|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}\left (x^{2}-1\right )^{2} y^{\prime \prime }+\left (x +1\right ) y^{\prime }-y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.628 |
|
|
\[
{}x y^{\prime \prime }+4 y^{\prime }-y x = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.696 |
|
|
\[
{}2 x y^{\prime \prime }+\left (x +1\right ) y^{\prime }-k y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.930 |
|
|
\[
{}x^{3} y^{\prime \prime }+x^{2} y^{\prime }+y = 0
\] |
[[_Emden, _Fowler]] |
✗ |
0.110 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime }-2 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✗ |
0.154 |
|
|
\[
{}2 x^{2} y^{\prime \prime }+x \left (1-x \right ) y^{\prime }-y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.795 |
|
|
\[
{}x \left (x -1\right ) y^{\prime \prime }+3 y^{\prime } x +y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.158 |
|
|
\[
{}y^{\prime \prime }-x^{2} y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.846 |
|
|
\[
{}x y^{\prime \prime }+y^{\prime }+y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.681 |
|
|
\[
{}x y^{\prime \prime }+x^{2} y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.608 |
|
|
\[
{}y^{\prime \prime }+\alpha ^{2} y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.500 |
|
|
\[
{}y^{\prime \prime }-\alpha ^{2} y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
3.097 |
|
|
\[
{}y^{\prime \prime }+\beta y^{\prime }+\gamma y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.973 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +n \left (n +1\right ) y = 0
\] |
[_Gegenbauer] |
✗ |
0.732 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +\left (-\nu ^{2}+x^{2}\right ) y = \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
7.248 |
|
|
\[
{}y^{\prime }+y \cos \left (x \right ) = \frac {\sin \left (2 x \right )}{2}
\] |
[_linear] |
✓ |
2.367 |
|
|
\[
{}{y^{\prime }}^{2}-y^{\prime }-y^{\prime } x +y = 0
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
0.339 |
|
|
\[
{}y {y^{\prime }}^{2}+2 y^{\prime } x -y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
1.891 |
|
|
\[
{}x y \left (1-{y^{\prime }}^{2}\right ) = \left (x^{2}-y^{2}-a^{2}\right ) y^{\prime }
\] |
[_rational] |
✓ |
99.690 |
|
|
\[
{}y^{\prime \prime \prime }+\frac {3 y^{\prime \prime }}{x} = 0
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.159 |
|
|
\[
{}y^{\prime \prime }-2 k y^{\prime }+k^{2} y = {\mathrm e}^{x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.837 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-y^{\prime } x -a^{2} y = 0
\] |
[_Gegenbauer, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.927 |
|
|
\[
{}y^{\prime \prime }+\frac {2 y^{\prime }}{x} = 0
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.621 |
|
|
\[
{}y-y^{\prime } x = 0
\] |
[_separable] |
✓ |
1.084 |
|
|
\[
{}\left (1+u \right ) v+\left (1-v\right ) u v^{\prime } = 0
\] |
[_separable] |
✓ |
1.161 |
|
|
\[
{}1+y-\left (1-x \right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
1.349 |
|
|
\[
{}\left (t^{2}+x t^{2}\right ) x^{\prime }+x^{2}+t x^{2} = 0
\] |
[_separable] |
✓ |
1.473 |
|
|
\[
{}y-a +x^{2} y^{\prime } = 0
\] |
[_separable] |
✓ |
0.842 |
|
|
\[
{}z-\left (-a^{2}+t^{2}\right ) z^{\prime } = 0
\] |
[_separable] |
✓ |
1.408 |
|
|
\[
{}y^{\prime } = \frac {1+y^{2}}{x^{2}+1}
\] |
[_separable] |
✓ |
1.612 |
|
|
\[
{}1+s^{2}-\sqrt {t}\, s^{\prime } = 0
\] |
[_separable] |
✓ |
1.855 |
|
|
\[
{}r^{\prime }+r \tan \left (t \right ) = 0
\] |
[_separable] |
✓ |
1.221 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime }-\sqrt {1-y^{2}} = 0
\] |
[_separable] |
✓ |
1.801 |
|
|
\[
{}\sqrt {-x^{2}+1}\, y^{\prime }-\sqrt {1-y^{2}} = 0
\] |
[_separable] |
✓ |
2.914 |
