|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y y^{\prime }+x y^{2} = x
\] |
[_separable] |
✓ |
1.796 |
|
|
\[
{}\sin \left (y\right ) y^{\prime }+\sin \left (x \right ) \cos \left (y\right ) = \sin \left (x \right )
\] |
[_separable] |
✓ |
40.596 |
|
|
\[
{}4 x y^{\prime }+3 y+{\mathrm e}^{x} x^{4} y^{5} = 0
\] |
[_Bernoulli] |
✓ |
1.813 |
|
|
\[
{}y^{\prime }-\frac {1+y}{x +1} = \sqrt {1+y}
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
3.872 |
|
|
\[
{}x^{4} y \left (3 y+2 x y^{\prime }\right )+x^{2} \left (4 y+3 x y^{\prime }\right ) = 0
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
5.250 |
|
|
\[
{}y^{2} \left (3 y-6 x y^{\prime }\right )-x \left (y-2 x y^{\prime }\right ) = 0
\] |
[_separable] |
✓ |
1.764 |
|
|
\[
{}2 x^{3} y-y^{2}-\left (2 x^{4}+x y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
3.941 |
|
|
\[
{}y^{2}-x y+x^{2} y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
1.862 |
|
|
\[
{}\frac {-y+x y^{\prime }}{\sqrt {x^{2}-y^{2}}} = x y^{\prime }
\] |
[‘y=_G(x,y’)‘] |
✓ |
2.013 |
|
|
\[
{}x +y-\left (x -y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.776 |
|
|
\[
{}x^{2}+y^{2}-2 x y y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
7.984 |
|
|
\[
{}x -y^{2}+2 x y y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
1.669 |
|
|
\[
{}-y+x y^{\prime } = y^{2}+x^{2}
\] |
[[_homogeneous, ‘class D‘], _rational, _Riccati] |
✓ |
1.457 |
|
|
\[
{}3 x^{2}+6 x y+3 y^{2}+\left (2 x^{2}+3 x y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
7.639 |
|
|
\[
{}2 x +\left (x^{2}+y^{2}+2 y\right ) y^{\prime } = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
1.224 |
|
|
\[
{}y^{4}+2 y+\left (x y^{3}+2 y^{4}-4 x \right ) y^{\prime } = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
2.972 |
|
|
\[
{}x^{3} y-y^{4}+\left (x y^{3}-x^{4}\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
1.336 |
|
|
\[
{}y^{2}-x^{2}+2 m y x +\left (m y^{2}-m \,x^{2}-2 x y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
9.985 |
|
|
\[
{}x y^{\prime }-y+2 x^{2} y-x^{3} = 0
\] |
[_linear] |
✓ |
1.323 |
|
|
\[
{}\left (x +y\right ) y^{\prime }-1 = 0
\] |
[[_homogeneous, ‘class C‘], [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
1.427 |
|
|
\[
{}x +y y^{\prime }+y-x y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.773 |
|
|
\[
{}x y^{\prime }-a y+b y^{2} = c \,x^{2 a}
\] |
[_rational, _Riccati] |
✓ |
1.973 |
|
|
\[
{}x \sqrt {1-y^{2}}+y \sqrt {-x^{2}+1}\, y^{\prime } = 0
\] |
[_separable] |
✓ |
3.111 |
|
|
\[
{}\sqrt {1-y^{2}}+\sqrt {-x^{2}+1}\, y^{\prime } = 0
\] |
[_separable] |
✓ |
18.627 |
|
|
\[
{}y^{\prime }-x^{2} y = x^{5}
\] |
[_linear] |
✓ |
1.957 |
|
|
\[
{}\left (y-x \right )^{2} y^{\prime } = 1
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
2.553 |
|
|
\[
{}x y^{\prime }+y+x^{4} y^{4} {\mathrm e}^{x} = 0
\] |
[_Bernoulli] |
✓ |
3.522 |
|
|
\[
{}\left (1-x \right ) y+\left (1-y\right ) x y^{\prime } = 0
\] |
[_separable] |
✓ |
1.346 |
|
|
\[
{}\left (y-x \right ) y^{\prime }+y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.516 |
|
|
\[
{}-y+x y^{\prime } = \sqrt {y^{2}+x^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
7.031 |
|
|
\[
{}-y+x y^{\prime } = \sqrt {x^{2}-y^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
80.707 |
|
|
\[
{}x \sin \left (\frac {y}{x}\right )-y \cos \left (\frac {y}{x}\right )+x \cos \left (\frac {y}{x}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
3.853 |
|
|
\[
{}x -2 y+5+\left (2 x -y+4\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.333 |
|
|
\[
{}y^{\prime }+\frac {y}{\left (-x^{2}+1\right )^{{3}/{2}}} = \frac {x +\sqrt {-x^{2}+1}}{\left (-x^{2}+1\right )^{2}}
\] |
[_linear] |
✓ |
3.441 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime }-x y = a x y^{2}
\] |
[_separable] |
✓ |
2.288 |
|
|
\[
{}x y^{2} \left (3 y+x y^{\prime }\right )-2 y+x y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
