| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
\pi y \sin \left (x \right ) y^{\prime }&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.103 |
|
| \begin{align*}
x \sin \left (x \right ) y^{\prime }&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.792 |
|
| \begin{align*}
x \sin \left (x \right ) {y^{\prime }}^{2}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.710 |
|
| \begin{align*}
y {y^{\prime }}^{2}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.378 |
|
| \begin{align*}
{y^{\prime }}^{n}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
0.744 |
|
| \begin{align*}
x {y^{\prime }}^{n}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
0.958 |
|
| \begin{align*}
{y^{\prime }}^{2}&=x \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.556 |
|
| \begin{align*}
{y^{\prime }}^{2}&=x +y \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
2.121 |
|
| \begin{align*}
{y^{\prime }}^{2}&=\frac {y}{x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
6.018 |
|
| \begin{align*}
{y^{\prime }}^{2}&=\frac {y^{2}}{x} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.026 |
|
| \begin{align*}
{y^{\prime }}^{2}&=\frac {y^{3}}{x} \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✓ |
32.365 |
|
| \begin{align*}
{y^{\prime }}^{3}&=\frac {y^{2}}{x} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
164.951 |
|
| \begin{align*}
{y^{\prime }}^{2}&=\frac {1}{y x} \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✓ |
32.129 |
|
| \begin{align*}
{y^{\prime }}^{2}&=\frac {1}{x y^{3}} \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✓ |
18.619 |
|
| \begin{align*}
{y^{\prime }}^{2}&=\frac {1}{x^{2} y^{3}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.399 |
|
| \begin{align*}
{y^{\prime }}^{4}&=\frac {1}{x y^{3}} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✗ |
33.902 |
|
| \begin{align*}
{y^{\prime }}^{2}&=\frac {1}{x^{3} y^{4}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
12.835 |
|
| \begin{align*}
y^{\prime }&=\sqrt {1+6 x +y} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
9.421 |
|
| \begin{align*}
y^{\prime }&=\left (1+6 x +y\right )^{{1}/{3}} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
5.488 |
|
| \begin{align*}
y^{\prime }&=\left (1+6 x +y\right )^{{1}/{4}} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
7.466 |
|
| \begin{align*}
y^{\prime }&=\left (a +b x +y\right )^{4} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
3.206 |
|
| \begin{align*}
y^{\prime }&=\left (\pi +x +7 y\right )^{{7}/{2}} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
69.816 |
|
| \begin{align*}
y^{\prime }&=\left (a +b x +c y\right )^{6} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
17.404 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{x +y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.657 |
|
| \begin{align*}
y^{\prime }&=10+{\mathrm e}^{x +y} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
3.281 |
|
| \begin{align*}
y^{\prime }&=10 \,{\mathrm e}^{x +y}+x^{2} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
3.220 |
|
| \begin{align*}
y^{\prime }&=x \,{\mathrm e}^{x +y}+\sin \left (x \right ) \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
3.996 |
|
| \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)]‘]] |
✓ |
✓ |
✓ |
✗ |
3.464 |
|
| \begin{align*}
x^{\prime }+y^{\prime }-x&=y+t \\
x^{\prime }+y^{\prime }&=2 x+3 y+{\mathrm e}^{t} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✗ |
0.252 |
|
| \begin{align*}
2 x^{\prime }+y^{\prime }-x&=y+t \\
x^{\prime }+y^{\prime }&=2 x+3 y+{\mathrm e}^{t} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
2.873 |
|
| \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 |
✓ |
✓ |
✓ |
✗ |
0.303 |
|
| \begin{align*}
y^{\prime } t +y&=t \\
y \left (0\right ) &= 5 \\
\end{align*} Using Laplace transform method. |
[_linear] |
✓ |
✓ |
✗ |
✓ |
0.705 |
|
| \begin{align*}
y^{\prime }-t y&=0 \\
y \left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.633 |
|
| \begin{align*}
y^{\prime } t +y&=0 \\
y \left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.403 |
|
| \begin{align*}
y^{\prime } t +y&=0 \\
y \left (0\right ) &= y_{0} \\
\end{align*} Using Laplace transform method. |
[_separable] |
✓ |
✓ |
✗ |
✓ |
0.405 |
|