|
|
\[
{}3 \,{\mathrm e}^{x} \tan \left (y\right )+\left (1-{\mathrm e}^{x}\right ) \sec \left (y\right )^{2} y^{\prime } = 0
\] |
[_separable] |
✓ |
3.067 |
|
|
\[
{}x -x y^{2}+\left (y-x^{2} y\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
1.755 |
|
|
\[
{}y-x +\left (x +y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.324 |
|
|
\[
{}x +y+y^{\prime } x = 0
\] |
[_linear] |
✓ |
1.623 |
|
|
\[
{}x +y+\left (-x +y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.437 |
|
|
\[
{}-y+y^{\prime } x = \sqrt {x^{2}+y^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
5.519 |
|
|
\[
{}8 y+10 x +\left (5 y+7 x \right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.003 |
|
|
\[
{}2 \sqrt {s t}-s+t s^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
5.891 |
|
|
\[
{}t -s+t s^{\prime } = 0
\] |
[_linear] |
✓ |
1.058 |
|
|
\[
{}x y^{2} y^{\prime } = x^{3}+y^{3}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
7.114 |
|
|
\[
{}x \cos \left (\frac {y}{x}\right ) \left (y^{\prime } x +y\right ) = y \sin \left (\frac {y}{x}\right ) \left (-y+y^{\prime } x \right )
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
6.194 |
|
|
\[
{}3 y-7 x +7-\left (3 x -7 y-3\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.044 |
|
|
\[
{}x +2 y+1-\left (4 y+2 x +3\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.197 |
|
|
\[
{}x +2 y+1-\left (2 x -3\right ) y^{\prime } = 0
\] |
[_linear] |
✓ |
1.073 |
|
|
\[
{}\frac {y-y^{\prime } x}{\sqrt {x^{2}+y^{2}}} = m
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
14.586 |
|
|
\[
{}\frac {x +y y^{\prime }}{\sqrt {x^{2}+y^{2}}} = m
\] |
[[_homogeneous, ‘class A‘], _exact, _dAlembert] |
✓ |
69.580 |
|
|
\[
{}y+\frac {x}{y^{\prime }} = \sqrt {x^{2}+y^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
4.851 |
|
|
\[
{}y y^{\prime } = -x +\sqrt {x^{2}+y^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
4.347 |
|
|
\[
{}y^{\prime }-\frac {2 y}{x +1} = \left (x +1\right )^{3}
\] |
[_linear] |
✓ |
1.179 |
|
|
\[
{}y^{\prime }-\frac {a y}{x} = \frac {x +1}{x}
\] |
[_linear] |
✓ |
1.095 |
|
|
\[
{}\left (-x^{2}+x \right ) y^{\prime }+\left (2 x^{2}-1\right ) y-a \,x^{3} = 0
\] |
[_linear] |
✓ |
1.340 |
|
|
\[
{}s^{\prime } \cos \left (t \right )+s \sin \left (t \right ) = 1
\] |
[_linear] |
✓ |
1.827 |
|
|
\[
{}s^{\prime }+s \cos \left (t \right ) = \frac {\sin \left (2 t \right )}{2}
\] |
[_linear] |
✓ |
2.304 |
|
|
\[
{}y^{\prime }-\frac {n y}{x} = {\mathrm e}^{x} x^{n}
\] |
[_linear] |
✓ |
1.162 |
|
|
\[
{}y^{\prime }+\frac {n y}{x} = a \,x^{-n}
\] |
[_linear] |
✓ |
0.893 |
|
|
\[
{}y^{\prime }+y = {\mathrm e}^{-x}
\] |
[[_linear, ‘class A‘]] |
✓ |
0.799 |
|
|
\[
{}y^{\prime }+\frac {\left (1-2 x \right ) y}{x^{2}}-1 = 0
\] |
[_linear] |
✓ |
1.362 |
|
|
\[
{}y^{\prime }+y x = x^{3} y^{3}
\] |
[_Bernoulli] |
✓ |
1.060 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime }-y x +a x y^{2} = 0
\] |
[_separable] |
✓ |
2.182 |
|
|
\[
{}3 y^{2} y^{\prime }-a y^{3}-x -1 = 0
\] |
[_rational, _Bernoulli] |
✓ |
1.521 |
|
|
\[
{}y^{\prime } \left (x^{2} y^{3}+y x \right ) = 1
\] |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✗ |
0.803 |
|
|
\[
{}y^{\prime } x = \left (y \ln \left (x \right )-2\right ) y
\] |
[_Bernoulli] |
✓ |
1.761 |
|
|
\[
{}y-y^{\prime } \cos \left (x \right ) = y^{2} \cos \left (x \right ) \left (1-\sin \left (x \right )\right )
\] |
[_Bernoulli] |
✓ |
8.356 |
|
|
\[
{}x^{2}+y+\left (x -2 y\right ) y^{\prime } = 0
\] |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.041 |
|
|
\[
{}y-3 x^{2}-\left (4 y-x \right ) y^{\prime } = 0
\] |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.069 |
|
|
\[
{}\left (y^{3}-x \right ) y^{\prime } = y
\] |
[[_homogeneous, ‘class G‘], _exact, _rational] |
