| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-2 y^{\prime }+4 y&=0\\ y \left (0\right )&=2\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.357 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+4 y^{\prime }+29 y&={\mathrm e}^{-2 t} \sin \left (5 t \right )\\ y \left (0\right )&=5\\ y^{\prime }\left (0\right )&=-2\\ \end {array} \]
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.478 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+w^{2} y&=\cos \left (2 t \right )\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.546 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-2 y^{\prime }+2 y&=\cos \left (t \right )\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.481 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-2 y^{\prime }+2 y&={\mathrm e}^{-t}\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.401 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+2 y^{\prime }+y&=18 \,{\mathrm e}^{-t}\\ y \left (0\right )&=7\\ y^{\prime }\left (0\right )&=-2\\ \end {array} \]
Using Laplace transform method. |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.385 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+6 y^{\prime \prime }-4 y^{\prime }+y&=0\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=1\\ y^{\prime \prime }\left (0\right )&=0\\ y^{\prime \prime \prime }\left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.449 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime \prime }-y&=0\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=0\\ y^{\prime \prime }\left (0\right )&=1\\ y^{\prime \prime \prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.319 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime \prime }-9 y&=0\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=0\\ y^{\prime \prime }\left (0\right )&=-3\\ y^{\prime \prime \prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.367 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=-5 y_{1}+y_{2}\\ y_{2}^{\prime }&=-9 y_{1}+5 y_{2}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.444 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=5 y_{1}-2 y_{2}\\ y_{2}^{\prime }&=6 y_{1}-2 y_{2}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.424 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=4 y_{1}-4 y_{2}\\ y_{2}^{\prime }&=5 y_{1}-4 y_{2}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.454 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=6 y_{2}\\ y_{2}^{\prime }&=-6 y_{1}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.434 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=-4 y_{1}-y_{2}\\ y_{2}^{\prime }&=y_{1}-2 y_{2}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.411 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=2 y_{1}-64 y_{2}\\ y_{2}^{\prime }&=y_{1}-14 y_{2}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.424 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=-4 y_{1}-y_{2}+2 \,{\mathrm e}^{t}\\ y_{2}^{\prime }&=y_{1}-2 y_{2}+\sin \left (2 t \right )\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.497 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=5 y_{1}-y_{2}+{\mathrm e}^{-t}\\ y_{2}^{\prime }&=y_{1}+3 y_{2}+2 \,{\mathrm e}^{t}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.510 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=-y_{1}-5 y_{2}+3\\ y_{2}^{\prime }&=y_{1}+3 y_{2}+5 \cos \left (t \right )\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.516 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=-2 y_{1}+y_{2}\\ y_{2}^{\prime }&=y_{1}-2 y_{2}+\sin \left (t \right )\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.491 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=y_{2}-y_{3}\\ y_{2}^{\prime }&=y_{1}+y_{3}-{\mathrm e}^{-t}\\ y_{3}^{\prime }&=y_{1}+y_{2}+{\mathrm e}^{t}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.666 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y&=\left \{\begin {array}{cc} 1 & 0\le t <\frac {\pi }{2} \\ 0 & \frac {\pi }{2}\le t \end {array}\right .\\ y \left (0\right )&=5\\ y^{\prime }\left (0\right )&=3\\ \end {array} \]
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.112 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+2 y^{\prime }+2 y&=\left \{\begin {array}{cc} 0 & 0\le t <\pi \\ 1 & \pi \le t \le 2 \pi \\ 0 & t \le 2 \pi \end {array}\right .\\ y \left (0\right )&=5\\ y^{\prime }\left (0\right )&=4\\ \end {array} \]
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.983 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+4 y&=\sin \left (t \right )-\operatorname {Heaviside}\left (t -2 \pi \right ) \sin \left (t \right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.447 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+4 y&=\sin \left (t \right )-\sin \left (t \right ) \operatorname {Heaviside}\left (t -\pi \right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
6.304 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+3 y^{\prime }+2 y&=\left \{\begin {array}{cc} 1 & 0\le t <10 \\ 0 & 10\le t \end {array}\right .\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.956 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+3 y^{\prime }+2 y&=\operatorname {Heaviside}\left (-2+t \right )\\ y \left (0\right )&=6\\ y^{\prime }\left (0\right )&=6\\ \end {array} \]
