|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}c y^{\prime } = y
\] |
[_quadrature] |
✓ |
0.900 |
|
|
\[
{}c y^{\prime } = b y
\] |
[_quadrature] |
✓ |
0.967 |
|
|
\[
{}c y^{\prime } = a x +b y^{2}
\] |
[[_Riccati, _special]] |
✓ |
1.210 |
|
|
\[
{}c y^{\prime } = \frac {a x +b y^{2}}{r}
\] |
[[_Riccati, _special]] |
✓ |
1.227 |
|
|
\[
{}c y^{\prime } = \frac {a x +b y^{2}}{r x}
\] |
[_rational, _Riccati] |
✓ |
4.059 |
|
|
\[
{}c y^{\prime } = \frac {a x +b y^{2}}{r \,x^{2}}
\] |
[_rational, _Riccati] |
✓ |
6.378 |
|
|
\[
{}c y^{\prime } = \frac {a x +b y^{2}}{y}
\] |
[_rational, _Bernoulli] |
✓ |
1.753 |
|
|
\[
{}a \sin \left (x \right ) y x y^{\prime } = 0
\] |
[_quadrature] |
✓ |
0.597 |
|
|
\[
{}f \left (x \right ) \sin \left (x \right ) y x y^{\prime } \pi = 0
\] |
[_quadrature] |
✓ |
0.583 |
|
|
\[
{}y^{\prime } = \sin \left (x \right )+y
\] |
[[_linear, ‘class A‘]] |
✓ |
1.423 |
|
|
\[
{}y^{\prime } = \sin \left (x \right )+y^{2}
\] |
[_Riccati] |
✓ |
2.941 |
|
|
\[
{}y^{\prime } = \cos \left (x \right )+\frac {y}{x}
\] |
[_linear] |
✓ |
1.533 |
|
|
\[
{}y^{\prime } = \cos \left (x \right )+\frac {y^{2}}{x}
\] |
[_Riccati] |
✗ |
5.191 |
|
|
\[
{}y^{\prime } = x +y+b y^{2}
\] |
[_Riccati] |
✓ |
1.223 |
|
|
\[
{}x y^{\prime } = 0
\] |
[_quadrature] |
✓ |
0.431 |
|
|
\[
{}5 y^{\prime } = 0
\] |
[_quadrature] |
✓ |
0.432 |
|
|
\[
{}{\mathrm e} y^{\prime } = 0
\] |
[_quadrature] |
✓ |
0.465 |
|
|
\[
{}\pi y^{\prime } = 0
\] |
[_quadrature] |
✓ |
0.458 |
|
|
\[
{}\sin \left (x \right ) y^{\prime } = 0
\] |
[_quadrature] |
✓ |
0.533 |
|
|
\[
{}f \left (x \right ) y^{\prime } = 0
\] |
[_quadrature] |
✓ |
0.467 |
|
|
\[
{}x y^{\prime } = 1
\] |
[_quadrature] |
✓ |
0.512 |
|
|
\[
{}x y^{\prime } = \sin \left (x \right )
\] |
[_quadrature] |
✓ |
0.586 |
|
|
\[
{}\left (-1+x \right ) y^{\prime } = 0
\] |
[_quadrature] |
✓ |
0.432 |
|
|
\[
{}y y^{\prime } = 0
\] |
[_quadrature] |
✓ |
0.541 |
|
|
\[
{}x y y^{\prime } = 0
\] |
[_quadrature] |
✓ |
0.550 |
|
|
\[
{}x y \sin \left (x \right ) y^{\prime } = 0
\] |
[_quadrature] |
✓ |
0.572 |
|
|
\[
{}\pi y \sin \left (x \right ) y^{\prime } = 0
\] |
[_quadrature] |
✓ |
0.585 |
|
|
\[
{}x \sin \left (x \right ) y^{\prime } = 0
\] |
[_quadrature] |
✓ |
0.483 |
|
|
\[
{}x \sin \left (x \right ) {y^{\prime }}^{2} = 0
\] |
[_quadrature] |
✓ |
0.150 |
|
|
\[
{}y {y^{\prime }}^{2} = 0
\] |
[_quadrature] |
✓ |
0.148 |
|
|
\[
{}{y^{\prime }}^{n} = 0
\] |
[_quadrature] |
✓ |
0.572 |
|
|
\[
{}x {y^{\prime }}^{n} = 0
\] |
[_quadrature] |
✓ |
0.577 |
|
|
\[
{}{y^{\prime }}^{2} = x
\] |
[_quadrature] |
✓ |
0.286 |
|
|
\[
{}{y^{\prime }}^{2} = x +y
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
0.626 |
|
|
\[
{}{y^{\prime }}^{2} = \frac {y}{x}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
2.449 |
|
|
\[
{}{y^{\prime }}^{2} = \frac {y^{2}}{x}
\] |
[_separable] |
✓ |
1.424 |
|
|
\[
{}{y^{\prime }}^{2} = \frac {y^{3}}{x}
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
0.901 |
|
|
\[
{}{y^{\prime }}^{3} = \frac {y^{2}}{x}
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
1.080 |
|
|
