|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}v^{\prime \prime }+\frac {2 v^{\prime }}{r} = 0
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.462 |
|
|
\[
{}y^{\prime \prime }-k^{2} y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
3.988 |
|
|
\[
{}\left (1-x \right ) y^{\prime }-y-1 = 0
\] |
[_separable] |
✓ |
1.391 |
|
|
\[
{}y^{\prime }+\sqrt {\frac {1-y^{2}}{-x^{2}+1}} = 0
\] |
unknown |
✓ |
1690.547 |
|
|
\[
{}y-x y^{\prime } = a \left (y^{2}+y^{\prime }\right )
\] |
[_separable] |
✓ |
191.412 |
|
|
\[
{}3 \,{\mathrm e}^{x} \tan \left (y\right )+\left (1-{\mathrm e}^{x}\right ) \sec \left (y\right )^{2} y^{\prime } = 0
\] |
[_separable] |
✓ |
510.199 |
|
|
\[
{}x^{2}+y^{2}-2 x y y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
454.347 |
|
|
\[
{}y^{2}+\left (x y+x^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
120.134 |
|
|
\[
{}x^{2} y-\left (x^{3}+y^{3}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
323.655 |
|
|
\[
{}\left (4 y+3 x \right ) y^{\prime }+y-2 x = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
450.299 |
|
|
\[
{}3 y-7 x +7+\left (7 y-3 x +3\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.437 |
|
|
\[
{}\left (y-3 x +3\right ) y^{\prime } = 2 y-x -4
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
5.693 |
|
|
\[
{}x^{2}-4 x y-2 y^{2}+\left (y^{2}-4 x y-2 x^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
7.023 |
|
|
\[
{}x +y^{\prime } y+\frac {-y+x y^{\prime }}{y^{2}+x^{2}} = 0
\] |
[[_1st_order, _with_linear_symmetries], _exact, _rational] |
✓ |
1.363 |
|
|
\[
{}a^{2}-2 x y-y^{2}-\left (x +y\right )^{2} y^{\prime } = 0
\] |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
1.521 |
|
|
\[
{}2 a x +b y+g +\left (2 c y+b x +e \right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.584 |
|
|
\[
{}\left (2 x^{2} y+4 x^{3}-12 x y^{2}+3 y^{2}-x \,{\mathrm e}^{y}+{\mathrm e}^{2 x}\right ) y^{\prime }+12 x^{2} y+2 x y^{2}+4 x^{3}-4 y^{3}+2 y \,{\mathrm e}^{2 x}-{\mathrm e}^{y} = 0
\] |
[_exact] |
✓ |
2.919 |
|
|
\[
{}y-x y^{\prime }+\ln \left (x \right ) = 0
\] |
[_linear] |
✓ |
0.876 |
|
|
\[
{}\left (x y+1\right ) y-\left (1-x y\right ) x y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
1.288 |
|
|
\[
{}a \left (x y^{\prime }+2 y\right ) = x y y^{\prime }
\] |
[_separable] |
✓ |
1.654 |
|
|
\[
{}x^{4} {\mathrm e}^{x}-2 m x y^{2}+2 m \,x^{2} y y^{\prime } = 0
\] |
[[_homogeneous, ‘class D‘], _Bernoulli] |
✓ |
2.044 |
|
|
\[
{}y \left (2 x y+{\mathrm e}^{x}\right )-{\mathrm e}^{x} y^{\prime } = 0
\] |
[_Bernoulli] |
✓ |
2.026 |
|
|
\[
{}x^{2} y-2 x y^{2}-\left (x^{3}-3 x^{2} y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
6.673 |
|
|
\[
{}y \left (x y+2 x^{2} y^{2}\right )+x \left (x y-x^{2} y^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
