| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
x^{\prime \prime }+x^{\prime }+x&=t \,{\mathrm e}^{-t} \sin \left (\pi t \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.191 |
|
| \begin{align*}
x^{\prime \prime }+x^{\prime }+x&=\left (t +2\right ) \sin \left (\pi t \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.181 |
|
| \begin{align*}
x^{\prime \prime }+x^{\prime }+x&=4 t +5 \,{\mathrm e}^{-t} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.771 |
|
| \begin{align*}
x^{\prime \prime }+x^{\prime }+x&=5 \sin \left (2 t \right )+{\mathrm e}^{t} t \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.635 |
|
| \begin{align*}
x^{\prime \prime }+x^{\prime }+x&=t^{3}+1-4 \cos \left (t \right ) t \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
2.481 |
|
| \begin{align*}
x^{\prime \prime }+x^{\prime }+x&=-6+2 \,{\mathrm e}^{2 t} \sin \left (t \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.120 |
|
| \begin{align*}
x^{\prime \prime }+7 x&=t \,{\mathrm e}^{3 t} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.850 |
|
| \begin{align*}
x^{\prime \prime }-x^{\prime }&=6+{\mathrm e}^{2 t} \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.682 |
|
| \begin{align*}
x^{\prime \prime }+x&=t^{2} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.712 |
|
| \begin{align*}
x^{\prime \prime }-3 x^{\prime }-4 x&=2 t^{2} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.673 |
|
| \begin{align*}
x^{\prime \prime }+x&=9 \,{\mathrm e}^{-t} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.715 |
|
| \begin{align*}
x^{\prime \prime }-4 x&=\cos \left (2 t \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.856 |
|
| \begin{align*}
x^{\prime \prime }+x^{\prime }+2 x&=t \sin \left (2 t \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.210 |
|
| \begin{align*}
x^{\prime \prime }-b x^{\prime }+x&=\sin \left (2 t \right ) \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.932 |
|
| \begin{align*}
x^{\prime \prime }-3 x^{\prime }-40 x&=2 \,{\mathrm e}^{-t} \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.891 |
|
| \begin{align*}
x^{\prime \prime }-2 x^{\prime }&=4 \\
x \left (0\right ) &= 1 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
2.174 |
|
| \begin{align*}
x^{\prime \prime }+2 x&=\cos \left (\sqrt {2}\, t \right ) \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.182 |
|
| \begin{align*}
x^{\prime \prime }+\frac {x^{\prime }}{100}+4 x&=\cos \left (2 t \right ) \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.115 |
|
| \begin{align*}
x^{\prime \prime }+w^{2} x&=\cos \left (\beta t \right ) \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.957 |
|
| \begin{align*}
x^{\prime \prime }+3025 x&=\cos \left (45 t \right ) \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.416 |
|
| \begin{align*}
x^{\prime \prime }&=-\frac {x}{t^{2}} \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.680 |
|
| \begin{align*}
x^{\prime \prime }&=\frac {4 x}{t^{2}} \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.614 |
|
| \begin{align*}
t^{2} x^{\prime \prime }+3 x^{\prime } t +x&=0 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
2.980 |
|
| \begin{align*}
t x^{\prime \prime }+4 x^{\prime }+\frac {2 x}{t}&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
4.296 |
|
| \begin{align*}
t^{2} x^{\prime \prime }-7 x^{\prime } t +16 x&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
2.619 |
|
| \begin{align*}
t^{2} x^{\prime \prime }+3 x^{\prime } t -8 x&=0 \\
x \left (1\right ) &= 0 \\
x^{\prime }\left (1\right ) &= 2 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
1.950 |
|
| \begin{align*}
t^{2} x^{\prime \prime }+x^{\prime } t&=0 \\
x \left (1\right ) &= 0 \\
x^{\prime }\left (1\right ) &= 2 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.201 |
|
| \begin{align*}
t^{2} x^{\prime \prime }-x^{\prime } t +2 x&=0 \\
x \left (1\right ) &= 0 \\
x^{\prime }\left (1\right ) &= 1 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
4.313 |
|
| \begin{align*}
x^{\prime \prime }+t^{2} x^{\prime }&=0 \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
40.150 |
|
| \begin{align*}
x^{\prime \prime }+x&=\tan \left (t \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.875 |
|
| \begin{align*}
x^{\prime \prime }-x&={\mathrm e}^{t} t \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.787 |
|
| \begin{align*}
x^{\prime \prime }-x&=\frac {1}{t} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.735 |
|
| \begin{align*}
t^{2} x^{\prime \prime }-2 x&=t^{3} \\
\end{align*} |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.334 |
|
| \begin{align*}