| \begin{align*}
y^{\prime } t +y&=0 \\
y \left (x_{0} \right ) &= y_{0} \\
\end{align*} Using Laplace transform method. |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.824 |
|
| \begin{align*}
y^{\prime } t +y&=0 \\
\end{align*} Using Laplace transform method. |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.373 |
|
| \begin{align*}
y^{\prime } t +y&=0 \\
y \left (1\right ) &= 5 \\
\end{align*} Using Laplace transform method. |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.647 |
|
| \begin{align*}
y^{\prime } t +y&=\sin \left (t \right ) \\
y \left (1\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
[_linear] |
✓ |
✗ |
✓ |
✓ |
1.063 |
|
| \begin{align*}
y^{\prime } t +y&=t \\
y \left (1\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
[_linear] |
✓ |
✓ |
✓ |
✓ |
0.790 |
|
| \begin{align*}
y^{\prime } t +y&=t \\
y \left (1\right ) &= 1 \\
\end{align*} Using Laplace transform method. |
[_linear] |
✓ |
✓ |
✓ |
✓ |
0.787 |
|
| \begin{align*}
t^{2} y+y^{\prime }&=0 \\
y \left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.618 |
|
| \begin{align*}
\left (a t +1\right ) y^{\prime }+y&=t \\
y \left (1\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
[_linear] |
✓ |
✓ |
✓ |
✗ |
0.909 |
|
| \begin{align*}
y^{\prime }+\left (a t +b t \right ) y&=0 \\
y \left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.609 |
|
| \begin{align*}
y^{\prime }+\left (a t +b t \right ) y&=0 \\
y \left (-3\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.684 |
|
| \begin{align*}
y^{\prime }+2 y x&=x \\
\end{align*} Series expansion around \(x=0\). |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.556 |
|
| \begin{align*}
y^{\prime }+y&=\sin \left (x \right ) \\
\end{align*} Series expansion around \(x=0\). |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
0.508 |
|
| \begin{align*}
y^{\prime } x +y&=0 \\
y \left (0\right ) &= 1 \\
\end{align*} Series expansion around \(x=0\). |
[_separable] |
✗ |
✗ |
✗ |
✗ |
0.193 |
|
| \begin{align*}
y^{\prime } x +y&=x \\
\end{align*} Series expansion around \(x=0\). |
[_linear] |
✓ |
✓ |
✓ |
✗ |
0.536 |
|
| \begin{align*}
y^{\prime } x +y&=1 \\
\end{align*} Series expansion around \(x=0\). |
[_separable] |
✓ |
✓ |
✓ |
✗ |
0.550 |
|
| \begin{align*}
y^{\prime } x +y&=\sin \left (x \right ) \\
\end{align*} Series expansion around \(x=0\). |
[_linear] |
✓ |
✓ |
✓ |
✗ |
0.630 |
|
| \begin{align*}
y^{\prime } x +y&=2 x^{4}+x^{3}+x \\
\end{align*} Series expansion around \(x=0\). |
[_linear] |
✓ |
✓ |
✓ |
✗ |
0.611 |
|
| \begin{align*}
y^{\prime } x +y&=\frac {1}{x^{3}} \\
\end{align*} Series expansion around \(x=0\). |
[_linear] |
✓ |
✓ |
✓ |
✗ |
0.492 |
|
| \begin{align*}
y^{\prime } x +2 y x&=\sqrt {x} \\
\end{align*} Series expansion around \(x=0\). |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
0.948 |
|
| \begin{align*}
y^{\prime }+\frac {y}{x}&=0 \\
\end{align*} Series expansion around \(x=0\). |
[_separable] |
✓ |
✓ |
✓ |
✗ |
0.474 |
|
| \begin{align*}
\cos \left (x \right ) y^{\prime }+\frac {y}{x}&=x \\
\end{align*} Series expansion around \(x=0\). |
[_linear] |
✓ |
✓ |
✗ |
✗ |
0.980 |
|
| \begin{align*}
\cos \left (x \right ) y^{\prime }+\frac {y}{x}&=x +\sin \left (x \right ) \\
\end{align*} Series expansion around \(x=0\). |
[_linear] |
✓ |
✓ |
✗ |
✗ |
1.262 |
|
| \begin{align*}
y^{\prime } x +y&=\tan \left (x \right ) \\
\end{align*} Series expansion around \(x=0\). |
[_linear] |
✓ |
✓ |
✓ |
✗ |
0.676 |
|
| \begin{align*}
y^{\prime } x +y&=\cos \left (x \right )+\sin \left (x \right ) \\
\end{align*} Series expansion around \(x=0\). |
[_linear] |
✓ |
✓ |
✓ |
✗ |
0.678 |
|
| \begin{align*}
y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.712 |
|
| \begin{align*}
{y^{\prime \prime }}^{2}&=0 \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
1.097 |
|
| \begin{align*}
{y^{\prime \prime }}^{n}&=0 \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✗ |
0.527 |
|
| \begin{align*}
a y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.845 |
|
| \begin{align*}
a {y^{\prime \prime }}^{2}&=0 \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
1.294 |
|
| \begin{align*}
a {y^{\prime \prime }}^{n}&=0 \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✗ |
0.560 |
|
| \begin{align*}
