|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}\cos \left (y\right )+\left (1+{\mathrm e}^{-x}\right ) \sin \left (y\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
3.053 |
|
|
\[
{}y^{2}+x y-y^{\prime } x = 0
\] |
[_rational, _Bernoulli] |
✓ |
1.388 |
|
|
\[
{}y^{\prime } = -2 \left (2 x +3 y\right )^{2}
\] |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
11.128 |
|
|
\[
{}x -2 \sin \left (y\right )+3+\left (2 x -4 \sin \left (y\right )-3\right ) \cos \left (y\right ) y^{\prime } = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✗ |
8.706 |
|
|
\[
{}x^{2}-y-y^{\prime } x = 0
\] |
[_linear] |
✓ |
0.307 |
|
|
\[
{}x^{2}+y^{2}+2 x y y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
0.415 |
|
|
\[
{}x +y \cos \left (x \right )+\sin \left (x \right ) y^{\prime } = 0
\] |
[_linear] |
✓ |
0.293 |
|
|
\[
{}2 x +3 y+4+\left (3 x +4 y+5\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
0.431 |
|
|
\[
{}4 x^{3} y^{3}+\frac {1}{x}+\left (3 x^{4} y^{2}-\frac {1}{y}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _exact, _rational] |
✓ |
0.555 |
|
|
\[
{}2 u^{2}+2 u v+\left (u^{2}+v^{2}\right ) v^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
0.355 |
|
|
\[
{}x \sqrt {x^{2}+y^{2}}-y+\left (y \sqrt {x^{2}+y^{2}}-x \right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
0.404 |
|
|
\[
{}x +y+1-\left (y-x +3\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
0.391 |
|
|
\[
{}y^{2}-\frac {y}{\left (x +y\right ) x}+2+\left (\frac {1}{x +y}+2 \left (x +1\right ) y\right ) y^{\prime } = 0
\] |
[_exact, _rational] |
✓ |
0.424 |
|
|
\[
{}2 x y \,{\mathrm e}^{x^{2} y}+y^{2} {\mathrm e}^{x y^{2}}+1+\left (x^{2} {\mathrm e}^{x^{2} y}+2 x y \,{\mathrm e}^{x y^{2}}-2 y\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
0.401 |
|
|
\[
{}y \left (x -2 y\right )-x^{2} y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
2.366 |
|
|
\[
{}x^{2}+y^{2}+x y y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
5.168 |
|
|
\[
{}x^{2}+y^{2}+2 x y y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
4.444 |
|
|
\[
{}1-\sqrt {a^{2}-x^{2}}\, y^{\prime } = 0
\] |
[_quadrature] |
✓ |
0.535 |
|
|
\[
{}x +y+1-\left (x -y-3\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.493 |
|
|
\[
{}x -x^{2}-y^{2}+y y^{\prime } = 0
\] |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
0.481 |
|
|
\[
{}2 y-3 x +y^{\prime } x = 0
\] |
[_linear] |
✓ |
0.293 |
|
|
\[
{}x -y^{2}+2 x y y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
0.445 |
|
|
\[
{}-y-3 x^{2} \left (x^{2}+y^{2}\right )+y^{\prime } x = 0
\] |
[[_homogeneous, ‘class D‘], _rational, _Riccati] |
✓ |
0.469 |
|
|
\[
{}y-\ln \left (x \right )-y^{\prime } x = 0
\] |
[_linear] |
✓ |
0.276 |
|
|
\[
{}3 x^{2}+y^{2}-2 x y y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
0.417 |
|
|
\[
{}x y-2 y^{2}-\left (x^{2}-3 x y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
0.546 |
|
|
\[
{}x +y-\left (x -y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
0.489 |
|
|
\[
{}2 y-3 x y^{2}-y^{\prime } x = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
0.797 |
|
|
\[
{}y+x \left (x^{2} y-1\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
0.395 |
|
|
\[
{}y+x^{3} y+2 x^{2}+\left (x +4 x y^{4}+8 y^{3}\right ) y^{\prime } = 0
\] |
[_rational] |
✓ |
0.437 |
|
|
\[
{}-y-x^{2} {\mathrm e}^{x}+y^{\prime } x = 0
\] |
[_linear] |
✓ |
0.321 |
|
|
\[
{}1+y^{2} = \left (x^{2}+x \right ) y^{\prime }
\] |
[_separable] |
✓ |
2.302 |
|
|
\[
{}2 y-x^{3}+y^{\prime } x = 0
\] |
[_linear] |
✓ |
0.296 |
|
|
\[
{}y+\left (-x +y^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
0.540 |
|
|
\[
