| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
x^{4} y^{\prime \prime \prime \prime }+4 x^{3} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }+y^{\prime } x -y&=-\ln \left (x \right ) \\
\end{align*} Series expansion around \(x=0\). |
[[_high_order, _exact, _linear, _nonhomogeneous]] |
✗ |
✗ |
✓ |
✗ |
0.061 |
|
| \begin{align*}
y^{\prime \prime } x +\left (1-x \right ) y^{\prime }+y p&=0 \\
\end{align*} Series expansion around \(x=0\). |
[_Laguerre] |
✓ |
✓ |
✓ |
✓ |
1.223 |
|
| \begin{align*}
y^{\prime }-5 y&=0 \\
y \left (0\right ) &= 2 \\
\end{align*} Using Laplace transform method. |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.282 |
|
| \begin{align*}
y^{\prime }-5 y&=0 \\
y \left (\pi \right ) &= 2 \\
\end{align*} Using Laplace transform method. |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.237 |
|
| \begin{align*}
y^{\prime }-5 y&={\mathrm e}^{5 t} \\
y \left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
0.239 |
|
| \begin{align*}
y+y^{\prime }&=t \\
y \left (0\right ) &= 1 \\
\end{align*} Using Laplace transform method. |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
0.378 |
|
| \begin{align*}
-2 y+y^{\prime }&={\mathrm e}^{5 t} \\
y \left (0\right ) &= 3 \\
\end{align*} Using Laplace transform method. |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
0.350 |
|
| \begin{align*}
y+y^{\prime }&=\sin \left (t \right ) \\
y \left (0\right ) &= 1 \\
\end{align*} Using Laplace transform method. |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
0.430 |
|
| \begin{align*}
y^{\prime }+2 y&=\cos \left (t \right ) \\
y \left (0\right ) &= 1 \\
\end{align*} Using Laplace transform method. |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
0.411 |
|
| \begin{align*}
y^{\prime }+b y&=1 \\
y \left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.348 |
|
| \begin{align*}
y^{\prime }+2 y&={\mathrm e}^{-t} \\
y \left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
0.336 |
|
| \begin{align*}
y^{\prime \prime }+y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.278 |
|
| \begin{align*}
y^{\prime \prime }+4 y&=0 \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.316 |
|
| \begin{align*}
y^{\prime \prime }+4 y^{\prime }+8 y&=\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]] |
✓ |
✓ |
✓ |
✓ |
0.482 |
|
| \begin{align*}
y^{\prime \prime }-3 y^{\prime }+2 y&={\mathrm e}^{-t} \\
y \left (1\right ) &= 0 \\
y^{\prime }\left (1\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.458 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }+y&=t \\
y \left (0\right ) &= -3 \\
y \left (1\right ) &= -1 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.402 |
|
| \begin{align*}
y^{\prime \prime }+y&=\left \{\begin {array}{cc} 0 & t <1 \\ 2 & 1\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]] | ✓ | ✓ | ✓ | ✓ | 2.787 |
|
| \begin{align*}
y^{\prime \prime }-3 y^{\prime }+2 y&=\left \{\begin {array}{cc} 0 & t <6 \\ 1 & 6\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]] |
✓ |
✓ |
✓ |
✓ |
2.552 |
|
| \begin{align*}
y^{\prime \prime }+4 y&=\left \{\begin {array}{cc} 4 t & 0\le t \le 1 \\ 4 & 1<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]] |
✓ |
✓ |
✓ |
✓ |
5.168 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }+5 y&=\left \{\begin {array}{cc} 1 & 0\le t <\pi \\ 0 & \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]] |
✓ |
✓ |
✓ |
✗ |
5.936 |
|
| \begin{align*}
y^{\prime \prime \prime }+y^{\prime }&={\mathrm e}^{t} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
y^{\prime \prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.461 |
|
| \begin{align*}
y^{\prime \prime \prime }+4 y^{\prime \prime }+5 y^{\prime }+2 y&=10 \cos \left (t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
