| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
3 y^{\prime \prime }+8 y^{\prime }-3 y&=0 \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= -4 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.122 |
|
| \begin{align*}
2 y^{\prime \prime }+20 y^{\prime }+51 y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= -5 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.143 |
|
| \begin{align*}
4 y^{\prime \prime }+40 y^{\prime }+101 y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= -5 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.123 |
|
| \begin{align*}
y^{\prime \prime }+6 y^{\prime }+34 y&=0 \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.147 |
|
| \begin{align*}
y^{\prime \prime \prime }+8 y^{\prime \prime }+16 y^{\prime }&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 1 \\
y^{\prime \prime }\left (0\right ) &= -8 \\
\end{align*} Using Laplace transform method. |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.162 |
|
| \begin{align*}
y^{\prime \prime \prime }+6 y^{\prime \prime }+13 y^{\prime }&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 1 \\
y^{\prime \prime }\left (0\right ) &= -6 \\
\end{align*} Using Laplace transform method. |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.176 |
|
| \begin{align*}
y^{\prime \prime \prime }-6 y^{\prime \prime }+13 y^{\prime }&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 1 \\
y^{\prime \prime }\left (0\right ) &= 6 \\
\end{align*} Using Laplace transform method. |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.177 |
|
| \begin{align*}
y^{\prime \prime \prime }+4 y^{\prime \prime }+29 y^{\prime }&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 5 \\
y^{\prime \prime }\left (0\right ) &= -20 \\
\end{align*} Using Laplace transform method. |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.188 |
|
| \begin{align*}
y^{\prime \prime \prime }+6 y^{\prime \prime }+25 y^{\prime }&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 4 \\
y^{\prime \prime }\left (0\right ) &= -24 \\
\end{align*} Using Laplace transform method. |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.185 |
|
| \begin{align*}
y^{\prime \prime \prime }-6 y^{\prime \prime }+10 y^{\prime }&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 3 \\
y^{\prime \prime }\left (0\right ) &= 8 \\
\end{align*} Using Laplace transform method. |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.171 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }+13 y^{\prime \prime }+36 y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= -1 \\
y^{\prime \prime }\left (0\right ) &= 5 \\
y^{\prime \prime \prime }\left (0\right ) &= 19 \\
\end{align*} Using Laplace transform method. |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.232 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }+3 y&=9 t \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.164 |
|
| \begin{align*}
4 y^{\prime \prime }+16 y^{\prime }+17 y&=17 t -1 \\
y \left (0\right ) &= -1 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.157 |
|
| \begin{align*}
4 y^{\prime \prime }+5 y^{\prime }+4 y&=3 \,{\mathrm e}^{-t} \\
y \left (0\right ) &= -1 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.229 |
|
| \begin{align*}
y^{\prime \prime }-4 y^{\prime }+4 y&={\mathrm e}^{2 t} t^{2} \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.122 |
|
| \begin{align*}
y^{\prime \prime }+9 y&={\mathrm e}^{-2 t} \\
y \left (0\right ) &= -{\frac {2}{13}} \\
y^{\prime }\left (0\right ) &= {\frac {1}{13}} \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.155 |
|
| \begin{align*}
2 y^{\prime \prime }-3 y^{\prime }+17 y&=17 t -1 \\
y \left (0\right ) &= -1 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.230 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }+y&={\mathrm e}^{-t} \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= -1 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.117 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime }+5 y&=t +2 \\
