| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
\pi y \sin \left (x \right ) y^{\prime }&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.158 |
|
| \begin{align*}
x \sin \left (x \right ) y^{\prime }&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.477 |
|
| \begin{align*}
x \sin \left (x \right ) {y^{\prime }}^{2}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.396 |
|
| \begin{align*}
y {y^{\prime }}^{2}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.294 |
|
| \begin{align*}
{y^{\prime }}^{n}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
0.511 |
|
| \begin{align*}
x {y^{\prime }}^{n}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
0.576 |
|
| \begin{align*}
{y^{\prime }}^{2}&=x \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.931 |
|
| \begin{align*}
{y^{\prime }}^{2}&=x +y \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.336 |
|
| \begin{align*}
{y^{\prime }}^{2}&=\frac {y}{x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
2.657 |
|
| \begin{align*}
{y^{\prime }}^{2}&=\frac {y^{2}}{x} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.021 |
|
| \begin{align*}
{y^{\prime }}^{2}&=\frac {y^{3}}{x} \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✓ |
10.283 |
|
| \begin{align*}
{y^{\prime }}^{3}&=\frac {y^{2}}{x} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
79.026 |
|
| \begin{align*}
{y^{\prime }}^{2}&=\frac {1}{y x} \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✓ |
16.381 |
|
| \begin{align*}
{y^{\prime }}^{2}&=\frac {1}{x y^{3}} \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✓ |
13.224 |
|
| \begin{align*}
{y^{\prime }}^{2}&=\frac {1}{x^{2} y^{3}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
1.330 |
|
| \begin{align*}
{y^{\prime }}^{4}&=\frac {1}{x y^{3}} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✗ |
21.702 |
|
| \begin{align*}
{y^{\prime }}^{2}&=\frac {1}{x^{3} y^{4}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.148 |
|
| \begin{align*}
y^{\prime }&=\sqrt {1+6 x +y} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
4.395 |
|
| \begin{align*}
y^{\prime }&=\left (1+6 x +y\right )^{{1}/{3}} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
2.848 |
|
| \begin{align*}
y^{\prime }&=\left (1+6 x +y\right )^{{1}/{4}} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
5.260 |
|
| \begin{align*}
y^{\prime }&=\left (a +b x +y\right )^{4} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
1.177 |
|
| \begin{align*}
y^{\prime }&=\left (\pi +x +7 y\right )^{{7}/{2}} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
38.938 |
|
| \begin{align*}
y^{\prime }&=\left (a +b x +c y\right )^{6} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
6.796 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{x +y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.362 |
|
| \begin{align*}
y^{\prime }&=10+{\mathrm e}^{x +y} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
2.069 |
|
| \begin{align*}
y^{\prime }&=10 \,{\mathrm e}^{x +y}+x^{2} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
2.180 |
|
| \begin{align*}
y^{\prime }&=x \,{\mathrm e}^{x +y}+\sin \left (x \right ) \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
2.802 |
|
| \begin{align*}
y^{\prime }&=5 \,{\mathrm e}^{x^{2}+20 y}+\sin \left (x \right ) \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
2.634 |
|
| \begin{align*}
x^{\prime }+y^{\prime }-x&=t +y \\
x^{\prime }+y^{\prime }&=2 x+3 y+{\mathrm e}^{t} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✗ |
0.175 |
|
| \begin{align*}
2 x^{\prime }+y^{\prime }-x&=t +y \\
x^{\prime }+y^{\prime }&=2 x+3 y+{\mathrm e}^{t} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.277 |
|
| \begin{align*}
x^{\prime }+y^{\prime }-x&=y+t +\sin \left (t \right )+\cos \left (t \right ) \\
x^{\prime }+y^{\prime }&=2 x+3 y+{\mathrm e}^{t} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✗ |
0.244 |
|
| \begin{align*}
t y^{\prime }+y&=t \\
y \left (0\right ) &= 5 \\
\end{align*}
Using Laplace transform method. |
[_linear] |
✓ |
✓ |
✗ |
✓ |
0.398 |
|
| \begin{align*}
y^{\prime }-y t&=0 \\
y \left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.379 |
|
| \begin{align*}
t y^{\prime }+y&=0 \\
y \left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.276 |
|
| \begin{align*}
t y^{\prime }+y&=0 \\