y^{\prime \prime }\left (0\right ) &= 3 \\
\end{align*} Using Laplace transform method. |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.530 |
|
| \begin{align*}
x^{\prime }-6 x+3 y&=8 \,{\mathrm e}^{t} \\
y^{\prime }-2 x-y&=4 \,{\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 |
✓ |
✓ |
✓ |
✓ |
0.483 |
|
| \begin{align*}
y^{\prime }+z&=t \\
z^{\prime }+4 y&=0 \\
\end{align*} With initial conditions \begin{align*}
z \left (0\right ) &= -1 \\
y \left (0\right ) &= 1 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.458 |
|
| \begin{align*}
w^{\prime }+y&=\sin \left (t \right ) \\
y^{\prime }-z&={\mathrm e}^{t} \\
w+y+z^{\prime }&=1 \\
\end{align*} With initial conditions \begin{align*}
w \left (0\right ) &= 0 \\
z \left (0\right ) &= 1 \\
y \left (0\right ) &= 1 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✗ |
0.618 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }-3 y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (1\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.375 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }-3 y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (1\right ) &= 2 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.342 |
|
| \begin{align*}
4 y+y^{\prime \prime }&=0 \\
y \left (0\right ) &= 0 \\
y \left (\frac {\pi }{4}\right ) &= 7 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
7.242 |
|
| \begin{align*}
4 y+y^{\prime \prime }&=0 \\
y \left (0\right ) &= 4 \\
y \left (\pi \right ) &= 4 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✗ |
2.327 |
|
| \begin{align*}
4 y+y^{\prime \prime }&=0 \\
y \left (0\right ) &= 0 \\
y \left (L \right ) &= 7 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
2.780 |
|
| \begin{align*}
y^{\prime \prime }+y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.440 |
|
| \begin{align*}
\sqrt {1-y^{2}}+\left (x +2 y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
✓ |
✓ |
216.308 |
|
| \begin{align*}
y^{\prime }&=-\sqrt {1-y^{2}} \\
x^{\prime }&=x+2 y \\
\end{align*} |
system_of_ODEs |
✗ |
✓ |
✓ |
✓ |
0.051 |
|
| \begin{align*}
y^{\prime \prime } \cos \left (y\right )+\left (\cos \left (y\right )-y^{\prime } \sin \left (y\right )\right ) y^{\prime }-2 y x&=0 \\
\end{align*} |
[NONE] |
✗ |
✗ |
✗ |
✗ |
0.911 |
|
| \begin{align*}
x^{\prime }&=8 x-y \\
y^{\prime }&=4 x+12 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.473 |
|
| \begin{align*}
x^{\prime }&=y \\
y^{\prime }&=-4 x+4 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.457 |
|
| \begin{align*}
x^{\prime }&=2 x-5 y \\
y^{\prime }&=2 x-4 y \\
\end{align*} | system_of_ODEs | ✓ | ✓ | ✓ | ✓ | 0.723 |
|
| \begin{align*}
x^{\prime }&=2 x+2 y-z \\
y^{\prime }&=y+z \\
z^{\prime }&=z-y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.010 |
|
| \begin{align*}
x^{\prime }&=x+y \\
y^{\prime }&=9 x+y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.555 |
|
| \begin{align*}
x^{\prime }&=x+2 y \\
y^{\prime }&=4 x+3 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.530 |
|
| \begin{align*}
x^{\prime }&=7 x-y+6 z \\
y^{\prime }&=-10 x+4 y-12 z \\
z^{\prime }&=-2 x+y-z \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.970 |
|
| \begin{align*}
x+y^{\prime }&=\sin \left (t \right )+\cos \left (t \right ) \\
x^{\prime }+y&=\cos \left (t \right )-\sin \left (t \right ) \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.098 |
|
| \begin{align*}
x^{\prime }&=y \\
y^{\prime }&=-2 x+3 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.504 |
|
| \begin{align*}
x^{\prime }&=3 x+2 y \\
y^{\prime }&=-5 x+y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.727 |
|
| \begin{align*}
x^{\prime }&=4 x-y \\
