|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}x y y^{\prime } = 2 x^{2}+2 y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
79.286 |
|
|
\[
{}y^{\prime } = \frac {x +2 y}{x +2 y+3}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.891 |
|
|
\[
{}y^{\prime } = \frac {x +2 y}{2 x -y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
40.450 |
|
|
\[
{}y^{\prime } = \frac {y}{x}+\tan \left (\frac {y}{x}\right )
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
4.048 |
|
|
\[
{}y^{\prime } = x y^{2}+3 y^{2}+x +3
\] |
[_separable] |
✓ |
2.345 |
|
|
\[
{}1-\left (x +2 y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
1.819 |
|
|
\[
{}\ln \left (y\right )+\left (\frac {x}{y}+3\right ) y^{\prime } = 0
\] |
[_exact, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
1.424 |
|
|
\[
{}y^{2}+1-y^{\prime } = 0
\] |
[_quadrature] |
✓ |
3.569 |
|
|
\[
{}y^{\prime }-3 y = 12 \,{\mathrm e}^{2 x}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.443 |
|
|
\[
{}x y y^{\prime } = y^{2}+x y+x^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
7.619 |
|
|
\[
{}\left (x +2\right ) y^{\prime }-x^{3} = 0
\] |
[_quadrature] |
✓ |
0.594 |
|
|
\[
{}x y^{3} y^{\prime } = y^{4}-x^{2}
\] |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
4.332 |
|
|
\[
{}y^{\prime } = 4 y-\frac {16 \,{\mathrm e}^{4 x}}{y^{2}}
\] |
[[_1st_order, _with_linear_symmetries], _Bernoulli] |
✓ |
2.748 |
|
|
\[
{}2 y-6 x +\left (x +1\right ) y^{\prime } = 0
\] |
[_linear] |
✓ |
1.881 |
|
|
\[
{}x y^{2}+\left (x^{2} y+10 y^{4}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _exact, _rational] |
✓ |
2.288 |
|
|
\[
{}y y^{\prime }-x y^{2} = 6 x \,{\mathrm e}^{4 x^{2}}
\] |
[_Bernoulli] |
✓ |
2.988 |
|
|
\[
{}\left (y-x +3\right )^{2} \left (y^{\prime }-1\right ) = 1
\] |
[[_homogeneous, ‘class C‘], _exact, _rational, _dAlembert] |
✓ |
4.184 |
|
|
\[
{}x +y \,{\mathrm e}^{x y}+x \,{\mathrm e}^{x y} y^{\prime } = 0
\] |
[_exact, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
1.551 |
|
|
\[
{}y^{2}-y^{2} \cos \left (x \right )+y^{\prime } = 0
\] |
[_separable] |
✓ |
2.382 |
|
|
\[
{}y^{\prime }+2 y = \sin \left (x \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
1.529 |
|
|
\[
{}y^{\prime }+2 x = \sin \left (x \right )
\] |
[_quadrature] |
✓ |
0.586 |
|
|
\[
{}y^{\prime } = y^{3}-y^{3} \cos \left (x \right )
\] |
[_separable] |
✓ |
3.497 |
|
|
\[
{}y^{2} {\mathrm e}^{x y^{2}}-2 x +2 x y \,{\mathrm e}^{x y^{2}} y^{\prime } = 0
\] |
[_exact, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
2.138 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{4 x +3 y}
\] |
[_separable] |
✓ |
2.804 |
|
|
\[
{}y^{\prime } = \tan \left (6 x +3 y+1\right )-2
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
354.445 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{4 x +3 y}
\] |
[_separable] |
✓ |
2.810 |
|
|
\[
{}y^{\prime } = x \left (6 y+{\mathrm e}^{x^{2}}\right )
\] |
[_linear] |
✓ |
1.477 |
|
|
\[
{}x \left (1-2 y\right )+\left (y-x^{2}\right ) y^{\prime } = 0
\] |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.352 |
|
|
\[
{}x^{2} y^{\prime }+3 x y = 6 \,{\mathrm e}^{-x^{2}}
\] |
[_linear] |
✓ |
1.480 |
|
|
\[
{}x y^{\prime \prime }+4 y^{\prime } = 18 x^{2}
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.132 |
|
|
\[
{}x y^{\prime \prime } = 2 y^{\prime }
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.810 |
|
|
\[
{}y^{\prime \prime } = y^{\prime }
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.623 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime } = 8 \,{\mathrm e}^{2 x}
\] |
[[_2nd_order, _missing_y]] |
✓ |
2.046 |
|
|
\[
{}x y^{\prime \prime } = y^{\prime }-2 x^{2} y^{\prime }
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.806 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+2 x y^{\prime } = 0
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.948 |
|
|
\[
{}y^{\prime \prime } = 4 x \sqrt {y^{\prime }}
\] |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
0.384 |
|
