| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
y^{\prime }+{\mathrm e}^{-x} y&=1 \\
y \left (0\right ) &= {\mathrm e} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.193 |
|
| \begin{align*}
x^{\prime }+x \tanh \left (t \right )&=3 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.462 |
|
| \begin{align*}
y^{\prime }+2 \cot \left (x \right ) y&=5 \\
y \left (\frac {\pi }{2}\right ) &= 1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.847 |
|
| \begin{align*}
x^{\prime }+5 x&=t \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
0.928 |
|
| \begin{align*}
x^{\prime }+\left (a +\frac {1}{t}\right ) x&=b \\
x \left (1\right ) &= x_{0} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✗ |
1.745 |
|
| \begin{align*}
T^{\prime }&=-k \left (T-\mu -a \cos \left (\omega \left (t -\phi \right )\right )\right ) \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.368 |
|
| \begin{align*}
2 y x -\sec \left (x \right )^{2}+\left (x^{2}+2 y\right ) y^{\prime }&=0 \\
\end{align*} |
[_exact, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
5.291 |
|
| \begin{align*}
1+{\mathrm e}^{x} y+y x \,{\mathrm e}^{x}+\left (x \,{\mathrm e}^{x}+2\right ) y^{\prime }&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.201 |
|
| \begin{align*}
\left (x \cos \left (y\right )+\cos \left (x \right )\right ) y^{\prime }-y \sin \left (x \right )+\sin \left (y\right )&=0 \\
\end{align*} |
[_exact] |
✓ |
✓ |
✓ |
✗ |
31.636 |
|
| \begin{align*}
{\mathrm e}^{x} \sin \left (y\right )+y+\left ({\mathrm e}^{x} \cos \left (y\right )+x +{\mathrm e}^{y}\right ) y^{\prime }&=0 \\
\end{align*} |
[_exact] |
✓ |
✓ |
✓ |
✗ |
3.723 |
|
| \begin{align*}
{\mathrm e}^{-y} \sec \left (x \right )+2 \cos \left (x \right )-{\mathrm e}^{-y} y^{\prime }&=0 \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
2.979 |
|
| \begin{align*}
V^{\prime }\left (x \right )+2 y^{\prime } y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.831 |
|
| \begin{align*}
\left (\frac {1}{y}-a \right ) y^{\prime }+\frac {2}{x}-b&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.066 |
|
| \begin{align*}
y x +y^{2}+x^{2}-x^{2} y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
3.685 |
|
| \begin{align*}
x^{\prime }&=\frac {x^{2}+t \sqrt {t^{2}+x^{2}}}{t x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
18.859 |
|
| \begin{align*}
x^{\prime }&=k x-x^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
3.527 |
|
| \begin{align*}
x^{\prime \prime }-3 x^{\prime }+2 x&=0 \\
x \left (0\right ) &= 2 \\
x^{\prime }\left (0\right ) &= 6 \\
\end{align*} | [[_2nd_order, _missing_x]] | ✓ | ✓ | ✓ | ✓ | 0.355 |
|
| \begin{align*}
y^{\prime \prime }-4 y^{\prime }+4 y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 3 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.464 |
|
| \begin{align*}
z^{\prime \prime }-4 z^{\prime }+13 z&=0 \\
z \left (0\right ) &= 7 \\
z^{\prime }\left (0\right ) &= 42 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.484 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }-6 y&=0 \\
y \left (0\right ) &= -1 \\
y^{\prime }\left (0\right ) &= 8 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.345 |
|
| \begin{align*}
y^{\prime \prime }-4 y^{\prime }&=0 \\
y \left (0\right ) &= 13 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
1.947 |
|
| \begin{align*}
\theta ^{\prime \prime }+4 \theta &=0 \\
\theta \left (0\right ) &= 0 \\
\theta ^{\prime }\left (0\right ) &= 10 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
1.134 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }+10 y&=0 \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.433 |
|
| \begin{align*}
2 z^{\prime \prime }+7 z^{\prime }-4 z&=0 \\
z \left (0\right ) &= 0 \\
z^{\prime }\left (0\right ) &= 9 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.358 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }+y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= -1 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.414 |
