| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
y^{\prime \prime }+y x&=0 \\
\end{align*} Series expansion around \(x=\infty \). |
[[_Emden, _Fowler]] |
✗ |
✗ |
✓ |
✓ |
0.160 |
|
| \begin{align*}
x^{2} \left (x -2\right ) y^{\prime \prime }+4 \left (x -2\right ) y^{\prime }+3 y&=0 \\
\end{align*} Series expansion around \(x=\infty \). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
5.746 |
|
| \begin{align*}
4 y^{\prime \prime } x +2 y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
0.843 |
|
| \begin{align*}
y^{\prime \prime }+\frac {y}{4 x^{2}}&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.459 |
|
| \begin{align*}
y^{\prime \prime } x +2 y^{\prime }+y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
[_Lienard] |
✓ |
✓ |
✓ |
✓ |
0.666 |
|
| \begin{align*}
y^{\prime \prime }+\frac {y^{\prime }}{2 x}-\frac {\left (x +1\right ) y}{2 x^{2}}&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.758 |
|
| \begin{align*}
4 x^{2} y^{\prime \prime }+4 y^{\prime } x +\left (4 x^{2}-1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.683 |
|
| \begin{align*}
2 x \left (x +1\right ) y^{\prime \prime }+3 \left (x +1\right ) y^{\prime }-y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.814 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-x \left (x +1\right ) y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.627 |
|
| \begin{align*}
y^{\prime \prime } x -\left (x +4\right ) y^{\prime }+2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[_Laguerre] |
✓ |
✓ |
✓ |
✗ |
0.883 |
|
| \begin{align*}
2 n y-2 y^{\prime } x +y^{\prime \prime }&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.465 |
|
| \begin{align*}
y^{\prime \prime }-y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.285 |
|
| \begin{align*}
y^{\prime \prime }-5 y^{\prime }+6 y&=0 \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.275 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }+5 y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.230 |
|
| \begin{align*}
y^{\prime \prime }-y&={\mathrm e}^{2 t} t \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.261 |
|
| \begin{align*}
y^{\prime \prime }-3 y^{\prime }-4 y&=t^{2} \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.260 |
|
| \begin{align*}
y^{\prime \prime }-3 y^{\prime }-2 y&={\mathrm e}^{t} \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. | [[_2nd_order, _with_linear_symmetries]] | ✓ | ✓ | ✓ | ✓ | 0.306 |
|
| \begin{align*}
y^{\prime \prime }+4 y&=\delta \left (-1+t \right ) \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
2.009 |
|
| \begin{align*}
y^{\prime \prime }-4 y^{\prime }+13 y&=\delta \left (-1+t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
2.788 |
|
| \begin{align*}
y^{\prime \prime }+6 y^{\prime }+18 y&=2 \operatorname {Heaviside}\left (\pi -t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
4.218 |
|
| \begin{align*}
x^{\prime }&=2 x+3 y+2 \sin \left (2 t \right ) \\
y^{\prime }&=-3 x+2 y \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.346 |
|
| \begin{align*}
x^{\prime }&=-4 x-y+{\mathrm e}^{-t} \\
y^{\prime }&=x-2 y+2 \,{\mathrm e}^{-3 t} \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 2 \\
y \left (0\right ) &= -1 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.300 |
|
| \begin{align*}
x^{\prime }&=x-y+2 \cos \left (t \right ) \\
y^{\prime }&=x+y+3 \sin \left (t \right ) \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 3 \\
y \left (0\right ) &= 2 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.304 |
|
| \begin{align*}
x^{\prime }&=-4 x-y \\