y \left (0\right ) &= y_{0} \\
\end{align*}
Using Laplace transform method. |
[_separable] |
✓ |
✓ |
✗ |
✓ |
0.268 |
|
| \begin{align*}
t y^{\prime }+y&=0 \\
y \left (x_{0} \right ) &= y_{0} \\
\end{align*}
Using Laplace transform method. |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.462 |
|
| \begin{align*}
t y^{\prime }+y&=0 \\
\end{align*}
Using Laplace transform method. |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.262 |
|
| \begin{align*}
t y^{\prime }+y&=0 \\
y \left (1\right ) &= 5 \\
\end{align*}
Using Laplace transform method. |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.427 |
|
| \begin{align*}
t y^{\prime }+y&=\sin \left (t \right ) \\
y \left (1\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[_linear] |
✓ |
✗ |
✓ |
✓ |
0.648 |
|
| \begin{align*}
t y^{\prime }+y&=t \\
y \left (1\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[_linear] |
✓ |
✓ |
✓ |
✓ |
0.474 |
|
| \begin{align*}
t y^{\prime }+y&=t \\
y \left (1\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
[_linear] |
✓ |
✓ |
✓ |
✓ |
0.471 |
|
| \begin{align*}
t^{2} y+y^{\prime }&=0 \\
y \left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.436 |
|
| \begin{align*}
\left (a t +1\right ) y^{\prime }+y&=t \\
y \left (1\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[_linear] |
✓ |
✓ |
✓ |
✗ |
0.503 |
|
| \begin{align*}
y^{\prime }+\left (a t +b t \right ) y&=0 \\
y \left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.313 |
|
| \begin{align*}
y^{\prime }+\left (a t +b t \right ) y&=0 \\
y \left (-3\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.350 |
|
| \begin{align*}
y^{\prime }+2 y x&=x \\
\end{align*}
Series expansion around \(x=0\). |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.437 |
|
| \begin{align*}
y^{\prime }+y&=\sin \left (x \right ) \\
\end{align*}
Series expansion around \(x=0\). |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
0.458 |
|
| \begin{align*}
x y^{\prime }+y&=0 \\
y \left (0\right ) &= 1 \\
\end{align*}
Series expansion around \(x=0\). |
[_separable] |
✗ |
✗ |
✗ |
✗ |
0.193 |
|
| \begin{align*}
x y^{\prime }+y&=x \\
\end{align*}
Series expansion around \(x=0\). |
[_linear] |
✓ |
✓ |
✓ |
✗ |
0.344 |
|
| \begin{align*}
x y^{\prime }+y&=1 \\
\end{align*}
Series expansion around \(x=0\). |
[_separable] |
✓ |
✓ |
✓ |
✗ |
0.339 |
|
| \begin{align*}
x y^{\prime }+y&=\sin \left (x \right ) \\
\end{align*}
Series expansion around \(x=0\). |
[_linear] |
✓ |
✓ |
✓ |
✗ |
0.411 |
|
| \begin{align*}
x y^{\prime }+y&=2 x^{4}+x^{3}+x \\
\end{align*}
Series expansion around \(x=0\). |
[_linear] |
✓ |
✓ |
✓ |
✗ |
0.393 |
|
| \begin{align*}
x y^{\prime }+y&=\frac {1}{x^{3}} \\
\end{align*}
Series expansion around \(x=0\). |
[_linear] |
✓ |
✓ |
✓ |
✗ |
0.328 |
|
| \begin{align*}
x y^{\prime }+2 y x&=\sqrt {x} \\
\end{align*}
Series expansion around \(x=0\). |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
0.628 |
|
| \begin{align*}
y^{\prime }+\frac {y}{x}&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[_separable] |
✓ |
✓ |
✓ |
✗ |
0.286 |
|
| \begin{align*}
\cos \left (x \right ) y^{\prime }+\frac {y}{x}&=x \\
\end{align*}
Series expansion around \(x=0\). |
[_linear] |
✓ |
✓ |
✗ |
✗ |
0.694 |
|
| \begin{align*}
\cos \left (x \right ) y^{\prime }+\frac {y}{x}&=x +\sin \left (x \right ) \\
\end{align*}
Series expansion around \(x=0\). |
[_linear] |
✓ |
✓ |
✗ |
✗ |
0.973 |
|
| \begin{align*}
x y^{\prime }+y&=\tan \left (x \right ) \\
\end{align*}
Series expansion around \(x=0\). |
[_linear] |
✓ |
✓ |
✓ |
✗ |
0.483 |
|
| \begin{align*}
x y^{\prime }+y&=\cos \left (x \right )+\sin \left (x \right ) \\
\end{align*}
Series expansion around \(x=0\). |
[_linear] |
✓ |
✓ |
✓ |
✗ |
0.471 |
|
| \begin{align*}
y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.595 |
|
| \begin{align*}
{y^{\prime \prime }}^{2}&=0 \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.707 |
|
| \begin{align*}
{y^{\prime \prime }}^{n}&=0 \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✗ |
0.385 |
|
| \begin{align*}
a y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.644 |
|
| \begin{align*}
a {y^{\prime \prime }}^{2}&=0 \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.797 |
|
| \begin{align*}
a {y^{\prime \prime }}^{n}&=0 \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✗ |