|
| \begin{align*}
x^{\prime \prime }+6 x^{\prime }+10 x&=0 \\
x \left (0\right ) &= 3 \\
x^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.401 |
|
| \begin{align*}
4 x^{\prime \prime }-20 x^{\prime }+21 x&=0 \\
x \left (0\right ) &= -4 \\
x^{\prime }\left (0\right ) &= -12 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.351 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }-2 y&=0 \\
y \left (0\right ) &= 4 \\
y^{\prime }\left (0\right ) &= -4 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.333 |
|
| \begin{align*}
y^{\prime \prime }-4 y&=0 \\
y \left (0\right ) &= 10 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
1.771 |
|
| \begin{align*}
y^{\prime \prime }+4 y^{\prime }+4 y&=0 \\
y \left (0\right ) &= 27 \\
y^{\prime }\left (0\right ) &= -54 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.405 |
|
| \begin{align*}
y^{\prime \prime }+\omega ^{2} y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
1.611 |
|
| \begin{align*}
x^{\prime \prime }-4 x&=t^{2} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.333 |
|
| \begin{align*}
x^{\prime \prime }-4 x^{\prime }&=t^{2} \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.997 |
|
| \begin{align*}
x^{\prime \prime }+x^{\prime }-2 x&=3 \,{\mathrm e}^{-t} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.351 |
|
| \begin{align*}
x^{\prime \prime }+x^{\prime }-2 x&={\mathrm e}^{t} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.396 |
|
| \begin{align*}
x^{\prime \prime }+2 x^{\prime }+x&={\mathrm e}^{-t} \\
\end{align*} | [[_2nd_order, _with_linear_symmetries]] | ✓ | ✓ | ✓ | ✓ | 0.419 |
|
| \begin{align*}
x^{\prime \prime }+\omega ^{2} x&=\sin \left (\alpha t \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.671 |
|
| \begin{align*}
x^{\prime \prime }+\omega ^{2} x&=\sin \left (\omega t \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.103 |
|
| \begin{align*}
x^{\prime \prime }+2 x^{\prime }+10 x&={\mathrm e}^{-t} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.384 |
|
| \begin{align*}
x^{\prime \prime }+2 x^{\prime }+10 x&={\mathrm e}^{-t} \cos \left (3 t \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.442 |
|
| \begin{align*}
x^{\prime \prime }+6 x^{\prime }+10 x&={\mathrm e}^{-2 t} \cos \left (t \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.415 |
|
| \begin{align*}
x^{\prime \prime }+4 x^{\prime }+4 x&={\mathrm e}^{2 t} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.405 |
|
| \begin{align*}
x^{\prime \prime }+x^{\prime }-2 x&=12 \,{\mathrm e}^{-t}-6 \,{\mathrm e}^{t} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.526 |
|
| \begin{align*}
x^{\prime \prime }+4 x&=289 t \,{\mathrm e}^{t} \sin \left (2 t \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.676 |
|
| \begin{align*}
x^{\prime \prime }+\omega ^{2} x&=\cos \left (\alpha t \right ) \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.833 |
|
| \begin{align*}
x^{\prime \prime }+\omega ^{2} x&=\cos \left (\omega t \right ) \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.352 |
|
| \begin{align*}
x^{\prime \prime \prime }-6 x^{\prime \prime }+11 x^{\prime }-6 x&={\mathrm e}^{-t} \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.140 |
|
| \begin{align*}
y^{\prime \prime \prime }-3 y^{\prime \prime }+2 y&=\sin \left (x \right ) \\
\end{align*} |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.136 |
|
| \begin{align*}
x^{\prime \prime \prime \prime }-4 x^{\prime \prime \prime }+8 x^{\prime \prime }-8 x^{\prime }+4 x&=\sin \left (t \right ) \\
\end{align*} |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.165 |
|
| \begin{align*}
x^{\prime \prime \prime \prime }-5 x^{\prime \prime }+4 x&={\mathrm e}^{t} \\
\end{align*} |
[[_high_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.129 |
|
| \begin{align*}