y^{\prime }&=x+2 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.431 |
|
| \begin{align*}
x^{\prime }&=6 x-3 y \\
y^{\prime }&=2 x+y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.539 |
|
| \begin{align*}
2 x^{\prime }-3 y^{\prime }&=2 \,{\mathrm e}^{2 t} \\
x^{\prime }-2 y^{\prime }&=0 \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 1 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.520 |
|
| \begin{align*}
y^{\prime }&=y-3 z \\
z^{\prime }&=2 y-4 z \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.526 |
|
| \begin{align*}
x^{\prime }&=4 x-y \\
y^{\prime }&=-4 x+4 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.552 |
|
| \begin{align*}
x^{\prime }&=7 x-y+6 z \\
y^{\prime }&=-10 x+4 y-12 z \\
z^{\prime }&=-2 x+y-z \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.907 |
|
| \begin{align*}
x^{\prime }&=3 x+y-z \\
y^{\prime }&=x+3 y-z \\
z^{\prime }&=3 x+3 y-z \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.738 |
|
| \begin{align*}
x^{\prime }&=x-y-z \\
y^{\prime }&=y+3 z \\
z^{\prime }&=3 y+z \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.787 |
|
| \begin{align*}
x^{\prime }&=y+{\mathrm e}^{t} \\
y^{\prime }&=-2 x+3 y+1 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.798 |
|
| \begin{align*}
x^{\prime }&=2 x-y-5 t \\
y^{\prime }&=3 x+6 y-4 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.346 |
|
| \begin{align*}
x^{\prime }&=2 x+y+3 \,{\mathrm e}^{2 t} \\
y^{\prime }&=-4 x+2 y+{\mathrm e}^{2 t} t \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.041 |
|
| \begin{align*}
2 x^{4} y y^{\prime }+y^{4}&=4 x^{6} \\
\end{align*} | [[_homogeneous, ‘class G‘], _rational] | ✓ | ✓ | ✓ | ✗ | 71.490 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime \prime }+1+{y^{\prime }}^{2}&=0 \\
\end{align*} |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
✓ |
✓ |
✓ |
1.136 |
|
| \begin{align*}
{y^{\prime \prime }}^{2} x^{2} \left (x^{2}-1\right )-1&=0 \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
2.686 |
|
| \begin{align*}
y^{\prime \prime } x -{y^{\prime }}^{3}-y^{\prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
✓ |
✓ |
✓ |
3.703 |
|
| \begin{align*}
y^{\prime }&=y^{\prime \prime } x +{y^{\prime \prime }}^{2} \\
y \left (-1\right ) &= 0 \\
y^{\prime }\left (-1\right ) &= 2 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✗ |
0.720 |
|
| \begin{align*}
2 y y^{\prime \prime }&=1+{y^{\prime }}^{2} \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
✓ |
✗ |
53.965 |
|
| \begin{align*}
2 y y^{\prime \prime }&={y^{\prime }}^{2} \\
\end{align*} |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✗ |
6.882 |
|
| \begin{align*}
y^{\prime \prime }&={\mathrm e}^{y} y^{\prime } \\
y \left (0\right ) &= -1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✗ |
✗ |
13.501 |
|
| \begin{align*}
y^{\prime \prime }-\frac {2 {y^{\prime }}^{2}}{y}-y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✗ |
37.560 |
|
| \begin{align*}
1+{y^{\prime }}^{2}+y y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✗ |
50.521 |
|
| \begin{align*}
x&=y-{y^{\prime }}^{2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
3.065 |
|
| \begin{align*}
y&=2 y^{\prime } x -{y^{\prime }}^{2} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
0.807 |
|
| \begin{align*}
y&=2 x +y^{\prime }-\frac {{y^{\prime }}^{3}}{3} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
133.033 |
|
| \begin{align*}
y {y^{\prime }}^{2}-2 y^{\prime } x +y&=0 \\
\end{align*} | [[_homogeneous, ‘class A‘], _rational, _dAlembert] | ✓ | ✓ | ✓ | ✓ | 1.056 |
|
| \begin{align*}
x {y^{\prime }}^{2}-3 y^{\prime } y+9 x^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✗ |
17.309 |
|
| \begin{align*}
