|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}c y^{\prime } = y
\] |
[_quadrature] |
✓ |
0.820 |
|
|
\[
{}c y^{\prime } = b y
\] |
[_quadrature] |
✓ |
0.977 |
|
|
\[
{}c y^{\prime } = a x +b y^{2}
\] |
[[_Riccati, _special]] |
✓ |
1.169 |
|
|
\[
{}c y^{\prime } = \frac {a x +b y^{2}}{r}
\] |
[[_Riccati, _special]] |
✓ |
1.303 |
|
|
\[
{}c y^{\prime } = \frac {a x +b y^{2}}{r x}
\] |
[_rational, _Riccati] |
✓ |
4.315 |
|
|
\[
{}c y^{\prime } = \frac {a x +b y^{2}}{r \,x^{2}}
\] |
[_rational, _Riccati] |
✓ |
6.841 |
|
|
\[
{}c y^{\prime } = \frac {a x +b y^{2}}{y}
\] |
[_rational, _Bernoulli] |
✓ |
1.565 |
|
|
\[
{}a \sin \left (x \right ) y x y^{\prime } = 0
\] |
[_quadrature] |
✓ |
0.701 |
|
|
\[
{}f \left (x \right ) \sin \left (x \right ) y x y^{\prime } \pi = 0
\] |
[_quadrature] |
✓ |
0.701 |
|
|
\[
{}y^{\prime } = \sin \left (x \right )+y
\] |
[[_linear, ‘class A‘]] |
✓ |
1.466 |
|
|
\[
{}y^{\prime } = \sin \left (x \right )+y^{2}
\] |
[_Riccati] |
✓ |
2.724 |
|
|
\[
{}y^{\prime } = \cos \left (x \right )+\frac {y}{x}
\] |
[_linear] |
✓ |
1.604 |
|
|
\[
{}y^{\prime } = \cos \left (x \right )+\frac {y^{2}}{x}
\] |
[_Riccati] |
✗ |
4.930 |
|
|
\[
{}y^{\prime } = x +y+b y^{2}
\] |
[_Riccati] |
✓ |
1.219 |
|
|
\[
{}y^{\prime } x = 0
\] |
[_quadrature] |
✓ |
0.682 |
|
|
\[
{}5 y^{\prime } = 0
\] |
[_quadrature] |
✓ |
0.685 |
|
|
\[
{}{\mathrm e} y^{\prime } = 0
\] |
[_quadrature] |
✓ |
0.684 |
|
|
\[
{}\pi y^{\prime } = 0
\] |
[_quadrature] |
✓ |
0.690 |
|
|
\[
{}\sin \left (x \right ) y^{\prime } = 0
\] |
[_quadrature] |
✓ |
0.742 |
|
|
\[
{}f \left (x \right ) y^{\prime } = 0
\] |
[_quadrature] |
✓ |
0.720 |
|
|
\[
{}y^{\prime } x = 1
\] |
[_quadrature] |
✓ |
0.493 |
|
|
\[
{}y^{\prime } x = \sin \left (x \right )
\] |
[_quadrature] |
✓ |
0.546 |
|
|
\[
{}\left (x -1\right ) y^{\prime } = 0
\] |
[_quadrature] |
✓ |
0.700 |
|
|
\[
{}y y^{\prime } = 0
\] |
[_quadrature] |
✓ |
0.721 |
|
|
\[
{}x y y^{\prime } = 0
\] |
[_quadrature] |
✓ |
0.694 |
|
|
\[
{}x y \sin \left (x \right ) y^{\prime } = 0
\] |
[_quadrature] |
✓ |
0.690 |
|
|
\[
{}\pi y \sin \left (x \right ) y^{\prime } = 0
\] |
[_quadrature] |
✓ |
0.683 |
|
|
\[
{}x \sin \left (x \right ) y^{\prime } = 0
\] |
[_quadrature] |
✓ |
0.750 |
|
|
\[
{}x \sin \left (x \right ) {y^{\prime }}^{2} = 0
\] |
[_quadrature] |
✓ |
0.175 |
|
|
\[
{}y {y^{\prime }}^{2} = 0
\] |
[_quadrature] |
✓ |
0.155 |
|
|
\[
{}{y^{\prime }}^{n} = 0
\] |
[_quadrature] |
✓ |
0.750 |
|
|
\[
{}x {y^{\prime }}^{n} = 0
\] |
[_quadrature] |
✓ |
0.614 |
|
|
\[
{}{y^{\prime }}^{2} = x
\] |
[_quadrature] |
✓ |
0.231 |
|
|
\[
{}{y^{\prime }}^{2} = x +y
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
0.520 |
|
|
\[
{}{y^{\prime }}^{2} = \frac {y}{x}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
1.537 |
|
|
\[
{}{y^{\prime }}^{2} = \frac {y^{2}}{x}
\] |
[_separable] |
✓ |
1.331 |
|
|
\[
{}{y^{\prime }}^{2} = \frac {y^{3}}{x}
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
0.809 |
|
|
\[
{}{y^{\prime }}^{3} = \frac {y^{2}}{x}
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
2.277 |
