|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{\prime } = 1+2 x y
\] |
[_linear] |
✓ |
1.124 |
|
|
\[
{}2 y^{\prime } x = y+2 x \cos \left (x \right )
\] |
[_linear] |
✓ |
2.023 |
|
|
\[
{}y^{\prime }+p \left (x \right ) y = 0
\] |
[_separable] |
✓ |
1.086 |
|
|
\[
{}y^{\prime }+p \left (x \right ) y = q \left (x \right )
\] |
[_linear] |
✓ |
1.444 |
|
|
\[
{}\left (x +y\right ) y^{\prime } = x -y
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
4.798 |
|
|
\[
{}2 x y y^{\prime } = x^{2}+2 y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
5.913 |
|
|
\[
{}y^{\prime } x = y+2 \sqrt {x y}
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
6.250 |
|
|
\[
{}\left (x -y\right ) y^{\prime } = x +y
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.696 |
|
|
\[
{}x \left (x +y\right ) y^{\prime } = y \left (x -y\right )
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
3.457 |
|
|
\[
{}\left (x +2 y\right ) y^{\prime } = y
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
4.023 |
|
|
\[
{}x y^{2} y^{\prime } = x^{3}+y^{3}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
8.123 |
|
|
\[
{}x^{2} y^{\prime } = x y+x^{2} {\mathrm e}^{\frac {y}{x}}
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
10.315 |
|
|
\[
{}x^{2} y^{\prime } = x y+y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
2.428 |
|
|
\[
{}x y y^{\prime } = x^{2}+3 y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
5.260 |
|
|
\[
{}\left (x^{2}-y^{2}\right ) y^{\prime } = 2 x y
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
4.674 |
|
|
\[
{}x y y^{\prime } = y^{2}+x \sqrt {4 x^{2}+y^{2}}
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
25.417 |
|
|
\[
{}y^{\prime } x = y+\sqrt {x^{2}+y^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
6.560 |
|
|
\[
{}x +y y^{\prime } = \sqrt {x^{2}+y^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
7.227 |
|
|
\[
{}x \left (x +y\right ) y^{\prime }+y \left (3 x +y\right ) = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
4.426 |
|
|
\[
{}y^{\prime } = \sqrt {x +y+1}
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
1.658 |
|
|
\[
{}y^{\prime } = \left (4 x +y\right )^{2}
\] |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
1.859 |
|
|
\[
{}\left (x +y\right ) y^{\prime } = 1
\] |
[[_homogeneous, ‘class C‘], [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
1.671 |
|
|
\[
{}x^{2} y^{\prime }+2 x y = 5 y^{3}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
2.547 |
|
|
\[
{}y^{2} y^{\prime }+2 x y^{3} = 6 x
\] |
[_separable] |
✓ |
1.994 |
|
|
\[
{}y^{\prime } = y+y^{3}
\] |
[_quadrature] |
✓ |
3.634 |
|
|
\[
{}x^{2} y^{\prime }+2 x y = 5 y^{4}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
2.856 |
|
|
\[
{}y^{\prime } x +6 y = 3 x y^{{4}/{3}}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
9.263 |
|
|
\[
{}2 y^{\prime } x +y^{3} {\mathrm e}^{-2 x} = 2 x y
\] |
[_Bernoulli] |
✓ |
2.191 |
|
|
\[
{}y^{2} \left (y^{\prime } x +y\right ) \sqrt {x^{4}+1} = x
\] |
[_Bernoulli] |
✓ |
6.086 |
|
|
\[
{}3 y^{2} y^{\prime }+y^{3} = {\mathrm e}^{-x}
\] |
[[_1st_order, _with_linear_symmetries], _Bernoulli] |
✓ |
2.055 |
|
|
\[
{}3 x y^{2} y^{\prime } = 3 x^{4}+y^{3}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
2.934 |
|
|
\[
{}x \,{\mathrm e}^{y} y^{\prime } = 2 \,{\mathrm e}^{y}+2 x^{3} {\mathrm e}^{2 x}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
1.524 |
|
|
\[
{}2 x \sin \left (y\right ) \cos \left (y\right ) y^{\prime } = 4 x^{2}+\sin \left (y\right )^{2}
\] |
[‘y=_G(x,y’)‘] |
✓ |
3.040 |
|
|
\[
{}\left ({\mathrm e}^{y}+x \right ) y^{\prime } = x \,{\mathrm e}^{-y}-1