|
\[
{}y^{\prime } y^{\prime \prime } = 1
\] |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_poly_yn]] |
✓ |
1.909 |
|
|
\[
{}y y^{\prime \prime } = -{y^{\prime }}^{2}
\] |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
1.705 |
|
|
\[
{}x y^{\prime \prime } = {y^{\prime }}^{2}-y^{\prime }
\] |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
0.312 |
|
|
\[
{}x y^{\prime \prime }-{y^{\prime }}^{2} = 6 x^{5}
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.506 |
|
|
\[
{}y y^{\prime \prime }-{y^{\prime }}^{2} = y^{\prime }
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.348 |
|
|
\[
{}y^{\prime \prime } = 2 y^{\prime }-6
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.042 |
|
|
\[
{}\left (y-3\right ) y^{\prime \prime } = 2 {y^{\prime }}^{2}
\] |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.215 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime } = 9 \,{\mathrm e}^{-3 x}
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.983 |
|
|
\[
{}y^{\prime \prime \prime } = y^{\prime \prime }
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.045 |
|
|
\[
{}x y^{\prime \prime \prime }+2 y^{\prime \prime } = 6 x
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.127 |
|
|
\[
{}y^{\prime \prime \prime } = 2 \sqrt {y^{\prime \prime }}
\] |
[[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2]] |
✓ |
0.998 |
|
|
\[
{}y^{\prime \prime \prime \prime } = -2 y^{\prime \prime \prime }
\] |
[[_high_order, _missing_x]] |
✓ |
0.053 |
|
|
\[
{}y y^{\prime \prime } = {y^{\prime }}^{2}
\] |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.584 |
|
|
\[
{}3 y y^{\prime \prime } = 2 {y^{\prime }}^{2}
\] |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.552 |
|
|
\[
{}\sin \left (y\right ) y^{\prime \prime }+\cos \left (y\right ) {y^{\prime }}^{2} = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.717 |
|
|
\[
{}y^{\prime \prime } = y^{\prime }
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.622 |
|
|
\[
{}{y^{\prime }}^{2}+y y^{\prime \prime } = 2 y y^{\prime }
\] |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
2.039 |
|
|
\[
{}y^{2} y^{\prime \prime }+y^{\prime \prime }+2 y {y^{\prime }}^{2} = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.472 |
|
|
\[
{}y^{\prime \prime } = 4 x \sqrt {y^{\prime }}
\] |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
0.369 |
|
|
\[
{}y^{\prime } y^{\prime \prime } = 1
\] |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_poly_yn]] |
✓ |
1.924 |
|
|
\[
{}x y^{\prime \prime } = {y^{\prime }}^{2}-y^{\prime }
\] |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
0.308 |
|
|
\[
{}x y^{\prime \prime }-y^{\prime } = 6 x^{5}
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.043 |
|
|
\[
{}y y^{\prime \prime }-{y^{\prime }}^{2} = y^{\prime }
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.346 |
|
|
\[
{}y y^{\prime \prime } = 2 {y^{\prime }}^{2}
\] |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.270 |
|
|
\[
{}\left (y-3\right ) y^{\prime \prime } = {y^{\prime }}^{2}
\] |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.279 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime } = 9 \,{\mathrm e}^{-3 x}
\] |
[[_2nd_order, _missing_y]] |
✓ |
2.081 |
|
|
\[
{}y^{\prime \prime } = y^{\prime } \left (y^{\prime }-2\right )
\] |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.971 |
|
|
\[
{}x y^{\prime \prime }+4 y^{\prime } = 18 x^{2}
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.617 |
|
|
\[
{}x y^{\prime \prime } = 2 y^{\prime }
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.112 |
|
|
\[
{}y^{\prime \prime } = y^{\prime }
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.134 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime } = 8 \,{\mathrm e}^{2 x}
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.964 |
|
|
\[
{}y^{\prime \prime \prime } = y^{\prime \prime }
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.120 |
|
|
\[
{}x y^{\prime \prime \prime }+2 y^{\prime \prime } = 6 x