|
|
\[
{}{y^{\prime }}^{2} = \frac {1}{x y}
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
0.724 |
|
|
\[
{}{y^{\prime }}^{2} = \frac {1}{x y^{3}}
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
0.729 |
|
|
\[
{}{y^{\prime }}^{2} = \frac {1}{x^{2} y^{3}}
\] |
[_separable] |
✓ |
0.792 |
|
|
\[
{}{y^{\prime }}^{4} = \frac {1}{x y^{3}}
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
1.177 |
|
|
\[
{}{y^{\prime }}^{2} = \frac {1}{x^{3} y^{4}}
\] |
[_separable] |
✓ |
0.984 |
|
|
\[
{}y^{\prime } = \sqrt {1+6 x +y}
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
2.374 |
|
|
\[
{}y^{\prime } = \left (1+6 x +y\right )^{{1}/{3}}
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
1.766 |
|
|
\[
{}y^{\prime } = \left (1+6 x +y\right )^{{1}/{4}}
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
1.648 |
|
|
\[
{}y^{\prime } = \left (a +b x +y\right )^{4}
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
178.410 |
|
|
\[
{}y^{\prime } = \left (\pi +x +7 y\right )^{{7}/{2}}
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
17.942 |
|
|
\[
{}y^{\prime } = \left (a +b x +c y\right )^{6}
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
6.635 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{x +y}
\] |
[_separable] |
✓ |
2.547 |
|
|
\[
{}y^{\prime } = 10+{\mathrm e}^{x +y}
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
2.401 |
|
|
\[
{}y^{\prime } = 10 \,{\mathrm e}^{x +y}+x^{2}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
1.758 |
|
|
\[
{}y^{\prime } = x \,{\mathrm e}^{x +y}+\sin \left (x \right )
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
2.292 |
|
|
\[
{}y^{\prime } = 5 \,{\mathrm e}^{x^{2}+20 y}+\sin \left (x \right )
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
2.567 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }+y^{\prime }-x=y+t \\ x^{\prime }+y^{\prime }=2 x+3 y+{\mathrm e}^{t} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.201 |
|
|
\[
{}\left [\begin {array}{c} 2 x^{\prime }+y^{\prime }-x=y+t \\ x^{\prime }+y^{\prime }=2 x+3 y+{\mathrm e}^{t} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.956 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }+y^{\prime }-x=y+t +\sin \left (t \right )+\cos \left (t \right ) \\ x^{\prime }+y^{\prime }=2 x+3 y+{\mathrm e}^{t} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.310 |
|
|
\[
{}t y^{\prime }+y = t
\] |
[_linear] |
✓ |
0.297 |
|
|
\[
{}y^{\prime }-t y = 0
\] |
[_separable] |
✓ |
0.677 |
|
|
\[
{}t y^{\prime }+y = 0
\] |
[_separable] |
✓ |
0.386 |
|
|
\[
{}t y^{\prime }+y = 0
\] |
[_separable] |
✓ |
0.349 |
|
|
\[
{}t y^{\prime }+y = 0
\] |
[_separable] |
✓ |
0.427 |
|
|
\[
{}t y^{\prime }+y = 0
\] |
[_separable] |
✓ |
0.334 |
|
|
\[
{}t y^{\prime }+y = 0
\] |
[_separable] |
✓ |
0.513 |
|
|
\[
{}t y^{\prime }+y = \sin \left (t \right )
\] |
[_linear] |
✗ |
0.628 |
|
|
\[
{}t y^{\prime }+y = t
\] |
[_linear] |
✓ |
0.619 |
|
|
\[
{}t y^{\prime }+y = t
\] |
[_linear] |
✓ |
0.621 |
|
|
\[
{}y^{\prime }+t^{2} y = 0
\] |
[_separable] |
✓ |
0.444 |
|
|
\[
{}\left (a t +1\right ) y^{\prime }+y = t