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.495 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y&=\operatorname {Heaviside}\left (t -3 \pi \right )\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.550 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y^{\prime }+\frac {5 y}{4}&=t -\operatorname {Heaviside}\left (t -\frac {\pi }{2}\right ) \left (t -\frac {\pi }{2}\right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.764 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y&=\left \{\begin {array}{cc} \frac {t}{2} & 0\le t <6 \\ 3 & 6\le t \end {array}\right .\\ y \left (0\right )&=6\\ y^{\prime }\left (0\right )&=8\\ \end {array} \]
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.352 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y^{\prime }+\frac {5 y}{4}&=\left \{\begin {array}{cc} \sin \left (t \right ) & 0\le t <\pi \\ 0 & \pi \le t \end {array}\right .\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✗ |
✗ |
1.907 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+4 y&=\operatorname {Heaviside}\left (t -\pi \right )-\operatorname {Heaviside}\left (t -3 \pi \right )\\ y \left (0\right )&=3\\ y^{\prime }\left (0\right )&=7\\ \end {array} \]
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.711 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime \prime }-y&=\operatorname {Heaviside}\left (t -1\right )-\operatorname {Heaviside}\left (-2+t \right )\\ y \left (0\right )&=12\\ y^{\prime }\left (0\right )&=7\\ y^{\prime \prime }\left (0\right )&=2\\ y^{\prime \prime \prime }\left (0\right )&=-9\\ \end {array} \]
Using Laplace transform method. |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.816 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime \prime }+5 y^{\prime \prime }+4 y&=1-\operatorname {Heaviside}\left (t -\pi \right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ y^{\prime \prime }\left (0\right )&=0\\ y^{\prime \prime \prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.713 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} u^{\prime \prime }+\frac {u^{\prime }}{4}+u&=\frac {\left (\left \{\begin {array}{cc} 1 & \frac {3}{2}\le t <\frac {5}{2} \\ 0 & \operatorname {otherwise} \end {array}\right .\right )}{2}\\ u \left (0\right )&=0\\ u^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
10.348 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} u^{\prime \prime }+\frac {u^{\prime }}{4}+u&=\left \{\begin {array}{cc} 1 & \frac {3}{2}\le t <\frac {5}{2} \\ 0 & \operatorname {otherwise} \end {array}\right .\\ u \left (0\right )&=0\\ u^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.541 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} u^{\prime \prime }+\frac {u^{\prime }}{4}+u&=2 \left (\left \{\begin {array}{cc} 1 & \frac {3}{2}\le t <\frac {5}{2} \\ 0 & \operatorname {otherwise} \end {array}\right .\right )\\ u \left (0\right )&=0\\ u^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.593 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+2 y^{\prime }+2 y&=\delta \left (t -\pi \right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.474 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+4 y&=\delta \left (t -\pi \right )-\delta \left (t -2 \pi \right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.440 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+3 y^{\prime }+2 y&=\delta \left (t -\pi \right )+\operatorname {Heaviside}\left (t -10\right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&={\frac {1}{2}}\\ \end {array} \]
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.618 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-y&=-20 \delta \left (t -3\right )\\ y \left (0\right )&=4\\ y^{\prime }\left (0\right )&=3\\ \end {array} \]
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.624 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+2 y^{\prime }+3 y&=\sin \left (t \right )+\delta \left (t -3 \pi \right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
2.283 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+4 y&=\delta \left (t -4 \pi \right )\\ y \left (0\right )&={\frac {1}{2}}\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.482 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y&=\delta \left (t -2 \pi \right ) \cos \left (t \right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.421 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+4 y&=2 \delta \left (t -\frac {\pi }{4}\right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.514 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y&=\operatorname {Heaviside}\left (t -\frac {\pi }{2}\right )+3 \delta \left (t -\frac {3 \pi }{2}\right )-\operatorname {Heaviside}\left (t -2 \pi \right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.772 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 y^{\prime \prime }+y^{\prime }+6 y&=\delta \left (t -\frac {\pi }{6}\right ) \sin \left (t \right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