✓ |
8.306 |
|
|
\[
{}\frac {y^{2}}{\left (x -y\right )^{2}}-\frac {1}{x}+\left (\frac {1}{y}-\frac {x^{2}}{\left (x -y\right )^{2}}\right ) y^{\prime } = 0
\] |
[_exact, _rational] |
✓ |
1.806 |
|
|
\[
{}6 x y^{2}+4 x^{3}+3 \left (2 x^{2} y+y^{2}\right ) y^{\prime } = 0
\] |
[_exact, _rational] |
✓ |
1.266 |
|
|
\[
{}\frac {x}{\left (x +y\right )^{2}}+\frac {\left (2 x +y\right ) y^{\prime }}{\left (x +y\right )^{2}} = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
2.062 |
|
|
\[
{}\frac {1}{x^{2}}+\frac {3 y^{2}}{x^{4}} = \frac {2 y y^{\prime }}{x^{3}}
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
3.460 |
|
|
\[
{}\frac {x^{2} y^{\prime }}{\left (x -y\right )^{2}}-\frac {y^{2}}{\left (x -y\right )^{2}} = 0
\] |
[_separable] |
✓ |
2.093 |
|
|
\[
{}x +y y^{\prime } = \frac {y}{x^{2}+y^{2}}-\frac {x y^{\prime }}{x^{2}+y^{2}}
\] |
[[_1st_order, _with_linear_symmetries], _exact, _rational] |
✓ |
1.490 |
|
|
\[
{}y = 2 y^{\prime } x +{y^{\prime }}^{2}
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
0.326 |
|
|
\[
{}y = x {y^{\prime }}^{2}+{y^{\prime }}^{2}
\] |
[[_homogeneous, ‘class C‘], _rational, _dAlembert] |
✓ |
0.444 |
|
|
\[
{}y = x \left (1+y^{\prime }\right )+{y^{\prime }}^{2}
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
0.393 |
|
|
\[
{}y = y {y^{\prime }}^{2}+2 y^{\prime } x
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
1.761 |
|
|
\[
{}y = y y^{\prime }+y^{\prime }-{y^{\prime }}^{2}
\] |
[_quadrature] |
✓ |
0.781 |
|
|
\[
{}y = y^{\prime } x +\sqrt {1-{y^{\prime }}^{2}}
\] |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
1.454 |
|
|
\[
{}y = y^{\prime } x +y^{\prime }
\] |
[_separable] |
✓ |
1.211 |
|
|
\[
{}y = y^{\prime } x +\frac {1}{y^{\prime }}
\] |
[[_homogeneous, ‘class G‘], _rational, _Clairaut] |
✓ |
0.334 |
|
|
\[
{}y = y^{\prime } x -\frac {1}{{y^{\prime }}^{2}}
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
0.615 |
|
|
\[
{}y^{\prime } = \frac {2 y}{x}-\sqrt {3}
\] |
[_linear] |
✓ |
1.837 |
|
|
\[
{}y^{\prime \prime \prime }-2 y^{\prime \prime }-y^{\prime }+2 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.061 |
|
|
\[
{}y^{\prime \prime } = \frac {1}{2 y^{\prime }}
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_poly_yn]] |
✓ |
1.518 |
|
|
\[
{}x y^{\prime \prime \prime } = 2
\] |
[[_3rd_order, _quadrature]] |
✓ |
0.183 |
|
|
\[
{}y^{\prime \prime } = a^{2} y
\] |
[[_2nd_order, _missing_x]] |
✓ |
3.135 |
|
|
\[
{}y^{\prime \prime } = \frac {a}{y^{3}}
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
1.073 |
|
|
\[
{}x y^{\prime \prime }-y^{\prime } = x^{2} {\mathrm e}^{x}
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.243 |
|
|
\[
{}y y^{\prime \prime }-{y^{\prime }}^{2}+{y^{\prime }}^{3} = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
0.372 |
|
|
\[
{}y^{\prime \prime }+\tan \left (x \right ) y^{\prime } = \sin \left (2 x \right )
\] |
[[_2nd_order, _missing_y]] |
✓ |
2.329 |
|
|
\[
{}{y^{\prime \prime }}^{2}+{y^{\prime }}^{2} = a^{2}
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.079 |
|
|
\[
{}y^{\prime \prime } = \frac {1}{2 y^{\prime }}
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_poly_yn]] |
✓ |
1.539 |
|
|
\[
{}y^{\prime \prime \prime } = {y^{\prime \prime }}^{2}
\] |
[[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2], [_3rd_order, _reducible, _mu_poly_yn]] |
✓ |
0.182 |
|
|
\[
{}y^{\prime } y^{\prime \prime \prime }-3 {y^{\prime \prime }}^{2} = 0
\] |
[[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2], [_3rd_order, _reducible, _mu_poly_yn]] |
✓ |
0.334 |
|
|
\[
{}y^{\prime \prime } = 9 y
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.932 |
|
|
\[
{}y^{\prime \prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.658 |
|