\[
{}{y^{\prime }}^{2} = \frac {1}{x y}
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
0.751 |
|
|
\[
{}{y^{\prime }}^{2} = \frac {1}{x y^{3}}
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
0.783 |
|
|
\[
{}{y^{\prime }}^{2} = \frac {1}{x^{2} y^{3}}
\] |
[_separable] |
✓ |
0.793 |
|
|
\[
{}{y^{\prime }}^{4} = \frac {1}{x y^{3}}
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
1.196 |
|
|
\[
{}{y^{\prime }}^{2} = \frac {1}{x^{3} y^{4}}
\] |
[_separable] |
✓ |
1.013 |
|
|
\[
{}y^{\prime } = \sqrt {1+6 x +y}
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
2.625 |
|
|
\[
{}y^{\prime } = \left (1+6 x +y\right )^{{1}/{3}}
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
2.017 |
|
|
\[
{}y^{\prime } = \left (1+6 x +y\right )^{{1}/{4}}
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
1.659 |
|
|
\[
{}y^{\prime } = \left (a +b x +y\right )^{4}
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
159.482 |
|
|
\[
{}y^{\prime } = \left (\pi +x +7 y\right )^{{7}/{2}}
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
17.236 |
|
|
\[
{}y^{\prime } = \left (a +b x +c y\right )^{6}
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
5.819 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{x +y}
\] |
[_separable] |
✓ |
2.599 |
|
|
\[
{}y^{\prime } = 10+{\mathrm e}^{x +y}
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
2.456 |
|
|
\[
{}y^{\prime } = 10 \,{\mathrm e}^{x +y}+x^{2}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
1.515 |
|
|
\[
{}y^{\prime } = x \,{\mathrm e}^{x +y}+\sin \left (x \right )
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
2.099 |
|
|
\[
{}y^{\prime } = 5 \,{\mathrm e}^{x^{2}+20 y}+\sin \left (x \right )
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
2.161 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }+y^{\prime }-x=y+t \\ x^{\prime }+y^{\prime }=2 x+3 y+{\mathrm e}^{t} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.172 |
|
|
\[
{}\left [\begin {array}{c} 2 x^{\prime }+y^{\prime }-x=y+t \\ x^{\prime }+y^{\prime }=2 x+3 y+{\mathrm e}^{t} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.910 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }+y^{\prime }-x=y+t +\sin \left (t \right )+\cos \left (t \right ) \\ x^{\prime }+y^{\prime }=2 x+3 y+{\mathrm e}^{t} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.361 |
|
|
\[
{}t y^{\prime }+y = t
\] |
[_linear] |
✓ |
0.304 |
|
|
\[
{}y^{\prime }-t y = 0
\] |
[_separable] |
✓ |
0.409 |
|
|
\[
{}t y^{\prime }+y = 0
\] |
[_separable] |
✓ |
0.401 |
|
|
\[
{}t y^{\prime }+y = 0
\] |
[_separable] |
✓ |
0.300 |
|
|
\[
{}t y^{\prime }+y = 0
\] |
[_separable] |
✓ |
0.452 |
|
|
\[
{}t y^{\prime }+y = 0
\] |
[_separable] |
✓ |
0.301 |
|
|
\[
{}t y^{\prime }+y = 0
\] |
[_separable] |
✓ |
0.579 |
|
|
\[
{}t y^{\prime }+y = \sin \left (t \right )
\] |
[_linear] |
✗ |
0.673 |
|
|
\[
{}t y^{\prime }+y = t
\] |
[_linear] |
✓ |
0.568 |
|
|
\[
{}t y^{\prime }+y = t
\] |
[_linear] |
✓ |
0.638 |
|
|
\[
{}y^{\prime }+t^{2} y = 0
\] |
[_separable] |
✓ |
0.401 |
|
|
\[
{}\left (a t +1\right ) y^{\prime }+y = t
\] |