x^{\prime \prime }+x&=\frac {1}{t +1} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.032 |
|
| \begin{align*}
x^{\prime \prime }-2 x^{\prime }+x&=\frac {{\mathrm e}^{t}}{2 t} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.925 |
|
| \begin{align*}
x^{\prime \prime }+\frac {x^{\prime }}{t}&=a \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.512 |
|
| \begin{align*}
t^{2} x^{\prime \prime }-3 x^{\prime } t +3 x&=4 t^{7} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
19.352 |
|
| \begin{align*}
x^{\prime \prime }-x&=\frac {{\mathrm e}^{t}}{1+{\mathrm e}^{t}} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.873 |
|
| \begin{align*}
x^{\prime \prime }+x^{\prime } t +x&=0 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.254 |
|
| \begin{align*}
x^{\prime \prime }-x^{\prime } t +x&=0 \\
\end{align*} |
[_Hermite] |
✓ |
✓ |
✓ |
✗ |
0.285 |
|
| \begin{align*}
x^{\prime \prime }-2 a x^{\prime }+a^{2} x&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.231 |
|
| \begin{align*}
x^{\prime \prime }-\frac {\left (t +2\right ) x^{\prime }}{t}+\frac {\left (t +2\right ) x}{t^{2}}&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.233 |
|
| \begin{align*}
t^{2} x^{\prime \prime }+x^{\prime } t +\left (t^{2}-\frac {1}{4}\right ) x&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.229 |
|
| \begin{align*}
x^{\prime \prime \prime }+x^{\prime }&=0 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.074 |
|
| \begin{align*}
x^{\prime \prime \prime }+x^{\prime }&=1 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.180 |
|
| \begin{align*}
x^{\prime \prime \prime }+x^{\prime \prime }&=0 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.070 |
|
| \begin{align*}
x^{\prime \prime \prime }-x^{\prime }-8 x&=0 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.149 |
|
| \begin{align*}
x^{\prime \prime \prime }+x^{\prime \prime }&=2 \,{\mathrm e}^{t}+3 t^{2} \\
\end{align*} |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.237 |
|
| \begin{align*}
x^{\prime \prime \prime }-8 x&=0 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.079 |
|
| \begin{align*}
x^{\prime \prime \prime }+x^{\prime \prime }-x^{\prime }-4 x&=0 \\
x \left (0\right ) &= 1 \\
x^{\prime }\left (0\right ) &= 0 \\
x^{\prime \prime }\left (0\right ) &= -1 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✗ |
1.750 |
|
| \begin{align*}
x^{\prime }+5 x&=\operatorname {Heaviside}\left (t -2\right ) \\
x \left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.823 |
|
| \begin{align*}
x^{\prime }+x&=\sin \left (2 t \right ) \\
x \left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
0.744 |
|
| \begin{align*}
x^{\prime \prime }-x^{\prime }-6 x&=0 \\
x \left (0\right ) &= 2 \\
x^{\prime }\left (0\right ) &= -1 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.412 |
|
| \begin{align*}
x^{\prime \prime }-2 x^{\prime }+2 x&=0 \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.390 |
|
| \begin{align*}
x^{\prime \prime }-2 x^{\prime }+2 x&={\mathrm e}^{-t} \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.524 |
|
| \begin{align*}
x^{\prime \prime }-x^{\prime }&=0 \\
x \left (0\right ) &= 1 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.249 |
|
| \begin{align*}
x^{\prime \prime }+\frac {2 x^{\prime }}{5}+2 x&=1-\operatorname {Heaviside}\left (t -5\right ) \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
11.339 |
|
| \begin{align*}
x^{\prime \prime }+9 x&=\sin \left (3 t \right ) \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.560 |
|
| \begin{align*}
x^{\prime \prime }-2 x&=1 \\
x \left (0\right ) &= 1 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.464 |
|
| \begin{align*}
x^{\prime }&=2 x+\operatorname {Heaviside}\left (t -1\right ) \\
x \left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.475 |
|
| \begin{align*}
x^{\prime \prime }+4 x&=\cos \left (2 t \right ) \operatorname {Heaviside}\left (2 \pi -t \right ) \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
2.606 |
|
| \begin{align*}
x^{\prime }&=x-2 \operatorname {Heaviside}\left (t -1\right ) \\
x \left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.484 |
|
| \begin{align*}
x^{\prime }&=-x+\operatorname {Heaviside}\left (t -1\right )-\operatorname {Heaviside}\left (t -2\right ) \\
x \left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.961 |
|
| \begin{align*}
x^{\prime \prime }+\pi ^{2} x&=\pi ^{2} \operatorname {Heaviside}\left (1-t \right ) \\
x \left (0\right ) &= 1 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
3.604 |
|
| \begin{align*}
x^{\prime \prime }-4 x&=1-\operatorname {Heaviside}\left (t -1\right ) \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