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
1.964 |
|
|
\[
{}2 x +3 y+\left (3 x +2 y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
4.868 |
|
|
\[
{}4 x -y+\left (6 y-x \right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
4.557 |
|
|
\[
{}3 x^{2}+2 y^{2}+\left (4 x y+6 y^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
6.867 |
|
|
\[
{}2 x y^{2}+3 x^{2}+\left (2 x^{2} y+4 y^{3}\right ) y^{\prime } = 0
\] |
[_exact, _rational] |
✓ |
1.685 |
|
|
\[
{}x^{3}+\frac {y}{x}+\left (y^{2}+\ln \left (x \right )\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
1.460 |
|
|
\[
{}1+y \,{\mathrm e}^{x y}+\left (2 y+x \,{\mathrm e}^{x y}\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
1.954 |
|
|
\[
{}\cos \left (x \right )+\ln \left (y\right )+\left (\frac {x}{y}+{\mathrm e}^{y}\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
2.780 |
|
|
\[
{}x +\arctan \left (y\right )+\frac {\left (x +y\right ) y^{\prime }}{1+y^{2}} = 0
\] |
[_exact] |
✓ |
1.668 |
|
|
\[
{}3 x^{2} y^{3}+y^{4}+\left (3 x^{3} y^{2}+y^{4}+4 x y^{3}\right ) y^{\prime } = 0
\] |
[_exact, _rational] |
✓ |
1.429 |
|
|
\[
{}{\mathrm e}^{x} \sin \left (y\right )+\tan \left (y\right )+\left ({\mathrm e}^{x} \cos \left (y\right )+x \sec \left (y\right )^{2}\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
13.983 |
|
|
\[
{}\frac {2 x}{y}-\frac {3 y^{2}}{x^{4}}+\left (\frac {2 y}{x^{3}}-\frac {x^{2}}{y^{2}}+\frac {1}{\sqrt {y}}\right ) y^{\prime } = 0
\] |
[_exact, _rational] |
✓ |
10.743 |
|
|
\[
{}\frac {2 x^{{5}/{2}}-3 y^{{5}/{3}}}{2 x^{{5}/{2}} y^{{2}/{3}}}+\frac {\left (3 y^{{5}/{3}}-2 x^{{5}/{2}}\right ) y^{\prime }}{3 x^{{3}/{2}} y^{{5}/{3}}} = 0
\] |
[[_1st_order, _with_linear_symmetries], _exact, _rational] |
✓ |
2.716 |
|
|
\[
{}x y^{\prime \prime } = y^{\prime }
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.014 |
|
|
\[
{}y^{\prime \prime } y+{y^{\prime }}^{2} = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.424 |
|
|
\[
{}y^{\prime \prime }+4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.344 |
|
|
\[
{}x y^{\prime \prime }+y^{\prime } = 4 x
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.060 |
|
|
\[
{}y^{\prime \prime } = {y^{\prime }}^{2}
\] |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.305 |
|
|
\[
{}x^{2} y^{\prime \prime }+3 y^{\prime } x = 2
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.007 |
|
|
\[
{}y^{\prime \prime } y+{y^{\prime }}^{2} = y y^{\prime }
\] |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.716 |
|
|
\[
{}y^{\prime \prime } = \left (x +y^{\prime }\right )^{2}
\] |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.400 |
|
|
\[
{}y^{\prime \prime } = 2 y {y^{\prime }}^{3}
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
0.270 |
|
|
\[
{}y^{3} y^{\prime \prime } = 1
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
1.094 |
|
|
\[
{}y^{\prime \prime } = 2 y y^{\prime }
\] |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Lagerstrom, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.637 |
|
|
\[
{}y^{\prime \prime } y = 3 {y^{\prime }}^{2}
\] |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.367 |
|
|
\[
{}y^{\prime } = f \left (a x +b y+c \right )
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
1.118 |
|
|
\[
{}y^{\prime }+p \left (x \right ) y = q \left (x \right ) y^{n}
\] |
[_Bernoulli] |
✓ |
2.024 |
|
|
\[
{}y^{\prime }+p \left (x \right ) y = q \left (x \right ) y \ln \left (y\right )
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
0.448 |
|
|
\[
{}y^{\prime } x -4 x^{2} y+2 y \ln \left (y\right ) = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
2.287 |
