-x_{1}+2 x_{2}+2 x_{4} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.316 |
|