6.838 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+2 y^{\prime }+2 y&=\cos \left (t \right )+\delta \left (t -\frac {\pi }{2}\right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.060 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime \prime }-y&=\delta \left (t -1\right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ y^{\prime \prime }\left (0\right )&=0\\ y^{\prime \prime \prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.717 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+\frac {y^{\prime }}{2}+y&=\delta \left (t -1\right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.073 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+\frac {y^{\prime }}{4}+y&=\delta \left (t -1\right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.024 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y&=\delta \left (t -1\right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.391 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+\frac {y^{\prime }}{5}+y&=k \delta \left (t -1\right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.018 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+\frac {y^{\prime }}{10}+y&=k \delta \left (t -1\right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.981 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+w^{2} y&=g \left (t \right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
2.109 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+6 y^{\prime }+25 y&=\sin \left (\alpha t \right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.635 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 y^{\prime \prime }+4 y^{\prime }+17 y&=g \left (t \right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
2.800 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y^{\prime }+\frac {5 y}{4}&=1-\operatorname {Heaviside}\left (t -\pi \right )\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=-1\\ \end {array} \]
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.567 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+4 y^{\prime }+4 y&=g \left (t \right )\\ y \left (0\right )&=2\\ y^{\prime }\left (0\right )&=-3\\ \end {array} \]
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.383 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+3 y^{\prime }+2 y&=\cos \left (\alpha t \right )\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.454 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime \prime }-16 y&=g \left (t \right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ y^{\prime \prime }\left (0\right )&=0\\ y^{\prime \prime \prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
9.033 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime \prime }+y^{\prime \prime }+16 y&=g \left (t \right )\\ y \left (0\right )&=2\\ y^{\prime }\left (0\right )&=0\\ y^{\prime \prime }\left (0\right )&=0\\ y^{\prime \prime \prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.487 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {7 y^{\prime \prime }}{5}+y&=\operatorname {Heaviside}\left (t \right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.451 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {8 y^{\prime \prime }}{5}+y&=\operatorname {Heaviside}\left (t \right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.404 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{1}+x_{2}+x_{3}\\ x_{2}^{\prime }&=2 x_{1}+x_{2}-x_{3}\\ x_{3}^{\prime }&=-x_{2}+x_{3}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.090 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{1}-x_{2}+4 x_{3}\\ x_{2}^{\prime }&=3 x_{1}+2 x_{2}-x_{3}\\ x_{3}^{\prime }&=2 x_{1}+x_{2}-x_{3}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.148 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime \prime }+6 y^{\prime \prime \prime }+3 y&=t \end {array} \]
|
[[_high_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.226 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t y^{\prime \prime \prime }+\sin \left (t \right ) y^{\prime \prime }+8 y&=\cos \left (t \right ) \end {array} \]
|
[[_3rd_order, _linear, _nonhomogeneous]] |
✗ |
✗ |
✗ |
✗ |
0.136 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t \left (t -1\right ) y^{\prime \prime \prime \prime }+{\mathrm e}^{t} y^{\prime \prime }+4 t^{2} y&=0 \end {array} \]
|
[[_high_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
✗ |
0.148 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime }+t y^{\prime \prime }+t^{2} y^{\prime }+t^{2} y&=\ln \left (t \right ) \end {array} \]
|
[[_3rd_order, _linear, _nonhomogeneous]] |
✗ |
✗ |
✗ |
✗ |
0.149 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x -4\right ) y^{\prime \prime \prime \prime }+\left (x +1\right ) y^{\prime \prime }+\tan \left (x \right ) y&=0 \end {array} \]
|
[[_high_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
✗ |
0.158 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x^{2}-2\right ) y^{\left (6\right )}+x^{2} y^{\prime \prime }+3 y&=0 \end {array} \]
|
[[_high_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
✗ |
0.211 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime \prime }+5 y^{\prime \prime \prime }+4 y&=0 \end {array} \]
|
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.153 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t y^{\prime \prime \prime }+\sin \left (t \right ) y^{\prime \prime }+4 y&=\cos \left (t \right ) \end {array} \]
|
[[_3rd_order, _linear, _nonhomogeneous]] |
✗ |
✗ |
✗ |
✗ |
0.119 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t \left (t -1\right ) y^{\prime \prime \prime \prime }+{\mathrm e}^{t} y^{\prime \prime }+7 t^{2} y&=0 \end {array} \]
|
[[_high_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
✗ |
0.179 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime }+t y^{\prime \prime }+5 t^{2} y^{\prime }+2 t^{3} y&=\ln \left (t \right ) \end {array} \]