0.425 |
|
| \begin{align*}
y^{\prime \prime }&=1 \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.753 |
|
| \begin{align*}
{y^{\prime \prime }}^{2}&=1 \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.105 |
|
| \begin{align*}
y^{\prime \prime }&=x \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.783 |
|
| \begin{align*}
{y^{\prime \prime }}^{2}&=x \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
1.050 |
|
| \begin{align*}
{y^{\prime \prime }}^{3}&=0 \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.779 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
1.065 |
|
| \begin{align*}
{y^{\prime \prime }}^{2}+y^{\prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
170.677 |
|
| \begin{align*}
y^{\prime \prime }+{y^{\prime }}^{2}&=0 \\
\end{align*} |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✓ |
0.749 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }&=1 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
1.057 |
|
| \begin{align*}
{y^{\prime \prime }}^{2}+y^{\prime }&=1 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
4.801 |
|
| \begin{align*}
y^{\prime \prime }+{y^{\prime }}^{2}&=1 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✗ |
3.158 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }&=x \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.877 |
|
| \begin{align*}
{y^{\prime \prime }}^{2}+y^{\prime }&=x \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✗ |
0.816 |
|
| \begin{align*}
y^{\prime \prime }+{y^{\prime }}^{2}&=x \\
\end{align*} |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✗ |
1.033 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }+y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.375 |
|
| \begin{align*}
{y^{\prime \prime }}^{2}+y^{\prime }+y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✗ |
✗ |
✗ |
✗ |
0.063 |
|
| \begin{align*}
y^{\prime \prime }+{y^{\prime }}^{2}+y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✗ |
1.308 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }+y&=1 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.458 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }+y&=x \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.487 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }+y&=x +1 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.492 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }+y&=x^{2}+x +1 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.506 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }+y&=x^{3}+x^{2}+x +1 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.516 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }+y&=\sin \left (x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.497 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }+y&=\cos \left (x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.513 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }&=1 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
1.042 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }&=x \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.868 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }&=x +1 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.884 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }&=x^{2}+x +1 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.919 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }&=x^{3}+x^{2}+x +1 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.954 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }&=\sin \left (x \right ) \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.947 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }&=\cos \left (x \right ) \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.938 |
|
| \begin{align*}
y^{\prime \prime }+y&=1 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
2.011 |
|
| \begin{align*}
y^{\prime \prime }+y&=x \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.602 |
|
| \begin{align*}
y^{\prime \prime }+y&=x +1 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.602 |
|
| \begin{align*}
y^{\prime \prime }+y&=x^{2}+x +1 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
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✓ |
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0.612 |
|