y \left (0\right ) &= 4 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.173 |
|
| \begin{align*}
y+2 y^{\prime }&={\mathrm e}^{-\frac {t}{2}} \\
y \left (0\right ) &= -1 \\
\end{align*} Using Laplace transform method. |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
0.195 |
|
| \begin{align*}
y^{\prime \prime }+8 y^{\prime }+20 y&=\sin \left (2 t \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= -4 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.178 |
|
| \begin{align*}
4 y^{\prime \prime }-4 y^{\prime }+y&=t^{2} \\
y \left (0\right ) &= -12 \\
y^{\prime }\left (0\right ) &= 7 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.145 |
|
| \begin{align*}
2 y^{\prime \prime }+y^{\prime }-y&=4 \sin \left (t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= -4 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.164 |
|
| \begin{align*}
-y+y^{\prime }&={\mathrm e}^{2 t} \\
y \left (0\right ) &= 1 \\
\end{align*} Using Laplace transform method. |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
0.141 |
|
| \begin{align*}
3 y^{\prime \prime }+5 y^{\prime }-2 y&=7 \,{\mathrm e}^{-2 t} \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.134 |
|
| \begin{align*}
y+y^{\prime }&=\operatorname {Heaviside}\left (t \right )-\operatorname {Heaviside}\left (-2+t \right ) \\
y \left (0\right ) &= 1 \\
\end{align*} Using Laplace transform method. |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
0.303 |
|
| \begin{align*}
-2 y+y^{\prime }&=4 t \left (\operatorname {Heaviside}\left (t \right )-\operatorname {Heaviside}\left (-2+t \right )\right ) \\
y \left (0\right ) &= 1 \\
\end{align*} Using Laplace transform method. |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
0.404 |
|
| \begin{align*}
y^{\prime \prime }+9 y&=24 \sin \left (t \right ) \left (\operatorname {Heaviside}\left (t \right )+\operatorname {Heaviside}\left (t -\pi \right )\right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.338 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }+y&=\operatorname {Heaviside}\left (t \right )-\operatorname {Heaviside}\left (t -1\right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= -1 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.533 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }+2 y&=5 \cos \left (t \right ) \left (\operatorname {Heaviside}\left (t \right )-\operatorname {Heaviside}\left (t -\frac {\pi }{2}\right )\right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= -1 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.332 |
|
| \begin{align*}
y^{\prime \prime }+5 y^{\prime }+6 y&=36 t \left (\operatorname {Heaviside}\left (t \right )-\operatorname {Heaviside}\left (t -1\right )\right ) \\
y \left (0\right ) &= -1 \\
y^{\prime }\left (0\right ) &= -2 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.617 |
|
| \begin{align*}
y^{\prime \prime }+4 y^{\prime }+13 y&=39 \operatorname {Heaviside}\left (t \right )-507 \left (-2+t \right ) \operatorname {Heaviside}\left (-2+t \right ) \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.883 |
|
| \begin{align*}
y^{\prime \prime }+4 y&=3 \operatorname {Heaviside}\left (t \right )-3 \operatorname {Heaviside}\left (t -4\right )+\left (2 t -5\right ) \operatorname {Heaviside}\left (t -4\right ) \\
y \left (0\right ) &= {\frac {3}{4}} \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.483 |
|
| \begin{align*}
4 y^{\prime \prime }+4 y^{\prime }+5 y&=25 t \left (\operatorname {Heaviside}\left (t \right )-\operatorname {Heaviside}\left (t -\frac {\pi }{2}\right )\right ) \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.404 |
|
| \begin{align*}
y^{\prime \prime }+4 y^{\prime }+3 y&=\operatorname {Heaviside}\left (t \right )-\operatorname {Heaviside}\left (t -1\right )+\operatorname {Heaviside}\left (-2+t \right )-\operatorname {Heaviside}\left (t -3\right ) \\