3.214 |
|
| \begin{align*}
x^{\prime \prime }+3 x^{\prime }+2 x&={\mathrm e}^{-4 t} \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.487 |
|
| \begin{align*}
x^{\prime }+3 x&=\delta \left (t -1\right )+\operatorname {Heaviside}\left (-4+t \right ) \\
x \left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
4.531 |
|
| \begin{align*}
x^{\prime \prime }-x&=\delta \left (t -5\right ) \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.602 |
|
| \begin{align*}
x^{\prime \prime }+x&=\delta \left (t -2\right ) \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.681 |
|
| \begin{align*}
x^{\prime \prime }+4 x&=\delta \left (t -2\right )-\delta \left (t -5\right ) \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
5.407 |
|
| \begin{align*}
x^{\prime \prime }+x&=3 \delta \left (t -2 \pi \right ) \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.767 |
|
| \begin{align*}
y^{\prime \prime }+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]] |
✓ |
✓ |
✓ |
✓ |
2.761 |
|
| \begin{align*}
x^{\prime \prime }+4 x&=\frac {\operatorname {Heaviside}\left (t -5\right ) \left (t -5\right )}{5}+\left (2-\frac {t}{5}\right ) \operatorname {Heaviside}\left (t -10\right ) \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
3.688 |
|
| \begin{align*}
x^{\prime }&=-3 y \\
y^{\prime }&=2 x \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.800 |
|
| \begin{align*}
x^{\prime }&=-2 y \\
y^{\prime }&=-4 x \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.773 |
|
| \begin{align*}
x^{\prime }&=-3 x \\
y^{\prime }&=2 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.453 |
|
| \begin{align*}
x^{\prime }&=4 y \\
y^{\prime }&=2 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.541 |
|
| \begin{align*}
x^{\prime }&=x \\
y^{\prime }&=x+2 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.530 |
|
| \begin{align*}
x^{\prime }&=x-y \\
y^{\prime }&=x+y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.663 |
|
| \begin{align*}
x^{\prime }&=x+2 y \\
y^{\prime }&=x \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.656 |
|
| \begin{align*}
x^{\prime }&=-x-2 y \\
y^{\prime }&=2 x-y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.694 |
|
| \begin{align*}
x^{\prime }&=-2 x-3 y \\
y^{\prime }&=-x+4 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.949 |
|
| \begin{align*}
x^{\prime }&=-3 y \\
y^{\prime }&=-2 x+y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.677 |
|
| \begin{align*}
x^{\prime }&=-2 x \\
y^{\prime }&=x \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.551 |
|
| \begin{align*}
x^{\prime }&=-2 x-y \\
y^{\prime }&=-4 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.601 |
|
| \begin{align*}
x^{\prime }&=x-2 y \\
y^{\prime }&=-2 x+4 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.669 |
|
| \begin{align*}
x^{\prime }&=-6 y \\
y^{\prime }&=6 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.519 |
|
| \begin{align*}
x^{\prime }&=2 x+3 y \\
y^{\prime }&=-x-14 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
3.182 |
|
| \begin{align*}
x^{\prime }&=3 y-3 x \\
y^{\prime }&=x+2 y-1 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.808 |
|
| \begin{align*}
x^{\prime }&=-x+y \\
y^{\prime }&=-3 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.571 |
|
| \begin{align*}
x^{\prime }&=x \\
y^{\prime }&=3 x-4 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.604 |
|
| \begin{align*}
x^{\prime }&=-x+y \\
y^{\prime }&=x-2 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.895 |
|
| \begin{align*}
x^{\prime }&=x+y \\
y^{\prime }&=3 y-3 x \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.348 |
|
| \begin{align*}
x^{\prime }&=x-2 y \\
y^{\prime }&=3 x-4 y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 3 \\
y \left (0\right ) &= 1 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.710 |
|
| \begin{align*}
x^{\prime }&=5 x-y \\
y^{\prime }&=3 x+y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 2 \\
y \left (0\right ) &= -1 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.710 |
|
| \begin{align*}
x^{\prime }&=-3 x+y \\
y^{\prime }&=-3 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.446 |
|
| \begin{align*}
x^{\prime }&=x-y \\
y^{\prime }&=x+3 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.543 |
|
| \begin{align*}
x^{\prime }&=x+2 y \\
y^{\prime }&=3 x+2 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.664 |
|
| \begin{align*}
x^{\prime }&=-3 x+4 y \\
y^{\prime }&=-3 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.435 |
|
| \begin{align*}
x^{\prime }&=2 x+2 y \\
y^{\prime }&=6 x+3 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.712 |
|