[_linear] |
✓ |
0.409 |
|
|
\[
{}y^{\prime }+\left (a t +t b \right ) y = 0
\] |
[_separable] |
✓ |
0.313 |
|
|
\[
{}y^{\prime }+\left (a t +t b \right ) y = 0
\] |
[_separable] |
✓ |
0.349 |
|
|
\[
{}y^{\prime \prime } = 0
\] |
[[_2nd_order, _quadrature]] |
✓ |
1.880 |
|
|
\[
{}{y^{\prime \prime }}^{2} = 0
\] |
[[_2nd_order, _quadrature]] |
✓ |
0.441 |
|
|
\[
{}{y^{\prime \prime }}^{n} = 0
\] |
[[_2nd_order, _quadrature]] |
✓ |
0.270 |
|
|
\[
{}a y^{\prime \prime } = 0
\] |
[[_2nd_order, _quadrature]] |
✓ |
1.988 |
|
|
\[
{}a {y^{\prime \prime }}^{2} = 0
\] |
[[_2nd_order, _quadrature]] |
✓ |
0.459 |
|
|
\[
{}a {y^{\prime \prime }}^{n} = 0
\] |
[[_2nd_order, _quadrature]] |
✓ |
0.200 |
|
|
\[
{}y^{\prime \prime } = 1
\] |
[[_2nd_order, _quadrature]] |
✓ |
2.107 |
|
|
\[
{}{y^{\prime \prime }}^{2} = 1
\] |
[[_2nd_order, _quadrature]] |
✓ |
1.560 |
|
|
\[
{}y^{\prime \prime } = x
\] |
[[_2nd_order, _quadrature]] |
✓ |
1.740 |
|
|
\[
{}{y^{\prime \prime }}^{2} = x
\] |
[[_2nd_order, _quadrature]] |
✓ |
0.422 |
|
|
\[
{}{y^{\prime \prime }}^{3} = 0
\] |
[[_2nd_order, _quadrature]] |
✓ |
0.510 |
|
|
\[
{}y^{\prime \prime }+y^{\prime } = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.752 |
|
|
\[
{}{y^{\prime \prime }}^{2}+y^{\prime } = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.329 |
|
|
\[
{}y^{\prime \prime }+{y^{\prime }}^{2} = 0
\] |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.373 |
|
|
\[
{}y^{\prime \prime }+y^{\prime } = 1
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.846 |
|
|
\[
{}{y^{\prime \prime }}^{2}+y^{\prime } = 1
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.025 |
|
|
\[
{}y^{\prime \prime }+{y^{\prime }}^{2} = 1
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] |
✓ |
1.525 |
|
|
\[
{}y^{\prime \prime }+y^{\prime } = x
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.888 |
|
|
\[
{}{y^{\prime \prime }}^{2}+y^{\prime } = x
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.760 |
|
|
\[
{}y^{\prime \prime }+{y^{\prime }}^{2} = x
\] |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.602 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.074 |
|
|
\[
{}{y^{\prime \prime }}^{2}+y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✗ |
0.052 |
|
|
\[
{}y^{\prime \prime }+{y^{\prime }}^{2}+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.984 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+y = 1
\] |
[[_2nd_order, _missing_x]] |
✓ |
15.274 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+y = x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
17.944 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+y = x +1
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
23.416 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+y = x^{2}+x +1
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
34.199 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+y = x^{3}+x^{2}+x +1
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
25.026 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+y = \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
45.608 |
|