|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}3 y^{\prime } = -2+\sqrt {2 x +3 y+4}
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
1.397 |
|
|
\[
{}3 y^{\prime }+\frac {2 y}{x} = 4 \sqrt {y}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
3.763 |
|
|
\[
{}y^{\prime } = 4+\frac {1}{\sin \left (4 x -y\right )}
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
38.788 |
|
|
\[
{}\left (y-x \right ) y^{\prime } = 1
\] |
[[_homogeneous, ‘class C‘], [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
1.370 |
|
|
\[
{}\left (x +y\right ) y^{\prime } = y
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.326 |
|
|
\[
{}\left (2 x y+2 x^{2}\right ) y^{\prime } = x^{2}+2 x y+2 y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
65.103 |
|
|
\[
{}y^{\prime }+\frac {y}{x} = x^{2} y^{3}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
2.879 |
|
|
\[
{}y^{\prime } = 2 \sqrt {2 x +y-3}-2
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
1.481 |
|
|
\[
{}y^{\prime } = 2 \sqrt {2 x +y-3}
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
2.167 |
|
|
\[
{}-y+x y^{\prime } = \sqrt {x y+x^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
8.467 |
|
|
\[
{}y^{\prime }+3 y = \frac {28 \,{\mathrm e}^{2 x}}{y^{3}}
\] |
[[_1st_order, _with_linear_symmetries], _Bernoulli] |
✓ |
2.832 |
|
|
\[
{}y^{\prime } = \left (x -y+3\right )^{2}
\] |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
3.421 |
|
|
\[
{}y^{\prime }+2 x = 2 \sqrt {y+x^{2}}
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
2.151 |
|
|
\[
{}\cos \left (y\right ) y^{\prime } = {\mathrm e}^{-x}-\sin \left (y\right )
\] |
[‘y=_G(x,y’)‘] |
✓ |
2.132 |
|
|
\[
{}y^{\prime } = x \left (1+\frac {2 y}{x^{2}}+\frac {y^{2}}{x^{4}}\right )
\] |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
1.550 |
|
|
\[
{}y^{\prime } = \frac {1}{y}-\frac {y}{2 x}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
1.916 |
|
|
\[
{}{\mathrm e}^{x y^{2}-x^{2}} \left (y^{2}-2 x \right )+2 \,{\mathrm e}^{x y^{2}-x^{2}} x y y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _exact, _rational, _Bernoulli] |
✓ |
2.000 |
|
|
\[
{}2 x y+y^{2}+\left (2 x y+x^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
4.718 |
|
|
\[
{}2 x y^{3}+4 x^{3}+3 x^{2} y^{2} y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _exact, _rational, _Bernoulli] |
✓ |
2.604 |
|
|
\[
{}2-2 x +3 y^{2} y^{\prime } = 0
\] |
[_separable] |
✓ |
1.784 |
|
|
\[
{}1+3 y^{2} x^{2}+\left (2 x^{3} y+6 y\right ) y^{\prime } = 0
\] |
[_exact, _rational, _Bernoulli] |
✓ |
1.644 |
|
|
\[
{}4 x^{3} y+\left (x^{4}-y^{4}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
73.186 |
|
|
\[
{}1+\ln \left (x y\right )+\frac {x y^{\prime }}{y} = 0
\] |
[[_homogeneous, ‘class G‘], _exact] |
✓ |
2.061 |
|
|
\[
{}1+{\mathrm e}^{y}+x \,{\mathrm e}^{y} y^{\prime } = 0
\] |
[_separable] |
✓ |
1.456 |
|
|
\[
{}{\mathrm e}^{y}+\left (x \,{\mathrm e}^{y}+1\right ) y^{\prime } = 0
\] |
[[_1st_order, _with_exponential_symmetries], _exact] |
✓ |
1.158 |
|
|
\[
{}1+y^{4}+x y^{3} y^{\prime } = 0
\] |
[_separable] |
✓ |
3.157 |
|
|
\[
{}y+\left (y^{4}-3 x \right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
7.532 |
|
|
\[
{}\frac {2 y}{x}+\left (4 x^{2} y-3\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
6.553 |
|
|
\[
{}1+\left (1-x \tan \left (y\right )\right ) y^{\prime } = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
1.265 |
|
|
\[
{}3 y+3 y^{2}+\left (2 x +4 x y\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
3.887 |
|
|
\[
{}2 x \left (1+y\right )-y^{\prime } = 0
\] |
[_separable] |
✓ |
1.104 |
|
|
\[
{}2 y^{3}+\left (4 x^{3} y^{3}-3 x y^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