y^{\prime } \left (y^{\prime }+y\right )&=x \left (x +y\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
0.307 |
|
| \begin{align*}
x^{2} {y^{\prime }}^{2}+4 x y^{\prime } y+3 y^{2}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.182 |
|
| \begin{align*}
x y {y^{\prime }}^{2}+\left (x +y\right ) y^{\prime }+1&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.369 |
|
| \begin{align*}
y {y^{\prime }}^{2}-\left (y x +x +y^{2}\right ) y^{\prime }+x^{2}+y x&=0 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✗ |
✗ |
0.352 |
|
| \begin{align*}
2 {y^{\prime }}^{2}-2 y^{\prime } y-1&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.950 |
|
| \begin{align*}
\left ({y^{\prime }}^{2}-y^{2}\right ) {\mathrm e}^{y^{\prime }}-x {y^{\prime }}^{2}+x y^{2}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.091 |
|
| \begin{align*}
x^{\prime }&=2 x-7 y \\
y^{\prime }&=3 x-8 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.548 |
|
| \begin{align*}
x^{\prime }&=2 x+4 y \\
y^{\prime }&=-2 x+6 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.768 |
|
| \begin{align*}
x^{\prime }&=x+4 y-y^{2} \\
y^{\prime }&=6 x-y+2 x y \\
\end{align*} |
system_of_ODEs |
✗ |
✗ |
✗ |
✗ |
0.061 |
|
| \begin{align*}
x^{\prime }&=\sin \left (x\right )-4 y \\
y^{\prime }&=\sin \left (2 x\right )-5 y \\
\end{align*} |
system_of_ODEs |
✗ |
✗ |
✗ |
✗ |
0.061 |
|
| \begin{align*}
x^{\prime }&=8 x-y^{2} \\
y^{\prime }&=6 x^{2}-6 y \\
\end{align*} |
system_of_ODEs |
✗ |
✗ |
✗ |
✗ |
0.064 |
|
| \begin{align*}
x^{\prime }&=-x^{2}-y \\
y^{\prime }&=x \\
\end{align*} |
system_of_ODEs |
✗ |
✓ |
✓ |
✗ |
0.058 |
|
| \begin{align*}
x^{\prime }&=-x^{3}-y \\
y^{\prime }&=x \\
\end{align*} |
system_of_ODEs |
✗ |
✗ |
✗ |
✗ |
0.056 |
|
| \begin{align*}
x^{\prime }&=2 x y \\
y^{\prime }&=3 y^{2}-x^{2} \\
\end{align*} |
system_of_ODEs |
✗ |
✓ |
✓ |
✗ |
0.058 |
|
| \begin{align*}
x^{\prime }&=x^{2} \\
y^{\prime }&=2 y^{2}-x y \\
\end{align*} |
system_of_ODEs |
✗ |
✓ |
✓ |
✓ |
0.058 |
|
| \begin{align*}
x^{\prime }&=-x+y^{2} \\
y^{\prime }&=x^{2}-y \\
\end{align*} |
system_of_ODEs |
✗ |
✓ |
✗ |
✗ |
0.062 |
|
| \begin{align*}
x^{\prime \prime }&=4 x^{3}-4 x \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
✓ |
✗ |
5.672 |
|
| \begin{align*}
x^{\prime \prime }+\sin \left (x\right )&=0 \\
\end{align*} | [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] | ✓ | ✓ | ✓ | ✗ | 49.154 |
|
| \begin{align*}
x^{\prime \prime }&=x^{2}-4 x+\lambda \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
✓ |
✗ |
102.660 |
|
| \begin{align*}
y^{\prime } x&=x +2 y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.037 |
|
| \begin{align*}
y^{\prime } y+x&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
22.436 |
|
| \begin{align*}
y^{\prime \prime }+y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
1.678 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }&=6 y+5 \,{\mathrm e}^{2 x} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.539 |
|
| \begin{align*}
y^{\prime }+y&=2 \,{\mathrm e}^{-x} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
36.431 |
|
| \begin{align*}
y^{\prime }&=-\frac {x}{4 y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
9.153 |
|
| \begin{align*}
y^{\prime }&=\frac {x}{y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
26.850 |
|
| \begin{align*}
3 x^{2}-2 y^{3} y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
11.879 |
|
| \begin{align*}
1+y+y^{2}+x \left (x^{2}-4\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
38.114 |
|
| \begin{align*}
r^{\prime } \sin \left (t \right )+r \cos \left (t \right )&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.425 |
|
| \begin{align*}
x^{3} y^{\prime }-x^{3}&=1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.548 |
|