1.553 |
|
|
\[
{}x^{2}+y^{2}+2 x +2 y^{\prime } y = 0
\] |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
2.016 |
|
|
\[
{}x^{2}+y^{2}-x^{2} y y^{\prime } = 0
\] |
[_rational, _Bernoulli] |
✓ |
1.329 |
|
|
\[
{}3 x^{2} y^{4}+2 x y+\left (2 x^{3} y^{3}-x^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
3.756 |
|
|
\[
{}y^{4}+2 y+\left (x y^{3}+2 y^{4}-4 x \right ) y^{\prime } = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
2.942 |
|
|
\[
{}y^{3}-2 x^{2} y+\left (2 x y^{2}-x^{3}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
85.610 |
|
|
\[
{}2 x^{2} y-3 y^{4}+\left (3 x^{3}+2 x y^{3}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
6.967 |
|
|
\[
{}y^{2}+2 x^{2} y+\left (2 x^{3}-x y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
2.836 |
|
|
\[
{}x y^{\prime }-a y = x +1
\] |
[_linear] |
✓ |
1.680 |
|
|
\[
{}y^{\prime }+y = {\mathrm e}^{-x}
\] |
[[_linear, ‘class A‘]] |
✓ |
0.964 |
|
|
\[
{}\cos \left (x \right )^{2} y^{\prime }+y = \tan \left (x \right )
\] |
[_linear] |
✓ |
4.297 |
|
|
\[
{}\left (x +1\right ) y^{\prime }-n y = {\mathrm e}^{x} \left (x +1\right )^{n +1}
\] |
[_linear] |
✓ |
2.054 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime }+2 x y = 4 x^{2}
\] |
[_linear] |
✓ |
1.321 |
|
|
\[
{}y^{\prime }+\frac {y}{x} = x^{2} y^{6}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
2.393 |
|
|
\[
{}1+y^{2} = \left (\arctan \left (y\right )-x \right ) y^{\prime }
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
536.425 |
|
|
\[
{}y^{\prime }+\frac {2 y}{x} = 3 x^{2} y^{{1}/{3}}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
456.019 |
|
|
\[
{}y^{\prime }+\frac {x y}{-x^{2}+1} = x \sqrt {y}
\] |
unknown |
✓ |
356.733 |
|
|
\[
{}3 x \left (-x^{2}+1\right ) y^{2} y^{\prime }+\left (2 x^{2}-1\right ) y^{3} = a \,x^{3}
\] |
[_rational, _Bernoulli] |
✓ |
97.450 |
|
|
\[
{}\left (x +y\right )^{2} y^{\prime } = a^{2}
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
174.097 |
|
|
\[
{}-y+x y^{\prime } = \sqrt {y^{2}+x^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
547.937 |
|
|
\[
{}-y+x y^{\prime } = x \sqrt {y^{2}+x^{2}}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✗ |
4.840 |
|
|
\[
{}\sec \left (x \right )^{2} \tan \left (y\right )+\sec \left (y\right )^{2} \tan \left (x \right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
37.369 |
|
|
\[
{}\left (x^{2}-x^{2} y\right ) y^{\prime }+y^{2}+x y^{2} = 0
\] |
[_separable] |
✓ |
1.638 |
|
|
\[
{}y^{\prime }+\frac {\left (-2 x +1\right ) y}{x^{2}} = 1
\] |
[_linear] |
✓ |
1.304 |
|
|
\[
{}3 y^{\prime }+\frac {2 y}{x +1} = \frac {x^{3}}{y^{2}}
\] |
[_rational, _Bernoulli] |
✓ |
2.423 |
|
|
\[
{}2 x -y+1+\left (2 y-x -1\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.001 |
