| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
y^{\prime }+6 y&={\mathrm e}^{4 t} \\
y \left (0\right ) &= 2 \\
\end{align*}
Using Laplace transform method. |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
0.513 |
|
| \begin{align*}
-y+y^{\prime }&=2 \cos \left (5 t \right ) \\
y \left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
0.758 |
|
| \begin{align*}
y^{\prime \prime }+5 y^{\prime }+4 y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.360 |
|
| \begin{align*}
y^{\prime \prime }-4 y^{\prime }&=6 \,{\mathrm e}^{3 t}-3 \,{\mathrm e}^{-t} \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= -1 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.530 |
|
| \begin{align*}
y^{\prime \prime }+y&=\sqrt {2}\, \sin \left (\sqrt {2}\, t \right ) \\
y \left (0\right ) &= 10 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.545 |
|
| \begin{align*}
y^{\prime \prime }+9 y&={\mathrm e}^{t} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.461 |
|
| \begin{align*}
2 y^{\prime \prime \prime }+3 y^{\prime \prime }-3 y^{\prime }-2 y&={\mathrm e}^{-t} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
y^{\prime \prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.563 |
|
| \begin{align*}
y^{\prime \prime \prime }+2 y^{\prime \prime }-y^{\prime }-2 y&=\sin \left (3 t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
y^{\prime \prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.631 |
|
| \begin{align*}
y+y^{\prime }&={\mathrm e}^{-3 t} \cos \left (2 t \right ) \\
y \left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
0.617 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime }+5 y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 3 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.377 |
|
| \begin{align*}
y^{\prime }+4 y&={\mathrm e}^{-4 t} \\
y \left (0\right ) &= 2 \\
\end{align*}
Using Laplace transform method. |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
0.542 |
|
| \begin{align*}
-y+y^{\prime }&=1+{\mathrm e}^{t} t \\
y \left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
0.596 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }+y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.344 |
|
| \begin{align*}
y^{\prime \prime }-4 y^{\prime }+4 y&=t^{3} {\mathrm e}^{2 t} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.315 |
|
| \begin{align*}
y^{\prime \prime }-6 y^{\prime }+9 y&=t \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.494 |
|
| \begin{align*}
y^{\prime \prime }-4 y^{\prime }+4 y&=t^{3} \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.591 |
|
| \begin{align*}
y^{\prime \prime }-6 y^{\prime }+13 y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= -3 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.375 |
|
| \begin{align*}
2 y^{\prime \prime }+20 y^{\prime }+51 y&=0 \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.410 |
|
| \begin{align*}
y^{\prime \prime }-y&={\mathrm e}^{t} \cos \left (t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.488 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime }+5 y&=t +1 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 4 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.514 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }+y&=0 \\
y \left (1\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.361 |
|
| \begin{align*}
y^{\prime \prime }+8 y^{\prime }+20 y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (\pi \right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.363 |
|
| \begin{align*}
y+y^{\prime }&=\left \{\begin {array}{cc} 0 & 0\le t <1 \\ 5 & 1\le t \end {array}\right . \\
y \left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
1.784 |
|
| \begin{align*}
y+y^{\prime }&=\left \{\begin {array}{cc} 1 & 0\le t <1 \\ -1 & 1\le t \end {array}\right . \\
y \left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
1.944 |
|
| \begin{align*}
y+y^{\prime }&=\left \{\begin {array}{cc} t & 0\le t <1 \\ 0 & 1\le t \end {array}\right . \\
y \left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
2.484 |
|
| \begin{align*}