y \left (0\right ) &= -{\frac {2}{3}} \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.837 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime }&=\left \{\begin {array}{cc} 4 & 0\le t <1 \\ 6 & 1\le t \end {array}\right . \\
y \left (0\right ) &= -6 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✗ |
0.622 |
|
| \begin{align*}
y^{\prime \prime }-3 y^{\prime }+2 y&=\left \{\begin {array}{cc} 0 & 0\le t <1 \\ 1 & 1\le t <2 \\ -1 & 2\le t \end {array}\right . \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= -1 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
1.120 |
|
| \begin{align*}
y^{\prime \prime }+3 y^{\prime }+2 y&=\left \{\begin {array}{cc} 1 & 0\le t <2 \\ -1 & 2\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]] |
✓ |
✓ |
✓ |
✗ |
0.605 |
|
| \begin{align*}
y^{\prime \prime }+y&=\left \{\begin {array}{cc} t & 0\le t <\pi \\ -t & \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]] |
✓ |
✓ |
✓ |
✓ |
0.598 |
|
| \begin{align*}
y^{\prime \prime }+4 y&=\left \{\begin {array}{cc} 8 t & 0\le t <\frac {\pi }{2} \\ 8 \pi & \frac {\pi }{2}\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]] |
✓ |
✓ |
✓ |
✓ |
0.821 |
|
| \begin{align*}
y^{\prime \prime }+4 \pi ^{2} y&=3 \delta \left (t -\frac {1}{3}\right )-\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]] |
✓ |
✓ |
✓ |
✓ |
1.829 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }+2 y&=3 \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]] |
✓ |
✓ |
✓ |
✓ |
0.426 |
|
| \begin{align*}
y^{\prime \prime }+4 y^{\prime }+29 y&=5 \delta \left (t -\pi \right )-5 \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]] |
✓ |
✓ |
✓ |
✓ |
0.974 |
|
| \begin{align*}
y^{\prime \prime }+3 y^{\prime }+2 y&=1-\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]] |
✓ |
✓ |
✓ |
✓ |
0.575 |
|
| \begin{align*}
4 y^{\prime \prime }+4 y^{\prime }+y&={\mathrm e}^{-\frac {t}{2}} \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]] |
✓ |
✓ |
✓ |
✓ |
0.314 |
|
| \begin{align*}
y^{\prime \prime }-7 y^{\prime }+6 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]] |
✓ |
✓ |
✓ |
✓ |
0.522 |
|
| \begin{align*}
10 Q^{\prime }+100 Q&=\operatorname {Heaviside}\left (t -1\right )-\operatorname {Heaviside}\left (-2+t \right ) \\
Q \left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
0.625 |
|
| \begin{align*}
y^{\prime \prime \prime }+y^{\prime \prime }+4 y^{\prime }+4 y&=8 \\
y \left (0\right ) &= 4 \\
y^{\prime }\left (0\right ) &= -3 \\
y^{\prime \prime }\left (0\right ) &= -3 \\
\end{align*} Using Laplace transform method. |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.199 |
|
| \begin{align*}
y^{\prime \prime \prime }-2 y^{\prime \prime }-y^{\prime }+2 y&=4 t \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= -2 \\
y^{\prime \prime }\left (0\right ) &= 4 \\
\end{align*} Using Laplace transform method. |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.190 |
|
| \begin{align*}
y^{\prime \prime \prime }-y^{\prime \prime }+4 y^{\prime }-4 y&=8 \,{\mathrm e}^{2 t}-5 \,{\mathrm e}^{t} \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 0 \\
y^{\prime \prime }\left (0\right ) &= 3 \\
\end{align*} Using Laplace transform method. |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.251 |
|
| \begin{align*}
y^{\prime \prime \prime }-5 y^{\prime \prime }+y^{\prime }-y&=-t^{2}+2 t -10 \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 0 \\
y^{\prime \prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.844 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-5 y^{\prime \prime }+4 y&=12 \operatorname {Heaviside}\left (t \right )-12 \operatorname {Heaviside}\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]] |
✓ |
✓ |
✓ |
✓ |
2.504 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-16 y&=32 \operatorname {Heaviside}\left (t \right )-32 \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]] |
✓ |
✓ |
✓ |
✓ |
1.566 |
|
| \begin{align*}
t^{2} y^{\prime \prime }+3 y^{\prime } t +y&=t^{7} \\