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.210 |
|
|
\[
{}x y^{\prime \prime }+2 y^{\prime } = 6
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.413 |
|
|
\[
{}2 x y^{\prime } y^{\prime \prime } = {y^{\prime }}^{2}-1
\] |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_poly_yn]] |
✓ |
0.747 |
|
|
\[
{}3 y y^{\prime \prime } = 2 {y^{\prime }}^{2}
\] |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.476 |
|
|
\[
{}y y^{\prime \prime }+2 {y^{\prime }}^{2} = 3 y y^{\prime }
\] |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
2.056 |
|
|
\[
{}y^{\prime \prime } = -y^{\prime } {\mathrm e}^{-y}
\] |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_xy]] |
✓ |
2.388 |
|
|
\[
{}y^{\prime \prime } = -2 x {y^{\prime }}^{2}
\] |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
0.425 |
|
|
\[
{}y^{\prime \prime } = -2 x {y^{\prime }}^{2}
\] |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✗ |
0.536 |
|
|
\[
{}y^{\prime \prime } = -2 x {y^{\prime }}^{2}
\] |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
1.132 |
|
|
\[
{}y^{\prime \prime } = -2 x {y^{\prime }}^{2}
\] |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
0.547 |
|
|
\[
{}y^{\prime \prime } = 2 y y^{\prime }
\] |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Lagerstrom, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
1.116 |
|
|
\[
{}y^{\prime \prime } = 2 y y^{\prime }
\] |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Lagerstrom, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
15.660 |
|
|
\[
{}y^{\prime \prime } = 2 y y^{\prime }
\] |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Lagerstrom, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.923 |
|
|
\[
{}y^{\prime \prime } = 2 y y^{\prime }
\] |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Lagerstrom, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
1.066 |
|
|
\[
{}y^{\prime \prime }+x^{2} y^{\prime }-4 y = x^{3}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
0.695 |
|
|
\[
{}y^{\prime \prime }+x^{2} y^{\prime }-4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.685 |
|
|
\[
{}y^{\prime \prime }+x^{2} y^{\prime } = 4 y
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.685 |
|
|
\[
{}y^{\prime \prime }+x^{2} y^{\prime }+4 y = y^{3}
\] |
[NONE] |
✗ |
0.132 |
|
|
\[
{}x y^{\prime }+3 y = {\mathrm e}^{2 x}
\] |
[_linear] |
✓ |
1.385 |
|
|
\[
{}y^{\prime \prime \prime }+y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.058 |
|
|
\[
{}\left (y+1\right ) y^{\prime \prime } = {y^{\prime }}^{3}
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
0.429 |
|
|
\[
{}y^{\prime \prime } = 2 y^{\prime }-5 y+30 \,{\mathrm e}^{3 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
13.451 |
|
|
\[
{}y^{\prime \prime \prime \prime }+6 y^{\prime \prime }+3 y^{\prime }-83 y-25 = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.138 |
|
|
\[
{}y y^{\prime \prime \prime }+6 y^{\prime \prime }+3 y^{\prime } = y
\] |
[[_3rd_order, _missing_x], [_3rd_order, _with_linear_symmetries]] |
✗ |
0.035 |
|
|
\[
{}y^{\prime \prime }-5 y^{\prime }+6 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.271 |
|
|
\[
{}y^{\prime \prime }-10 y^{\prime }+25 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.254 |
|
|
\[
{}x^{2} y^{\prime \prime }-6 x y^{\prime }+12 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.085 |
|
|
\[
{}2 x^{2} y^{\prime \prime }-x y^{\prime }+y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.101 |
|
|
\[
{}4 x^{2} y^{\prime \prime }+y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.082 |
|
|
\[
{}y^{\prime \prime }-\left (4+\frac {2}{x}\right ) y^{\prime }+\left (4+\frac {4}{x}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.104 |
|
|
\[
{}\left (x +1\right ) y^{\prime \prime }+x y^{\prime }-y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.109 |
|
|
\[
{}y^{\prime \prime }-\frac {y^{\prime }}{x}-4 x^{2} y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.111 |
|