y^{\prime \prime }+4 y&=\left \{\begin {array}{cc} 1 & 0\le t <1 \\ 0 & 1\le t \end {array}\right . \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= -1 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
2.398 |
|
| \begin{align*}
y^{\prime \prime }+4 y&=\operatorname {Heaviside}\left (t -2 \pi \right ) \sin \left (t \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.766 |
|
| \begin{align*}
y^{\prime \prime }-5 y^{\prime }+6 y&=\operatorname {Heaviside}\left (t -1\right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
3.818 |
|
| \begin{align*}
y^{\prime \prime }+y&=\left \{\begin {array}{cc} 0 & 0\le t <\pi \\ 1 & \pi \le t <2 \pi \\ 0 & 2 \pi \le t \end {array}\right . \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
3.743 |
|
| \begin{align*}
y^{\prime \prime }+4 y^{\prime }+3 y&=1-\operatorname {Heaviside}\left (t -2\right )-\operatorname {Heaviside}\left (-4+t \right )+\operatorname {Heaviside}\left (t -6\right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
12.833 |
|
| \begin{align*}
y+y^{\prime }&=t \sin \left (t \right ) \\
y \left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
0.787 |
|
| \begin{align*}
-y+y^{\prime }&=t \,{\mathrm e}^{t} \sin \left (t \right ) \\
y \left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
0.723 |
|
| \begin{align*}
y^{\prime \prime }+9 y&=\cos \left (3 t \right ) \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 5 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.530 |
|
| \begin{align*}
y^{\prime \prime }+y&=\sin \left (t \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= -1 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.503 |
|
| \begin{align*}
y^{\prime \prime }+16 y&=\left \{\begin {array}{cc} \cos \left (4 t \right ) & 0\le t <\pi \\ 0 & \pi \le t \end {array}\right . \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
2.224 |
|
| \begin{align*}
y^{\prime \prime }+y&=\left \{\begin {array}{cc} 1 & 0\le t <\frac {\pi }{2} \\ \sin \left (t \right ) & \frac {\pi }{2}\le t \end {array}\right . \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
2.347 |
|
| \begin{align*}
t y^{\prime \prime }-y^{\prime }&=2 t^{2} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.649 |
|
| \begin{align*}
2 y^{\prime \prime }+t y^{\prime }-2 y&=10 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.717 |
|
| \begin{align*}
y^{\prime \prime }+y&=\sin \left (t \right )+t \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]] |
✓ |
✓ |
✓ |
✓ |
0.621 |
|
| \begin{align*}
y^{\prime }-3 y&=\delta \left (t -2\right ) \\
y \left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.240 |
|
| \begin{align*}
y+y^{\prime }&=\delta \left (t -1\right ) \\
y \left (0\right ) &= 2 \\
\end{align*}
Using Laplace transform method. |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.478 |
|
| \begin{align*}
y^{\prime \prime }+y&=\delta \left (t -2 \pi \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.362 |
|
| \begin{align*}
y^{\prime \prime }+16 y&=\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]] |
✓ |
✓ |
✓ |
✓ |
1.253 |
|
| \begin{align*}
y^{\prime \prime }+y&=\delta \left (t -\frac {\pi }{2}\right )+\delta \left (t -\frac {3 \pi }{2}\right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.596 |
|
| \begin{align*}
y^{\prime \prime }+y&=\delta \left (t -2 \pi \right )+\delta \left (t -4 \pi \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
2.030 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }&=\delta \left (t -1\right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.781 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime }&=1+\delta \left (t -2\right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
2.919 |
|
| \begin{align*}
y^{\prime \prime }+4 y^{\prime }+5 y&=\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]] |
✓ |
✓ |
✓ |
✓ |
1.586 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\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]] |
✓ |
✓ |
✓ |
✓ |
1.378 |
|
| \begin{align*}
y^{\prime \prime }+4 y^{\prime }+13 y&=\delta \left (t -\pi \right )+\delta \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]] |
