|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}x y y^{\prime } = 0
\] |
[_quadrature] |
✓ |
0.369 |
|
|
\[
{}x y \sin \left (x \right ) y^{\prime } = 0
\] |
[_quadrature] |
✓ |
0.380 |
|
|
\[
{}\pi y \sin \left (x \right ) y^{\prime } = 0
\] |
[_quadrature] |
✓ |
0.386 |
|
|
\[
{}x \sin \left (x \right ) y^{\prime } = 0
\] |
[_quadrature] |
✓ |
0.446 |
|
|
\[
{}x \sin \left (x \right ) {y^{\prime }}^{2} = 0
\] |
[_quadrature] |
✓ |
0.158 |
|
|
\[
{}y {y^{\prime }}^{2} = 0
\] |
[_quadrature] |
✓ |
0.147 |
|
|
\[
{}{y^{\prime }}^{n} = 0
\] |
[_quadrature] |
✓ |
0.503 |
|
|
\[
{}x {y^{\prime }}^{n} = 0
\] |
[_quadrature] |
✓ |
0.396 |
|
|
\[
{}{y^{\prime }}^{2} = x
\] |
[_quadrature] |
✓ |
0.204 |
|
|
\[
{}{y^{\prime }}^{2} = x +y
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
0.487 |
|
|
\[
{}{y^{\prime }}^{2} = \frac {y}{x}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
1.412 |
|
|
\[
{}{y^{\prime }}^{2} = \frac {y^{2}}{x}
\] |
[_separable] |
✓ |
1.201 |
|
|
\[
{}{y^{\prime }}^{2} = \frac {y^{3}}{x}
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
0.777 |
|
|
\[
{}{y^{\prime }}^{3} = \frac {y^{2}}{x}
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
1.247 |
|
|
\[
{}{y^{\prime }}^{2} = \frac {1}{x y}
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
0.638 |
|
|
\[
{}{y^{\prime }}^{2} = \frac {1}{x y^{3}}
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
0.681 |
|
|
\[
{}{y^{\prime }}^{2} = \frac {1}{y^{3} x^{2}}
\] |
[_separable] |
✓ |
0.707 |
|
|
\[
{}{y^{\prime }}^{4} = \frac {1}{x y^{3}}
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
1.060 |
|
|
\[
{}{y^{\prime }}^{2} = \frac {1}{x^{3} y^{4}}
\] |
[_separable] |
✓ |
0.907 |
|
|
\[
{}y^{\prime } = \sqrt {1+6 x +y}
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
2.407 |
|
|
\[
{}y^{\prime } = \left (1+6 x +y\right )^{{1}/{3}}
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
1.757 |
|
|
\[
{}y^{\prime } = \left (1+6 x +y\right )^{{1}/{4}}
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
1.666 |
|
|
\[
{}y^{\prime } = \left (a +b x +y\right )^{4}
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
160.026 |
|
|
\[
{}y^{\prime } = \left (\pi +x +7 y\right )^{{7}/{2}}
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
16.673 |
|
|
\[
{}y^{\prime } = \left (a +b x +c y\right )^{6}
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
5.939 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{x +y}
\] |
[_separable] |
✓ |
1.889 |
|
|
\[
{}y^{\prime } = 10+{\mathrm e}^{x +y}
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
1.898 |
|
|
\[
{}y^{\prime } = 10 \,{\mathrm e}^{x +y}+x^{2}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
1.608 |
|
|
\[
{}y^{\prime } = x \,{\mathrm e}^{x +y}+\sin \left (x \right )
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
2.144 |
|
|
\[
{}y^{\prime } = 5 \,{\mathrm e}^{x^{2}+20 y}+\sin \left (x \right )
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
2.219 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }+y^{\prime }-x=y+t \\ x^{\prime }+y^{\prime }=2 x+3 y+{\mathrm e}^{t} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.164 |
|
|
\[
{}\left [\begin {array}{c} 2 x^{\prime }+y^{\prime }-x=y+t \\ x^{\prime }+y^{\prime }=2 x+3 y+{\mathrm e}^{t} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.891 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }+y^{\prime }-x=y+t +\sin \left (t \right )+\cos \left (t \right ) \\ x^{\prime }+y^{\prime }=2 x+3 y+{\mathrm e}^{t} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.276 |
|
|
\[
{}t y^{\prime }+y = t
\] |
[_linear] |
✓ |
0.281 |
|
|
\[
{}y^{\prime }-t y = 0
\] |
[_separable] |
✓ |
0.533 |
|
|
\[
{}t y^{\prime }+y = 0
\] |
[_separable] |
✓ |
0.279 |
|
|
\[
{}t y^{\prime }+y = 0
\] |
[_separable] |
✓ |
0.250 |
|
|
\[
{}t y^{\prime }+y = 0
\] |
[_separable] |
✓ |
0.320 |
|
|
\[
{}t y^{\prime }+y = 0
\] |
[_separable] |
✓ |
0.250 |
|
|
\[
{}t y^{\prime }+y = 0
\] |
[_separable] |
✓ |
0.388 |
|
|
\[
{}t y^{\prime }+y = \sin \left (t \right )
\] |
[_linear] |
✗ |
0.575 |
|
|
\[
{}t y^{\prime }+y = t
\] |
[_linear] |
✓ |
0.440 |
|
|
\[
{}t y^{\prime }+y = t
\] |
[_linear] |
✓ |
0.429 |
|
|
\[
{}y^{\prime }+t^{2} y = 0
\] |
[_separable] |
✓ |
0.329 |
|
|
\[
{}\left (a t +1\right ) y^{\prime }+y = t
\] |
[_linear] |
✓ |
0.369 |
|
|
\[
{}y^{\prime }+\left (a t +t b \right ) y = 0
\] |
[_separable] |
✓ |
0.274 |
|
|
\[
{}y^{\prime }+\left (a t +t b \right ) y = 0
\] |
[_separable] |
✓ |
0.304 |
|
|
\[
{}y^{\prime \prime } = 0
\] |
[[_2nd_order, _quadrature]] |
✓ |
1.325 |
|
|
\[
{}{y^{\prime \prime }}^{2} = 0
\] |
[[_2nd_order, _quadrature]] |
✓ |
0.193 |
|
|
\[
{}{y^{\prime \prime }}^{n} = 0
\] |
[[_2nd_order, _quadrature]] |
✓ |
0.139 |
|
|
\[
{}a y^{\prime \prime } = 0
\] |
[[_2nd_order, _quadrature]] |
✓ |
1.329 |
|
|
\[
{}a {y^{\prime \prime }}^{2} = 0
\] |
[[_2nd_order, _quadrature]] |
✓ |
0.234 |
|
|
\[
{}a {y^{\prime \prime }}^{n} = 0
\] |
[[_2nd_order, _quadrature]] |
✓ |
0.158 |
|
|
\[
{}y^{\prime \prime } = 1