t^{2} y^{\prime \prime }-\left (t^{2}+2 t \right ) y^{\prime }+\left (t +2\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.113 |
|
| \begin{align*}
\left (x -1\right ) y^{\prime \prime }-y^{\prime } x +y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.125 |
|
| \begin{align*}
\left (t \cos \left (t \right )-\sin \left (t \right )\right ) x^{\prime \prime }-x^{\prime } t \sin \left (t \right )-x \sin \left (t \right )&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
✗ |
0.247 |
|
| \begin{align*}
\left (-t^{2}+t \right ) x^{\prime \prime }+\left (-t^{2}+2\right ) x^{\prime }+\left (2-t \right ) x&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.127 |
|
| \begin{align*}
y^{\prime \prime }-y^{\prime } x +y&=0 \\
\end{align*} |
[_Hermite] |
✓ |
✓ |
✓ |
✗ |
0.177 |
|
| \begin{align*}
\tan \left (t \right ) x^{\prime \prime }-3 x^{\prime }+\left (\tan \left (t \right )+3 \cot \left (t \right )\right ) x&=0 \\
\end{align*} | [[_2nd_order, _with_linear_symmetries]] | ✓ | ✓ | ✓ | ✗ | 0.130 |
|
| \begin{align*}
y^{\prime \prime }-y^{\prime }-6 y&={\mathrm e}^{x} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.333 |
|
| \begin{align*}
x^{\prime \prime }-x&=\frac {1}{t} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.383 |
|
| \begin{align*}
4 y+y^{\prime \prime }&=\cot \left (2 x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.743 |
|
| \begin{align*}
t^{2} x^{\prime \prime }-2 x&=t^{3} \\
\end{align*} |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.630 |
|
| \begin{align*}
x^{\prime \prime }-4 x^{\prime }&=\tan \left (t \right ) \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.759 |
|
| \begin{align*}
\left (\tan \left (x \right )^{2}-1\right ) y^{\prime \prime }-4 \tan \left (x \right )^{3} y^{\prime }+2 y \sec \left (x \right )^{4}&=\left (\tan \left (x \right )^{2}-1\right ) \left (1-2 \sin \left (x \right )^{2}\right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.351 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y&=0 \\
y \left (1\right ) &= 0 \\
y^{\prime }\left (1\right ) &= 1 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
1.411 |
|
| \begin{align*}
4 x^{2} y^{\prime \prime }+y&=0 \\
y \left (1\right ) &= 1 \\
y^{\prime }\left (1\right ) &= 0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.369 |
|
| \begin{align*}
t^{2} x^{\prime \prime }-5 t x^{\prime }+10 x&=0 \\
x \left (1\right ) &= 2 \\
x^{\prime }\left (1\right ) &= 1 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
2.006 |
|
| \begin{align*}
t^{2} x^{\prime \prime }+t x^{\prime }-x&=0 \\
x \left (1\right ) &= 1 \\
x^{\prime }\left (1\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
2.102 |
|
| \begin{align*}
x^{2} z^{\prime \prime }+3 x z^{\prime }+4 z&=0 \\
z \left (1\right ) &= 0 \\
z^{\prime }\left (1\right ) &= 5 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
2.335 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-y^{\prime } x -3 y&=0 \\
y \left (1\right ) &= 1 \\
y^{\prime }\left (1\right ) &= -1 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.446 |
|
| \begin{align*}
4 t^{2} x^{\prime \prime }+8 t x^{\prime }+5 x&=0 \\
x \left (1\right ) &= 2 \\
x^{\prime }\left (1\right ) &= 0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.972 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-5 y^{\prime } x +5 y&=0 \\
y \left (1\right ) &= -2 \\
y^{\prime }\left (1\right ) &= 1 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.678 |
|
| \begin{align*}
3 x^{2} z^{\prime \prime }+5 x z^{\prime }-z&=0 \\
z \left (1\right ) &= 2 \\
z^{\prime }\left (1\right ) &= -1 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.468 |
|
| \begin{align*}
t^{2} x^{\prime \prime }+3 t x^{\prime }+13 x&=0 \\
x \left (1\right ) &= -1 \\
x^{\prime }\left (1\right ) &= 2 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
2.430 |
|
| \begin{align*}
a y^{\prime \prime }+\left (b -a \right ) y^{\prime }+c y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