y^{\prime }&=x-2 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.348 |
|
| \begin{align*}
x^{\prime }&=3 x \\
y^{\prime }&=-2 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.314 |
|
| \begin{align*}
x^{\prime }&=-y \\
y^{\prime }&=-5 x \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.484 |
|
| \begin{align*}
x^{\prime }&=2 y \\
y^{\prime }&=-3 x \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.501 |
|
| \begin{align*}
x^{\prime }&=x-y \\
y^{\prime }&=y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.307 |
|
| \begin{align*}
x^{\prime }&=2 x+3 y \\
y^{\prime }&=-3 x+2 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.454 |
|
| \begin{align*}
x^{\prime }&=3 x-y \\
y^{\prime }&=2 x-2 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.636 |
|
| \begin{align*}
x^{\prime }&=-y \\
y^{\prime }&=-5 x \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.432 |
|
| \begin{align*}
x^{\prime }&=x-y \\
y^{\prime }&=y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.292 |
|
| \begin{align*}
x^{\prime }&=2 x+3 y \\
y^{\prime }&=-3 x+2 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.411 |
|
| \begin{align*}
x^{\prime }&=-4 x-y \\
y^{\prime }&=x-2 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.353 |
|
| \begin{align*}
x^{\prime }&=x-y \\
y^{\prime }&=x+y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.417 |
|
| \begin{align*}
x^{\prime }&=x \\
y^{\prime }&=-2 x+2 y \\
\end{align*} | system_of_ODEs | ✓ | ✓ | ✓ | ✓ | 0.376 |
|
| \begin{align*}
x^{\prime }&=12 x-15 y \\
y^{\prime }&=4 x-4 y \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.475 |
|
| \begin{align*}
x^{\prime }&=2 x-y \\
y^{\prime }&=5 x-2 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.457 |
|
| \begin{align*}
x^{\prime }&=4 x-13 y \\
y^{\prime }&=2 x-6 y \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 2 \\
y \left (0\right ) &= 0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.607 |
|
| \begin{align*}
x^{\prime }&=4 x+2 y \\
y^{\prime }&=3 x+3 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.425 |
|
| \begin{align*}
x^{\prime }&=3 x+5 y \\
y^{\prime }&=-x+y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.611 |
|
| \begin{align*}
x^{\prime }&=8 x-5 y \\
y^{\prime }&=16 x+8 y \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= -1 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.580 |
|
| \begin{align*}
x^{\prime }&=x-2 y \\
y^{\prime }&=2 x-3 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.352 |
|
| \begin{align*}
x^{\prime }&=5 x+4 y+2 z \\
y^{\prime }&=4 x+5 y+2 z \\
z^{\prime }&=2 x+2 y+2 z \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.642 |
|
| \begin{align*}
x^{\prime }&=2 x-y+{\mathrm e}^{t} \\
y^{\prime }&=3 x-2 y+t \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 2 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.942 |
|
| \begin{align*}
x^{\prime }&=5 x+3 y+1 \\
y^{\prime }&=-6 x-4 y+{\mathrm e}^{t} \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.708 |
|
| \begin{align*}
x^{\prime }&=2 x-y+\cos \left (t \right ) \\
y^{\prime }&=5 x-2 y+\sin \left (t \right ) \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 1 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.979 |
|
| \begin{align*}
y^{\prime }&=k y-c y^{2} \\
y \left (0\right ) &= y_{0} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
12.358 |
|
| \begin{align*}
y^{\prime }&=y^{2}-6 y-16 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.474 |
|
| \begin{align*}
y^{\prime }&=\cos \left (y\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
21.076 |
|
| \begin{align*}