\] |
[[_2nd_order, _quadrature]] |
✓ |
1.631 |
|
|
\[
{}{y^{\prime \prime }}^{2} = 1
\] |
[[_2nd_order, _quadrature]] |
✓ |
0.258 |
|
|
\[
{}y^{\prime \prime } = x
\] |
[[_2nd_order, _quadrature]] |
✓ |
1.251 |
|
|
\[
{}{y^{\prime \prime }}^{2} = x
\] |
[[_2nd_order, _quadrature]] |
✓ |
0.352 |
|
|
\[
{}{y^{\prime \prime }}^{3} = 0
\] |
[[_2nd_order, _quadrature]] |
✓ |
0.226 |
|
|
\[
{}y^{\prime \prime }+y^{\prime } = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.302 |
|
|
\[
{}{y^{\prime \prime }}^{2}+y^{\prime } = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.674 |
|
|
\[
{}y^{\prime \prime }+{y^{\prime }}^{2} = 0
\] |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.138 |
|
|
\[
{}y^{\prime \prime }+y^{\prime } = 1
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.454 |
|
|
\[
{}{y^{\prime \prime }}^{2}+y^{\prime } = 1
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.661 |
|
|
\[
{}y^{\prime \prime }+{y^{\prime }}^{2} = 1
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.242 |
|
|
\[
{}y^{\prime \prime }+y^{\prime } = x
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.462 |
|
|
\[
{}{y^{\prime \prime }}^{2}+y^{\prime } = x
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.625 |
|
|
\[
{}y^{\prime \prime }+{y^{\prime }}^{2} = x
\] |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.789 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.064 |
|
|
\[
{}{y^{\prime \prime }}^{2}+y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✗ |
0.047 |
|
|
\[
{}y^{\prime \prime }+{y^{\prime }}^{2}+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.892 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+y = 1
\] |
[[_2nd_order, _missing_x]] |
✓ |
20.199 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+y = x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
17.460 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+y = x +1
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
22.740 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+y = x^{2}+x +1
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
32.719 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+y = x^{3}+x^{2}+x +1
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
32.816 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+y = \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
41.273 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+y = \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
72.489 |
|
|
\[
{}y^{\prime \prime }+y^{\prime } = 1
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.460 |
|
|
\[
{}y^{\prime \prime }+y^{\prime } = x
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.480 |
|
|
\[
{}y^{\prime \prime }+y^{\prime } = x +1
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.485 |
|
|
\[
{}y^{\prime \prime }+y^{\prime } = x^{2}+x +1
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.558 |
|
|
\[
{}y^{\prime \prime }+y^{\prime } = x^{3}+x^{2}+x +1
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.639 |
|
|
\[
{}y^{\prime \prime }+y^{\prime } = \sin \left (x \right )
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.772 |
|
|
\[
{}y^{\prime \prime }+y^{\prime } = \cos \left (x \right )
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.753 |
|
|
\[
{}y^{\prime \prime }+y = 1
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.105 |
|
|
\[
{}y^{\prime \prime }+y = x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.830 |
|
|
\[
{}y^{\prime \prime }+y = x +1
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.892 |
|
|
\[
{}y^{\prime \prime }+y = x^{2}+x +1
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.001 |
|
|
\[
{}y^{\prime \prime }+y = x^{3}+x^{2}+x +1
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.033 |
|
|
\[
{}y^{\prime \prime }+y = \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.856 |
|
|
\[
{}y^{\prime \prime }+y = \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.844 |
|
|
\[
{}y {y^{\prime \prime }}^{2}+y^{\prime } = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
11.357 |
|
|
\[
{}y {y^{\prime \prime }}^{2}+{y^{\prime }}^{3} = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.290 |
|
|
\[
{}y^{2} {y^{\prime \prime }}^{2}+y^{\prime } = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
5.412 |
|
|
\[
{}y {y^{\prime \prime }}^{4}+{y^{\prime }}^{2} = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
56.838 |
|
|
\[
{}y^{3} {y^{\prime \prime }}^{2}+y^{\prime } y = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
0.388 |
|
|
\[
{}y y^{\prime \prime }+{y^{\prime }}^{3} = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
0.526 |
|
|
\[
{}y {y^{\prime \prime }}^{3}+y^{3} y^{\prime } = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.459 |
|
|
\[
{}y {y^{\prime \prime }}^{3}+y^{3} {y^{\prime }}^{5} = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.213 |
|
|
\[
{}y^{\prime \prime }+x y^{\prime }+y {y^{\prime }}^{2} = 0
\] |
[_Liouville, [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.298 |
|