|
|
\[
{}y^{\prime }+\frac {y}{\sqrt {-x^{2}+1}} = \frac {x +\sqrt {-x^{2}+1}}{\left (-x^{2}+1\right )^{2}}
\] |
[_linear] |
✓ |
3.489 |
|
|
\[
{}x y^{\prime }+\frac {y^{2}}{x} = y
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
1.811 |
|
|
\[
{}x \left (x^{2}+y^{2}-a^{2}\right )+y \left (x^{2}-y^{2}-b^{2}\right ) y^{\prime } = 0
\] |
[_exact, _rational] |
✓ |
1.821 |
|
|
\[
{}y^{\prime }+\frac {4 x y}{x^{2}+1} = \frac {1}{\left (x^{2}+1\right )^{3}}
\] |
[_linear] |
✓ |
2.182 |
|
|
\[
{}x^{2} y-\left (x^{3}+y^{3}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
13.868 |
|
|
\[
{}x \left (-x^{2}+1\right ) y^{\prime }+\left (2 x^{2}-1\right ) y = a \,x^{3}
\] |
[_linear] |
✓ |
1.191 |
|
|
\[
{}x^{2}+y^{2}+1-2 x y y^{\prime } = 0
\] |
[_rational, _Bernoulli] |
✓ |
1.812 |
|
|
\[
{}x +y^{\prime } y = m \left (-y+x y^{\prime }\right )
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.676 |
|
|
\[
{}y^{\prime }+y \cos \left (x \right ) = y^{n} \sin \left (2 x \right )
\] |
[_Bernoulli] |
✓ |
5.617 |
|
|
\[
{}\left (x +1\right ) y^{\prime }+1 = 2 \,{\mathrm e}^{y}
\] |
[_separable] |
✓ |
1.470 |
|
|
\[
{}y^{\prime } = x^{3} y^{3}-x y
\] |
[_Bernoulli] |
✓ |
1.187 |
|
|
\[
{}y+\left (a \,x^{2} y^{n}-2 x \right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
1.346 |
|
|
\[
{}\left (1+6 y^{2}-3 x^{2} y\right ) y^{\prime } = 3 x y^{2}-x^{2}
\] |
[_exact, _rational] |
✓ |
1.498 |
|
|
\[
{}y \left (x^{2}+y^{2}+a^{2}\right ) y^{\prime }+x \left (x^{2}+y^{2}-a^{2}\right ) = 0
\] |
[_exact, _rational] |
✓ |
1.889 |
|
|
\[
{}\left (y^{3} x^{2}+x y\right ) y^{\prime } = 1
\] |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
1.966 |
|
|
\[
{}y^{\prime } y = a x
\] |
[_separable] |
✓ |
3.168 |
|
|
\[
{}\sqrt {a^{2}+x^{2}}\, y^{\prime }+y = \sqrt {a^{2}+x^{2}}-x
\] |
[_linear] |
✓ |
1.800 |
|
|
\[
{}\left (x +y\right ) y^{\prime }+x -y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.703 |
|
|
\[
{}y^{\prime } y+b y^{2} = a \cos \left (x \right )
\] |
[_Bernoulli] |
✓ |
2.743 |
|
|
\[
{}2 x y+\left (y^{2}-x^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
11.116 |
|
|
\[
{}y-x y^{\prime } = b \left (1+x^{2} y^{\prime }\right )
\] |
[_separable] |
✓ |
1.502 |
|
|
\[
{}3 y+2 x +4-\left (4 x +6 y+5\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.487 |
|
|
\[
{}\left (x^{3} y^{3}+x^{2} y^{2}+x y+1\right ) y+\left (x^{3} y^{3}-x^{2} y^{2}-x y+1\right ) x y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
2.083 |
|
|
\[
{}2 x^{2} y^{2}+y-\left (x^{3} y-3 x \right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
2.602 |
|
|
\[
{}y^{2}+x^{2} y^{\prime } = x y y^{\prime }
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
383.145 |
|
|
\[