5.292 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime }+y = \arctan \left (x \right )
\] |
[_linear] |
✓ |
1.805 |
|
|
\[
{}5 x y-3 y^{3}+\left (3 x^{2}-7 x y^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
2.341 |
|
|
\[
{}y^{\prime }+y \cos \left (x \right ) = \frac {\sin \left (2 x \right )}{2}
\] |
[_linear] |
✓ |
2.178 |
|
|
\[
{}x y^{2}+y-x y^{\prime } = 0
\] |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
1.846 |
|
|
\[
{}\left (1-x \right ) y-\left (1+y\right ) x y^{\prime } = 0
\] |
[_separable] |
✓ |
1.286 |
|
|
\[
{}3 x^{2} y+\left (x^{3}+x^{3} y^{2}\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
2.648 |
|
|
\[
{}\left (y^{2}+x^{2}\right ) \left (x +y y^{\prime }\right ) = \left (x^{2}+y^{2}+x \right ) \left (-y+x y^{\prime }\right )
\] |
[_rational] |
✗ |
2.856 |
|
|
\[
{}2 x +3 y-1+\left (2 x +3 y-5\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.386 |
|
|
\[
{}y^{3}-2 x^{2} y+\left (2 x y^{2}-x^{3}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
43.260 |
|
|
\[
{}2 x^{3} y^{2}-y+\left (2 x^{2} y^{3}-x \right ) y^{\prime } = 0
\] |
[_rational] |
✓ |
1.656 |
|
|
\[
{}\left (y^{2}+x^{2}\right ) \left (x +y y^{\prime }\right )+\sqrt {1+x^{2}+y^{2}}\, \left (y-x y^{\prime }\right ) = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
2.580 |
|
|
\[
{}1+{\mathrm e}^{\frac {y}{x}}+{\mathrm e}^{\frac {x}{y}} \left (1-\frac {x}{y}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
5.020 |
|
|
\[
{}x y^{\prime }+y-y^{2} \ln \left (x \right ) = 0
\] |
[_Bernoulli] |
✓ |
1.997 |
|
|
\[
{}x^{3} y^{4}+x^{2} y^{3}+x y^{2}+y+\left (x^{4} y^{3}-x^{3} y^{2}-x^{3} y+x \right ) y^{\prime } = 0
\] |
[_rational] |
✗ |
3.053 |
|
|
\[
{}\left (2 \sqrt {x y}-x \right ) y^{\prime }+y = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
85.065 |
|
|
\[
{}{y^{\prime }}^{2}+\left (x +y\right ) y^{\prime }+x y = 0
\] |
[_quadrature] |
✓ |
1.261 |
|
|
\[
{}x {y^{\prime }}^{2}-2 y y^{\prime }-x = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
1.470 |
|
|
\[
{}y^{2}+{y^{\prime }}^{2} = 1
\] |
[_quadrature] |
✓ |
0.545 |
|
|
\[
{}\left (2 x y^{\prime }-y\right )^{2} = 8 x^{3}
\] |
[_linear] |
✓ |
0.592 |
|
|
\[
{}\left (x^{2}+1\right ) {y^{\prime }}^{2} = 1
\] |
[_quadrature] |
✓ |
0.247 |
|
|
\[
{}{y^{\prime }}^{3}-\left (2 x +y^{2}\right ) {y^{\prime }}^{2}+\left (x^{2}-y^{2}+2 x y^{2}\right ) y^{\prime }-\left (x^{2}-y^{2}\right ) y^{2} = 0
\] |
[_quadrature] |
✓ |
2.461 |
|
|
\[
{}2 x y^{\prime }-y+\ln \left (y^{\prime }\right ) = 0
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
2.636 |
|
|
\[
{}4 x {y^{\prime }}^{2}+2 x y^{\prime }-y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
2.264 |
|
|
\[
{}x {y^{\prime }}^{2}-2 y y^{\prime }-x = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
1.435 |
|
|
\[
{}y^{\prime }+2 x y = y^{2}+x^{2}
\] |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
1.773 |
|
|
\[
{}y = -x y^{\prime }+x^{4} {y^{\prime }}^{2}
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
2.041 |
|
|
\[
{}{y^{\prime }}^{2}+2 x y^{\prime }-y = 0
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
0.398 |
|
|
\[
{}x +y^{\prime } y \left (2 {y^{\prime }}^{2}+3\right ) = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
5.137 |
|
|
\[
{}a^{2} y {y^{\prime }}^{2}-2 x y^{\prime }+y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
1.503 |
|
|
\[
{}x {y^{\prime }}^{2}-2 y y^{\prime }-x = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
1.511 |
|
|
\[
{}{y^{\prime }}^{3}-4 x y y^{\prime }+8 y^{2} = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
7.747 |
|
|
\[
{}\left (-y+x y^{\prime }\right )^{2} = 1+{y^{\prime }}^{2}
\] |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
0.609 |
|
|
\[
{}4 \,{\mathrm e}^{2 y} {y^{\prime }}^{2}+2 x y^{\prime }-1 = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
8.127 |
|