6.326 |
|
|
\[
{}4 x y+\left (3 x^{2}+5 y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.702 |
|
|
\[
{}6+12 y^{2} x^{2}+\left (7 x^{3} y+\frac {x}{y}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
2.533 |
|
|
\[
{}x y^{\prime } = 2 y-6 x^{3}
\] |
[_linear] |
✓ |
1.384 |
|
|
\[
{}x y^{\prime } = 2 y^{2}-6 y
\] |
[_separable] |
✓ |
2.093 |
|
|
\[
{}4 y^{2}-y^{2} x^{2}+y^{\prime } = 0
\] |
[_separable] |
✓ |
1.437 |
|
|
\[
{}y^{\prime } = \sqrt {x +y}
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
2.504 |
|
|
\[
{}x^{2} y^{\prime }-\sqrt {x} = 3
\] |
[_quadrature] |
✓ |
0.362 |
|
|
\[
{}x y y^{\prime }-y^{2} = \sqrt {x^{4}+y^{2} x^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
37.003 |
|
|
\[
{}y^{\prime } = y^{2}-2 x y+x^{2}
\] |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
1.773 |
|
|
\[
{}4 x y-6+x^{2} y^{\prime } = 0
\] |
[_linear] |
✓ |
1.405 |
|
|
\[
{}x y^{2}-6+x^{2} y y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _exact, _rational, _Bernoulli] |
✓ |
1.919 |
|
|
\[
{}x^{3}+y^{3}+x y^{2} y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
13.795 |
|
|
\[
{}3 y-x^{3}+x y^{\prime } = 0
\] |
[_linear] |
✓ |
1.323 |
|
|
\[
{}1+2 x y^{2}+\left (2 x^{2} y+2 y\right ) y^{\prime } = 0
\] |
[_exact, _rational, _Bernoulli] |
✓ |
1.602 |
|
|
\[
{}3 x y^{3}-y+x y^{\prime } = 0
\] |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
2.622 |
|
|
\[
{}2+2 x^{2}-2 x y+\left (x^{2}+1\right ) y^{\prime } = 0
\] |
[_linear] |
✓ |
1.490 |
|
|
\[
{}\left (y^{2}-4\right ) y^{\prime } = y
\] |
[_quadrature] |
✓ |
1.589 |
|
|
\[
{}\left (x^{2}-4\right ) y^{\prime } = x
\] |
[_quadrature] |
✓ |
0.378 |
|
|
\[
{}y^{\prime } = \frac {1}{x y-3 x}
\] |
[_separable] |
✓ |
1.427 |
|
|
\[
{}y^{\prime } = \frac {3 y}{x +1}-y^{2}
\] |
[[_1st_order, _with_linear_symmetries], _rational, _Bernoulli] |
✓ |
1.526 |
|
|
\[
{}\sin \left (y\right )+\left (x +y\right ) \cos \left (y\right ) y^{\prime } = 0
\] |
[_exact, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
3.813 |
|
|
\[
{}\sin \left (y\right )+\left (x +1\right ) \cos \left (y\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
3.690 |
|
|
\[
{}\sin \left (x \right )+2 y^{\prime } \cos \left (x \right ) = 0
\] |
[_quadrature] |
✓ |
0.481 |
|
|
\[
{}x y y^{\prime } = 2 y^{2}+2 x^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
10.210 |
|
|
\[
{}y^{\prime } = \frac {x +2 y}{x +2 y+3}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.355 |
|
|
\[
{}y^{\prime } = \frac {x +2 y}{2 x -y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.779 |
|
|
\[
{}y^{\prime } = \frac {y}{x}+\tan \left (\frac {y}{x}\right )
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
4.112 |
|
|
\[
{}y^{\prime } = x y^{2}+3 y^{2}+x +3
\] |
[_separable] |
✓ |
2.153 |
|
|
\[
{}1-\left (x +2 y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
1.515 |
|
|
\[
{}\ln \left (y\right )+\left (\frac {x}{y}+3\right ) y^{\prime } = 0
\] |
[_exact, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
1.195 |
|
|
\[
{}y^{2}+1-y^{\prime } = 0
\] |
[_quadrature] |
✓ |
0.981 |
|
|
\[
{}y^{\prime }-3 y = 12 \,{\mathrm e}^{2 x}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.112 |
|
|
\[
{}x y y^{\prime } = y^{2}+x y+x^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
36.654 |
|
|
\[
{}\left (x +2\right ) y^{\prime }-x^{3} = 0
\] |
[_quadrature] |
✓ |
0.382 |
|
|
\[
{}x y^{3} y^{\prime } = y^{4}-x^{2}
\] |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
3.542 |
|
|
\[
{}y^{\prime } = 4 y-\frac {16 \,{\mathrm e}^{4 x}}{y^{2}}
\] |
[[_1st_order, _with_linear_symmetries], _Bernoulli] |
✓ |
2.060 |
|
|
\[