✓ |
✓ |
✓ |
✓ |
5.174 |
|
| \begin{align*}
y^{\prime \prime }-7 y^{\prime }+6 y&={\mathrm e}^{t}+\delta \left (t -2\right )+\delta \left (-4+t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
6.073 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }+10 y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.385 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }+10 y&=\delta \left (t \right ) \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.403 |
|
| \begin{align*}
x^{\prime }&=3 x-5 y \\
y^{\prime }&=4 x+8 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.990 |
|
| \begin{align*}
x^{\prime }&=4 x-7 y \\
y^{\prime }&=5 x \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.957 |
|
| \begin{align*}
x^{\prime }&=-3 x+4 y-9 z \\
y^{\prime }&=6 x-y \\
z^{\prime }&=10 x+4 y+3 z \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✗ |
18.575 |
|
| \begin{align*}
x^{\prime }&=x-y \\
y^{\prime }&=x+2 z \\
z^{\prime }&=-x+z \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✗ |
15.328 |
|
| \begin{align*}
x^{\prime }&=x-y+z+t -1 \\
y^{\prime }&=2 x+y-z-3 t^{2} \\
z^{\prime }&=x+y+z+t^{2}-t +2 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
6.664 |
|
| \begin{align*}
x^{\prime }&=-3 x+4 y+{\mathrm e}^{-t} \sin \left (2 t \right ) \\
y^{\prime }&=5 x+9 z+4 \,{\mathrm e}^{-t} \cos \left (2 t \right ) \\
z^{\prime }&=y+6 z-{\mathrm e}^{-t} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✗ |
189.839 |
|
| \begin{align*}
x^{\prime }&=4 x+2 y+{\mathrm e}^{t} \\
y^{\prime }&=-x+3 y-{\mathrm e}^{t} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
2.782 |
|
| \begin{align*}
x^{\prime }&=7 x+5 y-9 z-8 \,{\mathrm e}^{-2 t} \\
y^{\prime }&=4 x+y+z+2 \,{\mathrm e}^{5 t} \\
z^{\prime }&=-2 y+3 z+{\mathrm e}^{5 t}-3 \,{\mathrm e}^{-2 t} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✗ |
47.398 |
|
| \begin{align*}
x^{\prime }&=x-y+2 z+{\mathrm e}^{-t}-3 t \\
y^{\prime }&=3 x-4 y+z+2 \,{\mathrm e}^{-t}+t \\
z^{\prime }&=-2 x+5 y+6 z+2 \,{\mathrm e}^{-t}-t \\
\end{align*} |
system_of_ODEs |
✓ |
✗ |
✓ |
✗ |
175.447 |
|
| \begin{align*}
x^{\prime }&=3 x-7 y+4 \sin \left (t \right )+\left (-4+t \right ) {\mathrm e}^{4 t} \\
y^{\prime }&=x+y+8 \sin \left (t \right )+\left (2 t +1\right ) {\mathrm e}^{4 t} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
8.753 |
|
| \begin{align*}
x^{\prime }&=3 x-4 y \\
y^{\prime }&=4 x-7 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.629 |
|
| \begin{align*}
x^{\prime }&=-2 x+5 y \\
y^{\prime }&=-2 x+4 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.848 |
|
| \begin{align*}
x^{\prime }&=-x+\frac {y}{4} \\
y^{\prime }&=x-y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.644 |
|
| \begin{align*}
x^{\prime }&=2 x+y \\
y^{\prime }&=-x \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.486 |
|
| \begin{align*}
x^{\prime }&=x+2 y+z \\
y^{\prime }&=6 x-y \\
z^{\prime }&=-x-2 y-z \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.168 |
|
| \begin{align*}
x^{\prime }&=x+z \\
y^{\prime }&=x+y \\
z^{\prime }&=-2 x-z \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.112 |
|
| \begin{align*}
x^{\prime }&=x+2 y \\
y^{\prime }&=4 x+3 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.610 |
|
| \begin{align*}
x^{\prime }&=2 x+2 y \\
y^{\prime }&=x+3 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.572 |
|
| \begin{align*}
x^{\prime }&=-4 x+2 y \\
y^{\prime }&=-\frac {5 x}{2}+2 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.648 |
|
| \begin{align*}
x^{\prime }&=-\frac {5 x}{2}+2 y \\
y^{\prime }&=\frac {3 x}{4}-2 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.657 |
|
| \begin{align*}
x^{\prime }&=10 x-5 y \\
y^{\prime }&=8 x-12 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.655 |
|
| \begin{align*}
x^{\prime }&=-6 x+2 y \\
y^{\prime }&=-3 x+y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.612 |
|
| \begin{align*}
x^{\prime }&=x+y-z \\
y^{\prime }&=2 y \\
z^{\prime }&=y-z \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.905 |
|