y^{\prime \prime }&=1 \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.894 |
|
| \begin{align*}
{y^{\prime \prime }}^{2}&=1 \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.107 |
|
| \begin{align*}
y^{\prime \prime }&=x \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.924 |
|
| \begin{align*}
{y^{\prime \prime }}^{2}&=x \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
1.574 |
|
| \begin{align*}
{y^{\prime \prime }}^{3}&=0 \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
1.135 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
1.703 |
|
| \begin{align*}
{y^{\prime \prime }}^{2}+y^{\prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
203.509 |
|
| \begin{align*}
y^{\prime \prime }+{y^{\prime }}^{2}&=0 \\
\end{align*} |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✓ |
1.254 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }&=1 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
1.447 |
|
| \begin{align*}
{y^{\prime \prime }}^{2}+y^{\prime }&=1 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
5.956 |
|
| \begin{align*}
y^{\prime \prime }+{y^{\prime }}^{2}&=1 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✗ |
4.645 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }&=x \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.050 |
|
| \begin{align*}
{y^{\prime \prime }}^{2}+y^{\prime }&=x \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✗ |
1.226 |
|
| \begin{align*}
y^{\prime \prime }+{y^{\prime }}^{2}&=x \\
\end{align*} |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✗ |
2.175 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }+y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.355 |
|
| \begin{align*}
{y^{\prime \prime }}^{2}+y^{\prime }+y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✗ |
✗ |
✗ |
✗ |
0.072 |
|
| \begin{align*}
y^{\prime \prime }+{y^{\prime }}^{2}+y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✗ |
2.549 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }+y&=1 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.371 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }+y&=x \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.460 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }+y&=x +1 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.460 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }+y&=x^{2}+x +1 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.464 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }+y&=x^{3}+x^{2}+x +1 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.499 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }+y&=\sin \left (x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.473 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }+y&=\cos \left (x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.459 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }&=1 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
1.420 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }&=x \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.042 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }&=x +1 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.100 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }&=x^{2}+x +1 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.135 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }&=x^{3}+x^{2}+x +1 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.190 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }&=\sin \left (x \right ) \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.167 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }&=\cos \left (x \right ) \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.151 |
|
| \begin{align*}
y^{\prime \prime }+y&=1 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
3.887 |
|
| \begin{align*}
y^{\prime \prime }+y&=x \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.412 |
|
| \begin{align*}
y^{\prime \prime }+y&=x +1 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.415 |
|
| \begin{align*}
y^{\prime \prime }+y&=x^{2}+x +1 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
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0.425 |
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