|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}\left (2 x -1\right ) \left (-1+y\right )+\left (x +2\right ) \left (x -3\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
1.444 |
|
|
\[
{}7 x +4 y+\left (4 x +3 y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.672 |
|
|
\[
{}{\mathrm e}^{x} \left (x^{4} y^{2}+4 x^{3} y^{2}+1\right )+\left (2 x^{4} y \,{\mathrm e}^{x}+2 y\right ) y^{\prime } = 0
\] |
[_exact, _Bernoulli] |
✓ |
2.413 |
|
|
\[
{}x^{3} y^{4}+x +\left (x^{4} y^{3}+y\right ) y^{\prime } = 0
\] |
[_exact, _rational] |
✓ |
2.524 |
|
|
\[
{}3 x^{2}+2 y+\left (2 y+2 x \right ) y^{\prime } = 0
\] |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.229 |
|
|
\[
{}x^{3} y^{4}+2 x +\left (x^{4} y^{3}+3 y\right ) y^{\prime } = 0
\] |
[_exact, _rational] |
✓ |
2.383 |
|
|
\[
{}x^{2}+y^{2}+2 x y y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
4.131 |
|
|
\[
{}y^{\prime }+\frac {2 y}{x} = -\frac {2 x y}{x^{2}+2 x^{2} y+1}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
3.825 |
|
|
\[
{}y^{\prime }-\frac {3 y}{x} = \frac {2 x^{4} \left (4 x^{3}-3 y\right )}{3 x^{5}+3 x^{3}+2 y}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
1.865 |
|
|
\[
{}y^{\prime }+2 y x = -\frac {{\mathrm e}^{-x^{2}} \left (3 x +2 y \,{\mathrm e}^{x^{2}}\right )}{2 x +3 y \,{\mathrm e}^{x^{2}}}
\] |
[[_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
79.186 |
|
|
\[
{}y+\left (2 x +\frac {1}{y}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
2.042 |
|
|
\[
{}-y^{2}+x^{2} y^{\prime } = 0
\] |
[_separable] |
✓ |
2.541 |
|
|
\[
{}y-y^{\prime } x = 0
\] |
[_separable] |
✓ |
1.076 |
|
|
\[
{}3 x^{2} y+2 x^{3} y^{\prime } = 0
\] |
[_separable] |
✓ |
1.774 |
|
|
\[
{}2 y^{3}+3 y^{2} y^{\prime } = 0
\] |
[_quadrature] |
✓ |
0.705 |
|
|
\[
{}5 y x +2 y+5+2 y^{\prime } x = 0
\] |
[_linear] |
✓ |
1.204 |
|
|
\[
{}y x +x +2 y+1+\left (x +1\right ) y^{\prime } = 0
\] |
[_linear] |
✓ |
1.692 |
|
|
\[
{}27 x y^{2}+8 y^{3}+\left (18 x^{2} y+12 x y^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
7.654 |
|
|
\[
{}6 x y^{2}+2 y+\left (12 x^{2} y+6 x +3\right ) y^{\prime } = 0
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
1.470 |
|
|
\[
{}y^{2}+\left (x y^{2}+6 y x +\frac {1}{y}\right ) y^{\prime } = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
1.522 |
|
|
\[
{}12 x^{3} y+24 x^{2} y^{2}+\left (9 x^{4}+32 x^{3} y+4 y\right ) y^{\prime } = 0
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
1.869 |
|
|
\[
{}x^{2} y+4 y x +2 y+\left (x^{2}+x \right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
1.434 |
|
|
\[
{}-y+\left (x^{4}-x \right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
1.742 |
|
|
\[
{}\cos \left (x \right ) \cos \left (y\right )+\left (\sin \left (x \right ) \cos \left (y\right )-\sin \left (x \right ) \sin \left (y\right )+y\right ) y^{\prime } = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
70.535 |
|
|
\[
{}2 y x +y^{2}+\left (2 y x +x^{2}-2 x^{2} y^{2}-2 x y^{3}\right ) y^{\prime } = 0
\] |
[_rational] |
✓ |
2.094 |
|
|
\[
{}y \sin \left (y\right )+x \left (\sin \left (y\right )-y \cos \left (y\right )\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
2.690 |
|
|
\[
{}a y+b x y+\left (c x +d x y\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
2.363 |
|
|
\[
{}3 x^{2} y^{3}-y^{2}+y+\left (-y x +2 x \right ) y^{\prime } = 0
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class C‘]] |
✗ |
1.332 |
|
|
\[
{}2 y+3 \left (x^{2}+x^{2} y^{3}\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
1.999 |
|
|
\[
{}a \cos \left (x \right ) y-y^{2} \sin \left (x \right )+\left (b \cos \left (x \right ) y-x \sin \left (x \right ) y\right ) y^{\prime } = 0
\] |
[_linear] |
✓ |
11.475 |
|
|
\[
{}x^{4} y^{4}+x^{5} y^{3} y^{\prime } = 0
\] |
[_separable] |
✓ |
1.557 |
|
|
\[
{}y \left (x \cos \left (x \right )+2 \sin \left (x \right )\right )+x \left (1+y\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
3.752 |
|
|
\[
{}x^{4} y^{3}+y+\left (x^{5} y^{2}-x \right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
2.095 |
|
|
\[
{}3 y x +2 y^{2}+y+\left (x^{2}+2 y x +x +2 y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class D‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
2.414 |
|
|
\[
{}12 y x +6 y^{3}+\left (9 x^{2}+10 x y^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
2.595 |