1.190 |
|
| \begin{align*}
n \left (n +1\right ) y-2 y^{\prime } x +\left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} Series expansion around \(x=0\). |
[_Gegenbauer] |
✓ |
✓ |
✓ |
✓ |
0.575 |
|
| \begin{align*}
y^{\prime \prime }-y^{\prime } x +y&=0 \\
\end{align*} Series expansion around \(x=0\). | [_Hermite] | ✓ | ✓ | ✓ | ✓ | 0.340 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime \prime }+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.416 |
|
| \begin{align*}
2 y^{\prime \prime } x +y^{\prime }-2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
0.788 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime } x -4 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.426 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime } x +4 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.394 |
|
| \begin{align*}
-y-3 y^{\prime } x +\left (1-x \right ) x y^{\prime \prime }&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
3.122 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x -x^{2} y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.540 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[_Bessel] |
✓ |
✓ |
✓ |
✓ |
2.658 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (-n^{2}+x^{2}\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[_Bessel] |
✓ |
✓ |
✓ |
✗ |
0.759 |
|
| \begin{align*}
x^{\prime }&=4 x-y \\
y^{\prime }&=2 x+y+t^{2} \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 1 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.725 |
|
| \begin{align*}
x^{\prime }&=x-4 y+\cos \left (2 t \right ) \\
y^{\prime }&=x+y \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 1 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.996 |
|
| \begin{align*}
x^{\prime }&=2 x+2 y \\
y^{\prime }&=6 x+3 y+{\mathrm e}^{t} \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 1 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.707 |
|
| \begin{align*}
x^{\prime }&=5 x-4 y+{\mathrm e}^{3 t} \\
y^{\prime }&=x+y \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= -1 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.644 |
|
| \begin{align*}
x^{\prime }&=2 x+5 y \\
y^{\prime }&=-2 x+\cos \left (3 t \right ) \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 2 \\
y \left (0\right ) &= -1 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.486 |
|
| \begin{align*}
x^{\prime }&=x+y+{\mathrm e}^{-t} \\
y^{\prime }&=4 x-2 y+{\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 |
✓ |
✓ |
✓ |
✓ |
0.802 |
|
| \begin{align*}
x^{\prime }&=8 x+14 y \\
y^{\prime }&=7 x+y \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 1 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.454 |
|
| \(\left [\begin {array}{cc} 2 & 2 \\ 0 & -4 \end {array}\right ]\) |
Eigenvectors |
✓ |
N/A |
N/A |
N/A |
0.258 |
|
| \(\left [\begin {array}{cc} 7 & -2 \\ 26 & -1 \end {array}\right ]\) |
Eigenvectors |
✓ |
N/A |
N/A |
N/A |
0.347 |
|
| \(\left [\begin {array}{cc} 9 & 2 \\ 2 & 6 \end {array}\right ]\) |
Eigenvectors |
✓ |
N/A |
N/A |
N/A |
0.273 |
|
| \(\left [\begin {array}{cc} 7 & 1 \\ -4 & 11 \end {array}\right ]\) |
Eigenvectors |
✓ |
N/A |
N/A |
N/A |
0.151 |
|
| \(\left [\begin {array}{cc} 2 & -3 \\ 3 & 2 \end {array}\right ]\) |
Eigenvectors |
✓ |
N/A |
N/A |
N/A |
0.270 |
|
| \(\left [\begin {array}{cc} 6 & 0 \\ 0 & -13 \end {array}\right ]\) |
Eigenvectors |
✓ |
N/A |
N/A |
N/A |
0.259 |
|
| \(\left [\begin {array}{cc} 4 & -2 \\ 1 & 2 \end {array}\right ]\) |
Eigenvectors |
✓ |
N/A |
N/A |
N/A |
0.344 |
|
| \(\left [\begin {array}{cc} 3 & -1 \\ 1 & 1 \end {array}\right ]\) | Eigenvectors | ✓ | N/A | N/A | N/A | 0.173 |
|
| \(\left [\begin {array}{cc} -7 & 6 \\ 12 & -1 \end {array}\right ]\) |
Eigenvectors |
✓ |
N/A |
N/A |
N/A |
0.300 |
|
| \begin{align*}
x^{\prime }&=8 x+14 y \\
y^{\prime }&=7 x+y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.392 |
|