\end{align*} |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
2.364 |
|
| \begin{align*}
t^{2} y^{\prime \prime }-6 y^{\prime } t +\sin \left (2 t \right ) y&=\ln \left (t \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
✗ |
✗ |
✗ |
12.681 |
|
| \begin{align*}
y^{\prime \prime }+3 y^{\prime }+\frac {y}{t}&=t \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
✓ |
✓ |
✗ |
31.183 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime } t -y \ln \left (t \right )&=\cos \left (2 t \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
✗ |
✗ |
✗ |
4.796 |
|
| \begin{align*}
t^{3} y^{\prime \prime }-2 y^{\prime } t +y&=t^{4} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
✓ |
✓ |
✗ |
42.055 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }+y&=1 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.302 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime }+5 y&={\mathrm e}^{t} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.336 |
|
| \begin{align*}
y^{\prime \prime }-3 y^{\prime }-7 y&=4 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.296 |
|
| \begin{align*}
y^{\prime \prime \prime }+3 y^{\prime \prime }+3 y^{\prime }+y&=5 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.086 |
|
| \begin{align*}
3 y^{\prime \prime }+5 y^{\prime }-2 y&=3 t^{2} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.297 |
|
| \begin{align*}
y^{\prime \prime \prime }&=2 y^{\prime \prime }-4 y^{\prime }+\sin \left (t \right ) \\
\end{align*} |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.116 |
|
| \begin{align*}
x^{\prime }&=x-2 y \\
y^{\prime }&=3 x-4 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.345 |
|
| \begin{align*}
x^{\prime }&=\frac {5 x}{4}+\frac {3 y}{4} \\
y^{\prime }&=\frac {x}{2}-\frac {3 y}{2} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.529 |
|
| \begin{align*}
x^{\prime }-x+2 y&=0 \\
y^{\prime }+y-x&=0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.344 |
|
| \begin{align*}
x^{\prime }+5 x-2 y&=0 \\
2 x+y^{\prime }-y&=0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.491 |
|
| \begin{align*}
x^{\prime }-3 x+2 y&=0 \\
y^{\prime }-x+3 y&=0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.451 |
|
| \begin{align*}
x^{\prime }+x-z&=0 \\
x+y^{\prime }-y&=0 \\
z^{\prime }+x+2 y-3 z&=0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.514 |
|
| \begin{align*}
x^{\prime }&=-\frac {x}{2}+2 y-3 z \\
y^{\prime }&=y-\frac {z}{2} \\
z^{\prime }&=-2 x+z \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.095 |
|
| \begin{align*}
x^{\prime }+y^{\prime }&=y \\
x^{\prime }-y^{\prime }&=x \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.366 |
|
| \begin{align*}
x^{\prime }+2 y^{\prime }&=t \\
x^{\prime }-y^{\prime }&=x+y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.515 |
|
| \begin{align*}
x^{\prime }-y^{\prime }&=x+y-t \\
2 x^{\prime }+3 y^{\prime }&=2 x+6 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.621 |
|
| \begin{align*}
2 x^{\prime }-y^{\prime }&=t \\
3 x^{\prime }+2 y^{\prime }&=y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.479 |
|
| \begin{align*}
5 x^{\prime }-3 y^{\prime }&=x+y \\
3 x^{\prime }-y^{\prime }&=t \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.531 |
|
| \begin{align*}
x^{\prime }-4 y^{\prime }&=0 \\
2 x^{\prime }-3 y^{\prime }&=y+t \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.497 |
|
| \begin{align*}
3 x^{\prime }+2 y^{\prime }&=\sin \left (t \right ) \\
x^{\prime }-2 y^{\prime }&=x+y+t \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.681 |
|
| \begin{align*}
x^{\prime }&=-4 x+9 y+12 \,{\mathrm e}^{-t} \\
y^{\prime }&=-5 x+2 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.880 |
|
| \begin{align*}
x^{\prime }&=-7 x+6 y+6 \,{\mathrm e}^{-t} \\
y^{\prime }&=-12 x+5 y+37 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.085 |
|
| \begin{align*}
x^{\prime }&=-7 x+10 y+18 \,{\mathrm e}^{t} \\