{}y^{\prime }+\frac {n y}{x} = a \,x^{-n}
\] |
[_linear] |
✓ |
240.335 |
|
|
\[
{}\left (x -y\right )^{2} y^{\prime } = a^{2}
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
51.046 |
|
|
\[
{}{y^{\prime }}^{3}+2 x {y^{\prime }}^{2}-y^{2} {y^{\prime }}^{2}-2 x y^{2} y^{\prime } = 0
\] |
[_quadrature] |
✓ |
4.030 |
|
|
\[
{}{y^{\prime }}^{2}-a \,x^{3} = 0
\] |
[_quadrature] |
✓ |
0.582 |
|
|
\[
{}{y^{\prime }}^{3} \left (x +2 y\right )+3 {y^{\prime }}^{2} \left (x +y\right )+\left (2 x +y\right ) y^{\prime } = 0
\] |
[_quadrature] |
✓ |
78.843 |
|
|
\[
{}{y^{\prime }}^{3} = a \,x^{4}
\] |
[_quadrature] |
✓ |
0.940 |
|
|
\[
{}4 y^{2} {y^{\prime }}^{2}+2 y^{\prime } x y \left (3 x +1\right )+3 x^{3} = 0
\] |
[_separable] |
✓ |
20.232 |
|
|
\[
{}{y^{\prime }}^{2}-7 y^{\prime }+12 = 0
\] |
[_quadrature] |
✓ |
1.653 |
|
|
\[
{}x -y^{\prime } y = a {y^{\prime }}^{2}
\] |
unknown |
✓ |
1500.431 |
|
|
\[
{}y = -a y^{\prime }+\frac {c +a \arcsin \left (y^{\prime }\right )}{\sqrt {1-{y^{\prime }}^{2}}}
\] |
[_quadrature] |
✓ |
888.254 |
|
|
\[
{}4 y = x^{2}+{y^{\prime }}^{2}
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
3.225 |
|
|
\[
{}x {y^{\prime }}^{2}-2 y^{\prime } y+a x = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
1.490 |
|
|
\[
{}y = 2 y^{\prime }+3 {y^{\prime }}^{2}
\] |
[_quadrature] |
✓ |
0.812 |
|
|
\[
{}x \left (1+{y^{\prime }}^{2}\right ) = 1
\] |
[_quadrature] |
✓ |
0.484 |
|
|
\[
{}x^{2} = a^{2} \left (1+{y^{\prime }}^{2}\right )
\] |
[_quadrature] |
✓ |
0.243 |
|
|
\[
{}y^{2} = a^{2} \left (1+{y^{\prime }}^{2}\right )
\] |
[_quadrature] |
✓ |
1.091 |
|
|
\[
{}y^{2}+x y y^{\prime }-x^{2} {y^{\prime }}^{2} = 0
\] |
[_separable] |
✓ |
0.652 |
|
|
\[
{}y = {y^{\prime }}^{2} y+2 x y^{\prime }
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
1.970 |
|
|
\[
{}y = \left (1+y^{\prime }\right ) x +{y^{\prime }}^{2}
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
0.536 |
|
|
\[
{}x^{2} \left (y-x y^{\prime }\right ) = {y^{\prime }}^{2} y
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
5.341 |
|
|
\[
{}y = x y^{\prime }+\arcsin \left (y^{\prime }\right )
\] |
[_Clairaut] |
✓ |
3.350 |
|
|
\[
{}{\mathrm e}^{4 x} \left (y^{\prime }-1\right )+{\mathrm e}^{2 y} {y^{\prime }}^{2} = 0
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
1.639 |
|
|
\[
{}x y \left (y-x y^{\prime }\right ) = x +y^{\prime } y
\] |
[_separable] |
✓ |
5.612 |
|
|
\[
{}y^{\prime }+2 x y = y^{2}+x^{2}
\] |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
2.789 |
|
|
\[
{}x^{2} {y^{\prime }}^{2}-2 x y y^{\prime }+2 y^{2}-x^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
5.017 |
|
|
\[
{}y = y^{\prime } \left (x -b \right )+\frac {a}{y^{\prime }}
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
0.711 |
|