y^{\prime }&=y \left (y-2\right ) \left (3+y\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
3.166 |
|
| \begin{align*}
y^{\prime }&=y^{2} \left (1+y\right ) \left (y-4\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
53.354 |
|
| \begin{align*}
y^{\prime }&=y-y^{2} \\
y \left (0\right ) &= y_{0} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.404 |
|
| \begin{align*}
y^{\prime }&=y-y^{2} \\
y \left (0\right ) &= {\frac {1}{4}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.858 |
|
| \begin{align*}
y^{\prime }&=y-y^{2} \\
y \left (0\right ) &= {\frac {3}{2}} \\
\end{align*} | [_quadrature] | ✓ | ✓ | ✓ | ✓ | 2.091 |
|
| \begin{align*}
y^{\prime }&=y-y^{2} \\
y \left (0\right ) &= -{\frac {1}{2}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.696 |
|
| \begin{align*}
y^{\prime }&=y-\mu y^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.851 |
|
| \begin{align*}
y^{\prime }&=y \left (\mu -y\right ) \left (\mu -2 y\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
74.530 |
|
| \begin{align*}
x^{\prime }&=\mu -x^{3} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
7.087 |
|
| \begin{align*}
x^{\prime }&=x-\frac {\mu x}{1+x^{2}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
25.166 |
|
| \begin{align*}
x^{\prime }&=x^{3}+a x^{2}-b x \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
57.283 |
|
| \begin{align*}
y^{\prime }&=\frac {1+y}{2+x}-{\mathrm e}^{\frac {1+y}{2+x}} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
32.688 |
|
| \begin{align*}
y^{\prime }&=\frac {1+y}{2+x}+{\mathrm e}^{\frac {1+y}{2+x}} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
14.630 |
|
| \begin{align*}
y^{\prime }&=\frac {x +y+1}{2+x}-{\mathrm e}^{\frac {x +y+1}{2+x}} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
29.241 |
|
| \begin{align*}
y^{\prime }&=\frac {x +2 y+1}{2 x +2+y} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
75.780 |
|
| \begin{align*}
y^{\prime }&=\frac {2 x +y+1}{x +2 y+2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
53.541 |
|
| \begin{align*}
y^{\prime }&=3 y^{{2}/{3}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
3.037 |
|
| \begin{align*}
y^{\prime }&=\sqrt {y \left (1-y\right )} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
7.750 |
|
| \begin{align*}
y^{\prime }&=\frac {{\mathrm e}^{-y^{2}}}{y \left (x^{2}+2 x \right )} \\
y \left (2\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
17.857 |
|
| \begin{align*}
y^{\prime }&=\frac {y \ln \left (y\right )}{\sin \left (x \right )} \\
y \left (\frac {\pi }{2}\right ) &= {\mathrm e}^{{\mathrm e}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
29.682 |
|
| \begin{align*}
y^{\prime }&=\frac {\cos \left (x \right )}{\cos \left (y\right )^{2}} \\
y \left (\pi \right ) &= \frac {\pi }{4} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.147 |
|
| \begin{align*}
y^{\prime }&=\left (x -y+3\right )^{2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
✓ |
✓ |
✓ |
9.120 |
|
| \begin{align*}
y^{\prime }&=\frac {2 y \left (y-1\right )}{x \left (2-y\right )} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
75.521 |
|
| \begin{align*}
y&=y^{\prime } x -\sqrt {y^{2}+x^{2}} \\
\end{align*} | [[_homogeneous, ‘class A‘], _rational, _dAlembert] | ✓ | ✓ | ✓ | ✓ | 165.532 |
|
| \begin{align*}
y^{\prime }&=f \left (x \right ) y \ln \left (\frac {1}{y}\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
14.245 |
|
| \begin{align*}
y^{\prime }-y+y^{2} {\mathrm e}^{x}+5 \,{\mathrm e}^{-x}&=0 \\
y \left (0\right ) &= \eta \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Riccati] |