y^{\prime }&=-10 x+9 y+37 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.432 |
|
| \begin{align*}
x^{\prime }&=-14 x+39 y+78 \sinh \left (t \right ) \\
y^{\prime }&=-6 x+16 y+6 \cosh \left (t \right ) \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.428 |
|
| \begin{align*}
x^{\prime }&=2 x+4 y-2 z-2 \sinh \left (t \right ) \\
y^{\prime }&=4 x+2 y-2 z+10 \cosh \left (t \right ) \\
z^{\prime }&=-x+3 y+z+5 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.495 |
|
| \begin{align*}
x^{\prime }&=2 x+6 y-2 z+50 \,{\mathrm e}^{t} \\
y^{\prime }&=6 x+2 y-2 z+21 \,{\mathrm e}^{-t} \\
z^{\prime }&=-x+6 y+z+9 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.296 |
|
| \begin{align*}
x^{\prime }&=-2 x-2 y+4 z \\
y^{\prime }&=-2 x+y+2 z \\
z^{\prime }&=-4 x-2 y+6 z+{\mathrm e}^{2 t} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.849 |
|
| \begin{align*}
x^{\prime }&=3 x-2 y+3 z \\
y^{\prime }&=x-y+2 z+2 \,{\mathrm e}^{-t} \\
z^{\prime }&=-2 x+2 y-2 z \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.062 |
|
| \begin{align*}
x^{\prime }&=7 x+y-1-6 \,{\mathrm e}^{t} \\
y^{\prime }&=-4 x+3 y+4 \,{\mathrm e}^{t}-3 \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= -1 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.570 |
|
| \begin{align*}
x^{\prime }&=3 x-2 y+24 \sin \left (t \right ) \\
y^{\prime }&=9 x-3 y+12 \cos \left (t \right ) \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= -1 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.814 |
|
| \begin{align*}
x^{\prime }&=7 x-4 y+10 \,{\mathrm e}^{t} \\
y^{\prime }&=3 x+14 y+6 \,{\mathrm e}^{2 t} \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= -1 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
20.602 |
|
| \begin{align*}
x^{\prime }&=-7 x+4 y+6 \,{\mathrm e}^{3 t} \\
y^{\prime }&=-5 x+2 y+6 \,{\mathrm e}^{2 t} \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= -1 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.634 |
|
| \begin{align*}
x^{\prime }&=-3 x-3 y+z \\
y^{\prime }&=2 y+2 z+29 \,{\mathrm e}^{-t} \\
z^{\prime }&=5 x+y+z+39 \,{\mathrm e}^{t} \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 2 \\
z \left (0\right ) &= 3 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✗ |
34.834 |
|
| \begin{align*}
x^{\prime }&=2 x+y-z+5 \sin \left (t \right ) \\
y^{\prime }&=y+z-10 \cos \left (t \right ) \\
z^{\prime }&=x+z+2 \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 2 \\
z \left (0\right ) &= 3 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
2.031 |
|
| \begin{align*}
x^{\prime }&=-3 x+3 y+z+5 \sin \left (2 t \right ) \\
y^{\prime }&=x-5 y-3 z+5 \cos \left (2 t \right ) \\
z^{\prime }&=-3 x+7 y+3 z+23 \,{\mathrm e}^{t} \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 2 \\
z \left (0\right ) &= 3 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
3.473 |
|
| \begin{align*}
x^{\prime }&=-3 x+y-3 z+2 \,{\mathrm e}^{t} \\
y^{\prime }&=4 x-y+2 z+4 \,{\mathrm e}^{t} \\
z^{\prime }&=4 x-2 y+3 z+4 \,{\mathrm e}^{t} \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 2 \\
z \left (0\right ) &= 3 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.625 |
|
| \begin{align*}
x^{\prime }&=x+5 y+10 \sinh \left (t \right ) \\
y^{\prime }&=19 x-13 y+24 \sinh \left (t \right ) \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.820 |
|
| \begin{align*}
x^{\prime }&=9 x-3 y-6 t \\
y^{\prime }&=-x+11 y+10 t \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.939 |
|
| \begin{align*}
\left (x -1\right ) y^{\prime \prime }-y^{\prime } x +y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.081 |
|
| \begin{align*}
y^{\prime \prime } x +2 y^{\prime }+y x&=0 \\
\end{align*} |
[_Lienard] |
✓ |
✓ |
✓ |
✓ |
0.146 |
|
| \begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&=x^{{3}/{2}} {\mathrm e}^{x} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.378 |
|
| \begin{align*}
4 y+y^{\prime \prime }&=2 \sec \left (2 x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.582 |
|