|
|
\[
{}y^{\prime } = \frac {x -y-1}{x +y+3}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.579 |
|
|
\[
{}y^{\prime } = \frac {2 y-x +7}{4 x -3 y-18}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
4.020 |
|
|
\[
{}y^{\prime } = \sin \left (x -y\right )
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
2.399 |
|
|
\[
{}y^{\prime } = -\frac {y \left (2 x^{3}-y^{3}\right )}{x \left (2 y^{3}-x^{3}\right )}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
7.106 |
|
|
\[
{}y^{\prime }+y^{2} = x^{2}+1
\] |
[_Riccati] |
✓ |
1.349 |
|
|
\[
{}y^{\prime }+2 x y = 1+x^{2}+y^{2}
\] |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
2.750 |
|
|
\[
{}y = y^{\prime } x -\frac {{y^{\prime }}^{2}}{4}
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
0.347 |
|
|
\[
{}r y^{\prime \prime } = \left (1+{y^{\prime }}^{2}\right )^{{3}/{2}}
\] |
[[_2nd_order, _missing_x]] |
✓ |
8.667 |
|
|
\[
{}x^{\prime } = x-x^{2}
\] |
[_quadrature] |
✓ |
2.359 |
|
|
\[
{}x^{\prime } = 10 x-x^{2}
\] |
[_quadrature] |
✓ |
2.381 |
|
|
\[
{}x^{\prime } = 1-x^{2}
\] |
[_quadrature] |
✓ |
1.585 |
|
|
\[
{}x^{\prime } = 9-4 x^{2}
\] |
[_quadrature] |
✓ |
1.805 |
|
|
\[
{}x^{\prime } = 3 x \left (5-x\right )
\] |
[_quadrature] |
✓ |
2.424 |
|
|
\[
{}x^{\prime } = 3 x \left (5-x\right )
\] |
[_quadrature] |
✓ |
2.397 |
|
|
\[
{}x^{\prime } = 4 x \left (7-x\right )
\] |
[_quadrature] |
✓ |
2.477 |
|
|
\[
{}x^{\prime } = 7 x \left (x-13\right )
\] |
[_quadrature] |
✓ |
2.056 |
|
|
\[
{}x^{3}+3 y-y^{\prime } x = 0
\] |
[_linear] |
✓ |
1.250 |
|
|
\[
{}x y^{2}+3 y^{2}-x^{2} y^{\prime } = 0
\] |
[_separable] |
✓ |
1.801 |
|
|
\[
{}x y+y^{2}-x^{2} y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
2.438 |
|
|
\[
{}2 x y^{3}+{\mathrm e}^{x}+\left (3 x^{2} y^{2}+\sin \left (y\right )\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
2.064 |
|
|
\[
{}3 y+x^{4} y^{\prime } = 2 x y
\] |
[_separable] |
✓ |
1.898 |
|
|
\[
{}2 x y^{2}+x^{2} y^{\prime } = y^{2}
\] |
[_separable] |
✓ |
1.827 |
|
|
\[
{}2 x^{2} y+x^{3} y^{\prime } = 1
\] |
[_linear] |
✓ |
1.250 |
|
|
\[
{}x^{2} y^{\prime }+2 x y = y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
2.992 |
|
|
\[
{}y^{\prime } x +2 y = 6 x^{2} \sqrt {y}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
2.232 |
|
|
\[
{}y^{\prime } = 1+x^{2}+y^{2}+x^{2} y^{2}
\] |
[_separable] |
✓ |
2.439 |
|
|
\[
{}x^{2} y^{\prime } = x y+3 y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
2.454 |
|
|
\[
{}6 x y^{3}+2 y^{4}+\left (9 x^{2} y^{2}+8 x y^{3}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
6.289 |
|
|
\[
{}4 x y^{2}+y^{\prime } = 5 x^{4} y^{2}
\] |
[_separable] |
✓ |
1.831 |
|
|
\[
{}x^{3} y^{\prime } = x^{2} y-y^{3}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
81.205 |
|
|
\[
{}y^{\prime }+3 y = 3 x^{2} {\mathrm e}^{-3 x}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.932 |
|
|
\[
{}y^{\prime } = x^{2}-2 x y+y^{2}
\] |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
1.542 |
|
|
\[
{}{\mathrm e}^{x}+y \,{\mathrm e}^{x y}+\left ({\mathrm e}^{y}+x \,{\mathrm e}^{x y}\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
2.345 |
|
|
\[
{}2 x^{2} y-x^{3} y^{\prime } = y^{3}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
85.114 |
|
|
\[
{}3 x^{5} y^{2}+x^{3} y^{\prime } = 2 y^{2}
\] |
[_separable] |
✓ |
1.687 |
|
|
\[
{}y^{\prime } x +3 y = \frac {3}{x^{{3}/{2}}}
\] |
[_linear] |
✓ |
1.863 |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime }+\left (x -1\right ) y = 1
\] |
[_linear] |
✓ |
1.385 |
|
|
\[
{}y^{\prime } x = 6 y+12 x^{4} y^{{2}/{3}}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
2.717 |
|