|
|
\[
{}3 x^{2} y^{2}+2 y+2 y^{\prime } x = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
2.132 |
|
|
\[
{}y^{\prime \prime }-7 y^{\prime }+10 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.583 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.970 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.154 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.940 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.456 |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime \prime }+4 y^{\prime } x +2 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.785 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }-3 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.720 |
|
|
\[
{}y^{\prime \prime }-6 y^{\prime }+9 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.373 |
|
|
\[
{}y^{\prime \prime }-2 a y^{\prime }+a^{2} y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.757 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x -y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.671 |
|
|
\[
{}x^{2} y^{\prime \prime }-y^{\prime } x +y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.529 |
|
|
\[
{}x^{2} y^{\prime \prime }-\left (2 a -1\right ) x y^{\prime }+a^{2} y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.445 |
|
|
\[
{}4 x^{2} y^{\prime \prime }-4 y^{\prime } x +\left (-16 x^{2}+3\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.305 |
|
|
\[
{}\left (x -1\right ) y^{\prime \prime }-y^{\prime } x +y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.374 |
|
|
\[
{}x^{2} y^{\prime \prime }-2 y^{\prime } x +\left (x^{2}+2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.398 |
|
|
\[
{}4 x^{2} \sin \left (x \right ) y^{\prime \prime }-4 x \left (x \cos \left (x \right )+\sin \left (x \right )\right ) y^{\prime }+\left (2 x \cos \left (x \right )+3 \sin \left (x \right )\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.809 |
|
|
\[
{}\left (3 x -1\right ) y^{\prime \prime }-\left (3 x +2\right ) y^{\prime }+\left (6 x -8\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.642 |
|
|
\[
{}\left (x^{2}-4\right ) y^{\prime \prime }+4 y^{\prime } x +2 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.116 |
|
|
\[
{}\left (2 x +1\right ) y^{\prime \prime }-2 \left (2 x^{2}-1\right ) y^{\prime }-4 \left (x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.596 |
|
|
\[
{}\left (x^{2}-2 x \right ) y^{\prime \prime }+\left (-x^{2}+2\right ) y^{\prime }+\left (2 x -2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.473 |
|
|
\[
{}\left (2 x +1\right ) y^{\prime \prime }-2 y^{\prime }-\left (2 x +3\right ) y = \left (2 x +1\right )^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.652 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x -y = \frac {4}{x^{2}}
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
0.200 |
|
|
\[
{}x^{2} y^{\prime \prime }-y^{\prime } x +y = x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.224 |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime }+2 y = \frac {1}{1+{\mathrm e}^{-x}}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.614 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+y = 7 x^{{3}/{2}} {\mathrm e}^{x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.296 |
|
|
\[
{}4 x^{2} y^{\prime \prime }+\left (-8 x^{2}+4 x \right ) y^{\prime }+\left (4 x^{2}-4 x -1\right ) y = 4 \sqrt {x}\, {\mathrm e}^{x} \left (1+4 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.279 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+2 y = {\mathrm e}^{x} \sec \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.640 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime } x +\left (4 x^{2}+2\right ) y = 8 \,{\mathrm e}^{-x \left (x +2\right )}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.283 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x -4 y = -6 x -4
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.217 |
|
|
\[
{}x^{2} y^{\prime \prime }+2 x \left (x -1\right ) y^{\prime }+\left (x^{2}-2 x +2\right ) y = x^{3} {\mathrm e}^{2 x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.246 |
|
|
\[
{}x^{2} y^{\prime \prime }-x \left (2 x -1\right ) y^{\prime }+\left (x^{2}-x -1\right ) y = x^{2} {\mathrm e}^{x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.249 |
|
|
\[