✓ |
✓ |
✓ |
✓ |
14.710 |
|
| \begin{align*}
\cos \left (x +y^{2}\right )+3 y+\left (2 y \cos \left (x +y^{2}\right )+3 x \right ) y^{\prime }&=0 \\
\end{align*} |
[_exact] |
✓ |
✓ |
✓ |
✗ |
19.078 |
|
| \begin{align*}
x y^{2}-y^{3}+\left (1-x y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[_rational] |
✓ |
✓ |
✓ |
✓ |
10.027 |
|
| \begin{align*}
\left (y x +1\right ) y&=y^{\prime } x \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
7.368 |
|
| \begin{align*}
y^{\prime }+p \left (x \right ) y&=q \left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.407 |
|
| \begin{align*}
y&=y^{\prime } x -\sqrt {y^{\prime }-1} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✗ |
0.986 |
|
| \begin{align*}
y&=y^{\prime } x +{y^{\prime }}^{2} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✓ |
0.233 |
|
| \begin{align*}
y&=y^{\prime } x +a y^{\prime }+b \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
8.400 |
|
| \begin{align*}
y&=x {y^{\prime }}^{2}+\ln \left ({y^{\prime }}^{2}\right ) \\
\end{align*} |
[_dAlembert] |
✓ |
✓ |
✓ |
✗ |
53.731 |
|
| \begin{align*}
x&=y \left (y^{\prime }+\frac {1}{y^{\prime }}\right )+{y^{\prime }}^{5} \\
\end{align*} |
[_dAlembert] |
✓ |
✓ |
✓ |
✗ |
1.155 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{x}+x \cos \left (y\right ) \\
y \left (0\right ) &= 0 \\
\end{align*} Series expansion around \(x=0\). |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✓ |
✓ |
0.904 |
|
| \begin{align*}
y^{\prime }&=x^{3}+y^{3} \\
y \left (0\right ) &= 1 \\
\end{align*} Series expansion around \(x=0\). |
[_Abel] |
✓ |
✓ |
✓ |
✓ |
0.168 |
|
| \begin{align*}
u^{\prime }&=u^{3} \\
u \left (0\right ) &= 1 \\
\end{align*} Series expansion around \(x=0\). |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.132 |
|
| \begin{align*}
y^{\prime }&=x^{3}+y^{3} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_Abel] |
✗ |
✗ |
✗ |
✗ |
28.991 |
|
| \begin{align*}
y^{\prime }&=x +\sqrt {1+y^{2}} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✓ |
✗ |
327.753 |
|
| \begin{align*}
x^{\prime }&=x \cos \left (t \right )-\sin \left (t \right ) y \\
y^{\prime }&=x \sin \left (t \right )+y \cos \left (t \right ) \\
\end{align*} |
system_of_ODEs |
✗ |
✓ |
✓ |
✓ |
0.052 |
|
| \begin{align*}
x^{\prime }&=\left (3 t -1\right ) x-\left (1-t \right ) y+t \,{\mathrm e}^{t^{2}} \\
y^{\prime }&=-\left (t +2\right ) x+\left (t -2\right ) y-{\mathrm e}^{t^{2}} \\
\end{align*} | system_of_ODEs | ✗ | ✓ | ✓ | ✗ | 0.037 |
|
| \begin{align*}
x^{\prime }&=2 x-4 y \\
y^{\prime }&=-x+2 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.404 |
|
| \begin{align*}
x^{\prime }&=3 x+6 y \\
y^{\prime }&=-2 x-3 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.083 |
|
| \begin{align*}
x^{\prime }&=8 x+y \\
y^{\prime }&=-4 x+4 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.367 |
|
| \begin{align*}
x^{\prime }&=x-y+2 z \\
y^{\prime }&=-x+y+2 z \\
z^{\prime }&=x+y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.607 |
|
| \begin{align*}
x^{\prime }&=-x+y-z \\
y^{\prime }&=2 x-y+2 z \\
z^{\prime }&=2 x+2 y-z \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.711 |
|
| \begin{align*}
y^{\prime \prime }+4 y^{\prime }+4 y&={\mathrm e}^{x} \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.623 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime }+5 y&={\mathrm e}^{x} \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.732 |
|
| \begin{align*}
u^{\prime \prime }+2 a u^{\prime }+\omega ^{2} u&=c \cos \left (\omega t \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.920 |
|