{}2 y-6 x +\left (x +1\right ) y^{\prime } = 0
\] |
[_linear] |
✓ |
1.492 |
|
|
\[
{}x y^{2}+\left (x^{2} y+10 y^{4}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _exact, _rational] |
✓ |
1.957 |
|
|
\[
{}y y^{\prime }-x y^{2} = 6 x \,{\mathrm e}^{4 x^{2}}
\] |
[_Bernoulli] |
✓ |
2.387 |
|
|
\[
{}\left (y-x +3\right )^{2} \left (y^{\prime }-1\right ) = 1
\] |
[[_homogeneous, ‘class C‘], _exact, _rational, _dAlembert] |
✓ |
11.450 |
|
|
\[
{}x +y \,{\mathrm e}^{x y}+x \,{\mathrm e}^{x y} y^{\prime } = 0
\] |
[_exact, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
1.302 |
|
|
\[
{}y^{2}-y^{2} \cos \left (x \right )+y^{\prime } = 0
\] |
[_separable] |
✓ |
1.795 |
|
|
\[
{}y^{\prime }+2 y = \sin \left (x \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
1.232 |
|
|
\[
{}y^{\prime }+2 x = \sin \left (x \right )
\] |
[_quadrature] |
✓ |
0.354 |
|
|
\[
{}y^{\prime } = y^{3}-y^{3} \cos \left (x \right )
\] |
[_separable] |
✓ |
2.720 |
|
|
\[
{}y^{2} {\mathrm e}^{x y^{2}}-2 x +2 x y \,{\mathrm e}^{x y^{2}} y^{\prime } = 0
\] |
[_exact, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
1.678 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{4 x +3 y}
\] |
[_separable] |
✓ |
2.009 |
|
|
\[
{}y^{\prime } = \tan \left (6 x +3 y+1\right )-2
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
388.497 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{4 x +3 y}
\] |
[_separable] |
✓ |
2.023 |
|
|
\[
{}y^{\prime } = x \left (6 y+{\mathrm e}^{x^{2}}\right )
\] |
[_linear] |
✓ |
1.238 |
|
|
\[
{}x \left (1-2 y\right )+\left (y-x^{2}\right ) y^{\prime } = 0
\] |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.204 |
|
|
\[
{}x^{2} y^{\prime }+3 x y = 6 \,{\mathrm e}^{-x^{2}}
\] |
[_linear] |
✓ |
1.260 |
|
|
\[
{}x y^{\prime \prime }+4 y^{\prime } = 18 x^{2}
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.241 |
|
|
\[
{}x y^{\prime \prime } = 2 y^{\prime }
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.971 |
|
|
\[
{}y^{\prime \prime } = y^{\prime }
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.212 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime } = 8 \,{\mathrm e}^{2 x}
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.546 |
|
|
\[
{}x y^{\prime \prime } = y^{\prime }-2 x^{2} y^{\prime }
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.989 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+2 x y^{\prime } = 0
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.097 |
|
|
\[
{}y^{\prime \prime } = 4 x \sqrt {y^{\prime }}
\] |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
0.467 |
|
|
\[
{}y^{\prime } y^{\prime \prime } = 1
\] |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_poly_yn]] |
✓ |
1.846 |
|
|
\[
{}y y^{\prime \prime } = -{y^{\prime }}^{2}
\] |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.804 |
|
|
\[
{}x y^{\prime \prime } = {y^{\prime }}^{2}-y^{\prime }
\] |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
0.331 |
|
|
\[
{}x y^{\prime \prime }-{y^{\prime }}^{2} = 6 x^{5}
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.738 |
|
|
\[
{}y y^{\prime \prime }-{y^{\prime }}^{2} = y^{\prime }
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.276 |
|
|
\[
{}y^{\prime \prime } = 2 y^{\prime }-6
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.484 |
|
|
\[
{}\left (-3+y\right ) y^{\prime \prime } = 2 {y^{\prime }}^{2}
\] |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.204 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime } = 9 \,{\mathrm e}^{-3 x}
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.536 |
|
|
\[
{}y^{\prime \prime \prime } = y^{\prime \prime }
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.061 |
|