|
[[_3rd_order, _linear, _nonhomogeneous]] |
✗ |
✗ |
✗ |
✗ |
0.144 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (-1+x \right ) y^{\prime \prime \prime \prime }+\left (x +5\right ) y^{\prime \prime }+\tan \left (x \right ) y&=0 \end {array} \]
|
[[_high_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
✗ |
0.141 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x^{2}-25\right ) y^{\left (6\right )}+x^{2} y^{\prime \prime }+5 y&=0 \end {array} \]
|
[[_high_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
✗ |
0.192 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{2}+x_{3}\\ x_{2}^{\prime }&=x_{1}+x_{3}\\ x_{3}^{\prime }&=x_{1}+x_{2}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.776 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=3 x_{1}+2 x_{2}+4 x_{3}\\ x_{2}^{\prime }&=2 x_{1}+2 x_{3}\\ x_{3}^{\prime }&=4 x_{1}+2 x_{2}+3 x_{3}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.910 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime }+y^{\prime }&=0 \end {array} \]
|
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.053 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime \prime }+y^{\prime \prime }&=0 \end {array} \]
|
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.053 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime }+4 y^{\prime \prime }-4 y^{\prime }-16 y&=0 \end {array} \]
|
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.072 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime \prime }+6 y^{\prime \prime \prime }+9 y^{\prime \prime }&=0 \end {array} \]
|
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.076 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x y^{\prime \prime \prime }-y^{\prime \prime }&=0 \end {array} \]
|
[[_3rd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.366 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{3} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y&=0 \end {array} \]
|
[[_3rd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.215 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=-4 x_{1}+x_{2}\\ x_{2}^{\prime }&=x_{1}-5 x_{2}+x_{3}\\ x_{3}^{\prime }&=x_{2}-4 x_{3}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.044 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{1}+4 x_{2}+4 x_{3}\\ x_{2}^{\prime }&=3 x_{2}+2 x_{3}\\ x_{3}^{\prime }&=2 x_{2}+3 x_{3}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
6.577 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=2 x_{1}-4 x_{2}+2 x_{3}\\ x_{2}^{\prime }&=-4 x_{1}+2 x_{2}-2 x_{3}\\ x_{3}^{\prime }&=2 x_{1}-2 x_{2}-x_{3}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.902 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=-2 x_{1}+2 x_{2}-x_{3}\\ x_{2}^{\prime }&=-2 x_{1}+3 x_{2}-2 x_{3}\\ x_{3}^{\prime }&=-2 x_{1}+4 x_{2}-3 x_{3}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.914 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{1}+x_{2}+6 x_{3}\\ x_{2}^{\prime }&=x_{1}+6 x_{2}+x_{3}\\ x_{3}^{\prime }&=6 x_{1}+x_{2}+x_{3}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.977 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=3 x_{1}+2 x_{2}+4 x_{3}\\ x_{2}^{\prime }&=2 x_{1}+2 x_{3}\\ x_{3}^{\prime }&=4 x_{1}+2 x_{2}+3 x_{3}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.844 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{1}+x_{2}+x_{3}\\ x_{2}^{\prime }&=2 x_{1}+x_{2}-x_{3}\\ x_{3}^{\prime }&=-8 x_{1}-5 x_{2}-3 x_{3}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.279 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{1}-x_{2}+4 x_{3}\\ x_{2}^{\prime }&=3 x_{1}+2 x_{2}-x_{3}\\ x_{3}^{\prime }&=2 x_{1}+x_{2}-x_{3}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.969 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{1}+x_{2}+2 x_{3}\\ x_{2}^{\prime }&=2 x_{2}+2 x_{3}\\ x_{3}^{\prime }&=-x_{1}+x_{2}+3 x_{3}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
6.744 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=-x_{3}\\ x_{2}^{\prime }&=2 x_{1}\\ x_{3}^{\prime }&=-x_{1}+2 x_{2}+4 x_{3}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.053 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{1}+3 x_{3}\\ x_{2}^{\prime }&=-2 x_{2}\\ x_{3}^{\prime }&=3 x_{1}-x_{3}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.208 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=\frac {x_{1}}{2}-x_{2}-\frac {3 x_{3}}{2}\\ x_{2}^{\prime }&=\frac {3 x_{1}}{2}-2 x_{2}-\frac {3 x_{3}}{2}\\ x_{3}^{\prime }&=-2 x_{1}+2 x_{2}+x_{3}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.017 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{1}+5 x_{2}+3 x_{3}-5 x_{4}\\ x_{2}^{\prime }&=2 x_{1}+3 x_{2}+2 x_{3}-4 x_{4}\\ x_{3}^{\prime }&=-x_{2}-2 x_{3}+x_{4}\\ x_{4}^{\prime }&=2 x_{1}+4 x_{2}+2 x_{3}-5 x_{4}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.543 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=-5 x_{1}+x_{2}-4 x_{3}-x_{4}\\ x_{2}^{\prime }&=-3 x_{2}\\ x_{3}^{\prime }&=x_{1}-x_{2}+x_{4}\\ x_{4}^{\prime }&=2 x_{1}-x_{2}+2 x_{3}-2 x_{4}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.543 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=2 x_{1}+2 x_{2}-x_{4}\\ x_{2}^{\prime }&=2 x_{1}-x_{2}+2 x_{4}\\ x_{3}^{\prime }&=3 x_{3}\\ x_{4}^{\prime }&=-x_{1}+2 x_{2}+2 x_{4}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
6.821 |
|