|
\[
{}4 \,{\mathrm e}^{2 y} {y^{\prime }}^{2}+2 \,{\mathrm e}^{2 x} y^{\prime }-{\mathrm e}^{2 x} = 0
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
1.103 |
|
|
\[
{}{\mathrm e}^{2 y} {y^{\prime }}^{3}+\left ({\mathrm e}^{2 x}+{\mathrm e}^{3 x}\right ) y^{\prime }-{\mathrm e}^{3 x} = 0
\] |
[‘y=_G(x,y’)‘] |
✓ |
294.658 |
|
|
\[
{}x y^{2} {y^{\prime }}^{2}-y^{3} y^{\prime }+x = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
11.013 |
|
|
\[
{}\left (y^{2}+x^{2}\right ) \left (1+y^{\prime }\right )^{2}-2 \left (x +y\right ) \left (1+y^{\prime }\right ) \left (x +y y^{\prime }\right )+\left (x +y y^{\prime }\right )^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
4.622 |
|
|
\[
{}y = 2 x y^{\prime }+y^{2} {y^{\prime }}^{3}
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
105.284 |
|
|
\[
{}a^{2} y {y^{\prime }}^{2}-2 x y^{\prime }+y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
1.505 |
|
|
\[
{}\left (x -y^{\prime }-y\right )^{2} = x^{2} \left (2 x y-x^{2} y^{\prime }\right )
\] |
[‘y=_G(x,y’)‘] |
✓ |
79.704 |
|
|
\[
{}y^{2} \left (1+{y^{\prime }}^{2}\right ) = a^{2}
\] |
[_quadrature] |
✓ |
4.806 |
|
|
\[
{}y y^{\prime } = \left (x -b \right ) {y^{\prime }}^{2}+a
\] |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
0.533 |
|
|
\[
{}x^{3} {y^{\prime }}^{2}+x^{2} y y^{\prime }+1 = 0
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
4.806 |
|
|
\[
{}3 x {y^{\prime }}^{2}-6 y y^{\prime }+x +2 y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
2.628 |
|
|
\[
{}y = {y^{\prime }}^{2} \left (x +1\right )
\] |
[[_homogeneous, ‘class C‘], _rational, _dAlembert] |
✓ |
0.756 |
|
|
\[
{}\left (-y+x y^{\prime }\right ) \left (x +y y^{\prime }\right ) = a^{2} y^{\prime }
\] |
[_rational] |
✓ |
118.201 |
|
|
\[
{}{y^{\prime }}^{2}+2 y^{\prime } y \cot \left (x \right ) = y^{2}
\] |
[_separable] |
✓ |
1.090 |
|
|
\[
{}\left (x^{2}+1\right ) {y^{\prime }}^{2}-2 x y y^{\prime }+y^{2}-1 = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
0.611 |
|
|
\[
{}x^{2} {y^{\prime }}^{2}-2 \left (x y+2 y^{\prime }\right ) y^{\prime }+y^{2} = 0
\] |
[_separable] |
✓ |
2.599 |
|
|
\[
{}y = x y^{\prime }+\frac {y {y^{\prime }}^{2}}{x^{2}}
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
3.267 |
|
|
\[
{}x^{2} {y^{\prime }}^{2}-2 x y y^{\prime }+y^{2} = y^{2} x^{2}+x^{4}
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
9.795 |
|
|
\[
{}y = x y^{\prime }+\frac {1}{y^{\prime }}
\] |
[[_homogeneous, ‘class G‘], _rational, _Clairaut] |
✓ |
0.455 |
|
|
\[
{}x {y^{\prime }}^{2}-2 y y^{\prime }-x = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
1.422 |
|
|
\[
{}x^{2} {y^{\prime }}^{2}-2 \left (x y-2\right ) y^{\prime }+y^{2} = 0
\] |
[[_homogeneous, ‘class G‘], _Clairaut] |
✓ |
0.613 |
|
|
\[
{}x^{2} {y^{\prime }}^{2}-\left (x -1\right )^{2} = 0
\] |
[_quadrature] |
✓ |
0.578 |
|
|
\[
{}8 \left (1+y^{\prime }\right )^{3} = 27 \left (x +y\right ) \left (1-y^{\prime }\right )^{3}
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
30.239 |
|
|
\[
{}4 {y^{\prime }}^{2} = 9 x
\] |
[_quadrature] |
✓ |
0.264 |
|
|
\[
{}y \left (3-4 y\right )^{2} {y^{\prime }}^{2} = 4-4 y
\] |
[_quadrature] |
✓ |
12.700 |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime }+2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.819 |
|
|
\[
{}y^{\prime \prime }-6 y^{\prime }+25 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.879 |
|
|
\[
{}y^{\prime \prime \prime }-y^{\prime } = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.063 |
|
|
\[
{}y^{\prime \prime \prime }-2 y^{\prime \prime }-y^{\prime }+2 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.068 |
|
|
\[
{}4 y^{\prime \prime \prime }-3 y^{\prime }+y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.070 |
|
|
\[
{}y^{\prime \prime \prime }-y^{\prime \prime }-y^{\prime }+y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.073 |
|