| \begin{align*}
x^{\prime }&=2 x-7 y \\
y^{\prime }&=5 x+10 y+4 z \\
z^{\prime }&=5 y+2 z \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.148 |
|
| \begin{align*}
x^{\prime }&=-x+y \\
y^{\prime }&=x+2 y+z \\
z^{\prime }&=3 y-z \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.069 |
|
| \begin{align*}
x^{\prime }&=x+z \\
y^{\prime }&=y \\
z^{\prime }&=x+z \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.834 |
|
| \begin{align*}
x^{\prime }&=-x-y \\
y^{\prime }&=\frac {3 x}{4}-\frac {3 y}{2}+3 z \\
z^{\prime }&=\frac {x}{8}+\frac {y}{4}-\frac {z}{2} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.385 |
|
| \begin{align*}
x^{\prime }&=-x-y \\
y^{\prime }&=\frac {3 x}{4}-\frac {3 y}{2}+3 z \\
z^{\prime }&=\frac {x}{8}+\frac {y}{4}-\frac {z}{2} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.240 |
|
| \begin{align*}
x^{\prime }&=-x+4 y+2 z \\
y^{\prime }&=4 x-y-2 z \\
z^{\prime }&=6 z \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.993 |
|
| \begin{align*}
x^{\prime }&=\frac {x}{2} \\
y^{\prime }&=x-\frac {y}{2} \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 4 \\
y \left (0\right ) &= 5 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.555 |
|
| \begin{align*}
x^{\prime }&=x+y+4 z \\
y^{\prime }&=2 y \\
z^{\prime }&=x+y+z \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 3 \\
z \left (0\right ) &= 0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.977 |
|
| \begin{align*}
x^{\prime }&=\frac {9 x}{10}+\frac {21 y}{10}+\frac {16 z}{5} \\
y^{\prime }&=\frac {7 x}{10}+\frac {13 y}{2}+\frac {21 z}{5} \\
z^{\prime }&=\frac {11 x}{10}+\frac {17 y}{10}+\frac {17 z}{5} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✗ |
94.423 |
|
| \begin{align*}
x_{1}^{\prime }&=x_{1}+2 x_{3}-\frac {9 x_{4}}{5} \\
x_{2}^{\prime }&=\frac {51 x_{2}}{10}-x_{4}+3 x_{5} \\
x_{3}^{\prime }&=x_{1}+2 x_{2}-3 x_{3} \\
x_{4}^{\prime }&=x_{2}-\frac {31 x_{3}}{10}+4 x_{4} \\
x_{5}^{\prime }&=-\frac {14 x_{1}}{5}+\frac {3 x_{4}}{2}-x_{5} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✗ |
53.359 |
|
| \begin{align*}
x^{\prime }&=3 x-y \\
y^{\prime }&=9 x-3 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.523 |
|
| \begin{align*}
x^{\prime }&=-6 x+5 y \\
y^{\prime }&=-5 x+4 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.509 |
|
| \begin{align*}
x^{\prime }&=-x+3 y \\
y^{\prime }&=-3 x+5 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.472 |
|
| \begin{align*}
x^{\prime }&=12 x-9 y \\
y^{\prime }&=4 x \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.554 |
|
| \begin{align*}
x^{\prime }&=3 x-y-z \\
y^{\prime }&=x+y-z \\
z^{\prime }&=x-y+z \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.802 |
|
| \begin{align*}
x^{\prime }&=3 x+2 y+4 z \\
y^{\prime }&=2 x+2 z \\
z^{\prime }&=4 x+2 y+3 z \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.945 |
|
| \begin{align*}
x^{\prime }&=5 x-4 y \\
y^{\prime }&=x+2 z \\
z^{\prime }&=2 y+5 z \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.006 |
|
| \begin{align*}
x^{\prime }&=x \\
y^{\prime }&=3 y+z \\
z^{\prime }&=-y+z \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.776 |
|
| \begin{align*}
x^{\prime }&=x \\
y^{\prime }&=2 x+2 y-z \\
z^{\prime }&=y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.685 |
|
| \begin{align*}
x^{\prime }&=4 x+y \\
y^{\prime }&=4 y+z \\
z^{\prime }&=4 z \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.609 |
|
| \begin{align*}
x^{\prime }&=2 x+4 y \\
y^{\prime }&=-x+6 y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= -1 \\
y \left (0\right ) &= 6 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.579 |
|
| \begin{align*}
x^{\prime }&=z \\
y^{\prime }&=y \\
z^{\prime }&=x \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 2 \\
z \left (0\right ) &= 5 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.706 |
|
| \begin{align*}
x^{\prime }&=6 x-y \\
y^{\prime }&=5 x+2 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.885 |
|
| \begin{align*}
x^{\prime }&=x+y \\
y^{\prime }&=-2 x-y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.667 |
|