\] |
[_linear] |
✓ |
0.389 |
|
|
\[
{}y^{\prime }+\left (a t +b t \right ) y = 0
\] |
[_separable] |
✓ |
0.304 |
|
|
\[
{}y^{\prime }+\left (a t +b t \right ) y = 0
\] |
[_separable] |
✓ |
0.341 |
|
|
\[
{}y^{\prime \prime } = 0
\] |
[[_2nd_order, _quadrature]] |
✓ |
2.132 |
|
|
\[
{}{y^{\prime \prime }}^{2} = 0
\] |
[[_2nd_order, _quadrature]] |
✓ |
0.414 |
|
|
\[
{}{y^{\prime \prime }}^{n} = 0
\] |
[[_2nd_order, _quadrature]] |
✓ |
0.229 |
|
|
\[
{}a y^{\prime \prime } = 0
\] |
[[_2nd_order, _quadrature]] |
✓ |
2.301 |
|
|
\[
{}a {y^{\prime \prime }}^{2} = 0
\] |
[[_2nd_order, _quadrature]] |
✓ |
0.494 |
|
|
\[
{}a {y^{\prime \prime }}^{n} = 0
\] |
[[_2nd_order, _quadrature]] |
✓ |
0.232 |
|
|
\[
{}y^{\prime \prime } = 1
\] |
[[_2nd_order, _quadrature]] |
✓ |
2.540 |
|
|
\[
{}{y^{\prime \prime }}^{2} = 1
\] |
[[_2nd_order, _quadrature]] |
✓ |
4.664 |
|
|
\[
{}y^{\prime \prime } = x
\] |
[[_2nd_order, _quadrature]] |
✓ |
1.972 |
|
|
\[
{}{y^{\prime \prime }}^{2} = x
\] |
[[_2nd_order, _quadrature]] |
✓ |
0.349 |
|
|
\[
{}{y^{\prime \prime }}^{3} = 0
\] |
[[_2nd_order, _quadrature]] |
✓ |
0.523 |
|
|
\[
{}y^{\prime \prime }+y^{\prime } = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.982 |
|
|
\[
{}{y^{\prime \prime }}^{2}+y^{\prime } = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
3.114 |
|
|
\[
{}y^{\prime \prime }+{y^{\prime }}^{2} = 0
\] |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.338 |
|
|
\[
{}y^{\prime \prime }+y^{\prime } = 1
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.175 |
|
|
\[
{}{y^{\prime \prime }}^{2}+y^{\prime } = 1
\] |
[[_2nd_order, _missing_x]] |
✓ |
280.872 |
|
|
\[
{}y^{\prime \prime }+{y^{\prime }}^{2} = 1
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] |
✓ |
6.989 |
|
|
\[
{}y^{\prime \prime }+y^{\prime } = x
\] |
[[_2nd_order, _missing_y]] |
✓ |
2.191 |
|
|
\[
{}{y^{\prime \prime }}^{2}+y^{\prime } = x
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.662 |
|
|
\[
{}y^{\prime \prime }+{y^{\prime }}^{2} = x
\] |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.569 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.435 |
|
|
\[
{}{y^{\prime \prime }}^{2}+y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✗ |
0.065 |
|
|
\[
{}y^{\prime \prime }+{y^{\prime }}^{2}+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.923 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+y = 1
\] |
[[_2nd_order, _missing_x]] |
✓ |
22.916 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+y = x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
33.287 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+y = x +1
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
24.772 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+y = x^{2}+x +1
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
35.566 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+y = x^{3}+x^{2}+x +1
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
26.189 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+y = \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
47.221 |
|