{}\left (1-2 x \right ) y^{\prime \prime }+2 y^{\prime }+\left (2 x -3\right ) y = \left (4 x^{2}-4 x +1\right ) {\mathrm e}^{x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.283 |
|
|
\[
{}x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y = 4 x^{4}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.230 |
|
|
\[
{}2 x y^{\prime \prime }+\left (1+4 x \right ) y^{\prime }+\left (2 x +1\right ) y = 3 \sqrt {x}\, {\mathrm e}^{-x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.641 |
|
|
\[
{}x y^{\prime \prime }-\left (2 x +1\right ) y^{\prime }+\left (x +1\right ) y = -{\mathrm e}^{-x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.271 |
|
|
\[
{}4 x^{2} y^{\prime \prime }-4 x \left (x +1\right ) y^{\prime }+\left (2 x +3\right ) y = 4 x^{{5}/{2}} {\mathrm e}^{2 x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.245 |
|
|
\[
{}x^{2} y^{\prime \prime }-5 y^{\prime } x +8 y = 4 x^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.580 |
|
|
\[
{}x y^{\prime \prime }+\left (2-2 x \right ) y^{\prime }+\left (x -2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.153 |
|
|
\[
{}x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.151 |
|
|
\[
{}x^{2} \ln \left (x \right )^{2} y^{\prime \prime }-2 x \ln \left (x \right ) y^{\prime }+\left (2+\ln \left (x \right )\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.153 |
|
|
\[
{}4 x y^{\prime \prime }+2 y^{\prime }+y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.162 |
|
|
\[
{}x y^{\prime \prime }-\left (2 x +2\right ) y^{\prime }+\left (x +2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.135 |
|
|
\[
{}x^{2} y^{\prime \prime }-\left (2 a -1\right ) x y^{\prime }+a^{2} y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.139 |
|
|
\[
{}x^{2} y^{\prime \prime }-2 y^{\prime } x +\left (x^{2}+2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.135 |
|
|
\[
{}x y^{\prime \prime }-\left (1+4 x \right ) y^{\prime }+\left (4 x +2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.137 |
|
|
\[
{}4 x^{2} \sin \left (x \right ) y^{\prime \prime }-4 x \left (x \cos \left (x \right )+\sin \left (x \right )\right ) y^{\prime }+\left (2 x \cos \left (x \right )+3 \sin \left (x \right )\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.516 |
|
|
\[
{}4 x^{2} y^{\prime \prime }-4 y^{\prime } x +\left (-16 x^{2}+3\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.146 |
|
|
\[
{}\left (2 x +1\right ) x y^{\prime \prime }-2 \left (2 x^{2}-1\right ) y^{\prime }-4 \left (x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.140 |
|
|
\[
{}\left (x^{2}-2 x \right ) y^{\prime \prime }+\left (-x^{2}+2\right ) y^{\prime }+\left (2 x -2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.141 |
|
|
\[
{}x y^{\prime \prime }-\left (1+4 x \right ) y^{\prime }+\left (4 x +2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.144 |
|
|
\[
{}x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y = 4 x^{4}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.235 |
|
|
\[
{}\left (3 x -1\right ) y^{\prime \prime }-\left (3 x +2\right ) y^{\prime }-\left (6 x -8\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.168 |
|
|
\[
{}\left (x +1\right )^{2} y^{\prime \prime }-2 \left (x +1\right ) y^{\prime }-\left (x^{2}+2 x -1\right ) y = \left (x +1\right )^{3} {\mathrm e}^{x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.673 |
|
|
\[
{}x^{2} y^{\prime \prime }+2 y^{\prime } x -2 y = x^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.227 |
|
|
\[
{}\left (x^{2}-4\right ) y^{\prime \prime }+4 y^{\prime } x +2 y = x +2
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
0.276 |
|
|
\[
{}y^{\prime }+y^{2}+k^{2} = 0
\] |
[_quadrature] |
✓ |
0.743 |
|
|
\[
{}y^{\prime }+y^{2}-3 y+2 = 0
\] |
[_quadrature] |
✓ |
0.496 |
|
|
\[
{}y^{\prime }+y^{2}+5 y-6 = 0
\] |
[_quadrature] |
✓ |
0.902 |
|
|
\[
{}y^{\prime }+y^{2}+8 y+7 = 0
\] |
[_quadrature] |
✓ |
0.520 |
|
|
\[
{}y^{\prime }+y^{2}+14 y+50 = 0
\] |
[_quadrature] |
✓ |
0.701 |
|
|
\[
{}6 y^{\prime }+6 y^{2}-y-1 = 0
\] |
[_quadrature] |
✓ |
0.500 |
|
|
\[
{}36 y^{\prime }+36 y^{2}-12 y+1 = 0
\] |
[_quadrature] |
✓ |
0.289 |
|
|
\[
{}x^{2} \left (y^{\prime }+y^{2}\right )-x \left (x +2\right ) y+x +2 = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
2.040 |
|
|
\[
{}y^{\prime }+y^{2}+4 y x +4 x^{2}+2 = 0
\] |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
2.688 |
|