{}3 y^{3}-x y-\left (x^{2}+6 x y^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
0.566 |
|
|
\[
{}3 x^{2} y^{2}+4 \left (x^{3} y-3\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
0.337 |
|
|
\[
{}y \left (x +y\right )-x^{2} y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
0.349 |
|
|
\[
{}2 y+3 x y^{2}+\left (x +2 x^{2} y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
0.520 |
|
|
\[
{}y \left (y^{2}-2 x^{2}\right )+x \left (2 y^{2}-x^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
0.796 |
|
|
\[
{}-y+y^{\prime } x = 0
\] |
[_separable] |
✓ |
0.277 |
|
|
\[
{}y^{\prime }+y = 2+2 x
\] |
[[_linear, ‘class A‘]] |
✓ |
1.483 |
|
|
\[
{}y^{\prime }-y = x y
\] |
[_separable] |
✓ |
1.661 |
|
|
\[
{}-3 y-\left (x -2\right ) {\mathrm e}^{x}+y^{\prime } x = 0
\] |
[_linear] |
✓ |
2.655 |
|
|
\[
{}i^{\prime }-6 i = 10 \sin \left (2 t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
1.503 |
|
|
\[
{}y^{\prime }+y = y^{2} {\mathrm e}^{x}
\] |
[[_1st_order, _with_linear_symmetries], _Bernoulli] |
✓ |
1.195 |
|
|
\[
{}y+\left (x y+x -3 y\right ) y^{\prime } = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
1.116 |
|
|
\[
{}\left (2 s-{\mathrm e}^{2 t}\right ) s^{\prime } = 2 s \,{\mathrm e}^{2 t}-2 \cos \left (2 t \right )
\] |
[_exact, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
6.390 |
|
|
\[
{}y^{\prime } x +y-x^{3} y^{6} = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
2.540 |
|
|
\[
{}r^{\prime }+2 r \cos \left (\theta \right )+\sin \left (2 \theta \right ) = 0
\] |
[_linear] |
✓ |
1.822 |
|
|
\[
{}y \left (1+y^{2}\right ) = 2 \left (1-2 x y^{2}\right ) y^{\prime }
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
1.717 |
|
|
\[
{}y y^{\prime }-x y^{2}+x = 0
\] |
[_separable] |
✓ |
1.961 |
|
|
\[
{}\left (x -x \sqrt {x^{2}-y^{2}}\right ) y^{\prime }-y = 0
\] |
[‘y=_G(x,y’)‘] |
✗ |
4.516 |
|
|
\[
{}2 x^{\prime }-\frac {x}{y}+x^{3} \cos \left (y \right ) = 0
\] |
[_Bernoulli] |
✓ |
6.248 |
|
|
\[
{}y^{\prime } x = y \left (1-x \tan \left (x \right )\right )+x^{2} \cos \left (x \right )
\] |
[_linear] |
✓ |
15.003 |
|
|
\[
{}2+y^{2}-\left (x y+2 y+y^{3}\right ) y^{\prime } = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
6.447 |
|
|
\[
{}1+y^{2} = \left (\arctan \left (y\right )-x \right ) y^{\prime }
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
5.732 |
|
|
\[
{}2 x y^{5}-y+2 y^{\prime } x = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
3.020 |
|
|
\[
{}1+\sin \left (y\right ) = \left (2 y \cos \left (y\right )-x \left (\sec \left (y\right )+\tan \left (y\right )\right )\right ) y^{\prime }
\] |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
36.906 |
|
|
\[
{}y^{\prime } x = 2 y+x^{3} {\mathrm e}^{x}
\] |
[_linear] |
✓ |
1.907 |
|
|
\[
{}L i^{\prime }+R i = E \sin \left (2 t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
1.541 |
|
|
\[
{}x^{2} \cos \left (y\right ) y^{\prime } = 2 x \sin \left (y\right )-1
\] |
[‘y=_G(x,y’)‘] |
✓ |
2.220 |
|
|
\[
{}4 x^{2} y y^{\prime } = 3 x \left (3 y^{2}+2\right )+2 \left (3 y^{2}+2\right )^{3}
\] |
[_rational] |
✗ |
2.386 |
|
|
\[
{}x y^{3}-y^{3}-x^{2} {\mathrm e}^{x}+3 x y^{2} y^{\prime } = 0
\] |
[_Bernoulli] |
✓ |
2.401 |
|
|
\[
{}y^{\prime }+\left (x +y\right ) x = x^{3} \left (x +y\right )^{3}-1
\] |
[_Abel] |
✓ |
1.923 |
|
|
\[
{}y+{\mathrm e}^{y}-{\mathrm e}^{-x}+\left (1+{\mathrm e}^{y}\right ) y^{\prime } = 0
\] |
[‘y=_G(x,y’)‘] |
✓ |
1.813 |
|
|
\[
{}x^{2} {y^{\prime }}^{2}+x y y^{\prime }-6 y^{2} = 0
\] |
[_separable] |
✓ |
4.269 |
|
|
\[
{}x {y^{\prime }}^{2}+\left (y-1-x^{2}\right ) y^{\prime }-x \left (-1+y\right ) = 0
\] |
[_quadrature] |
✓ |
2.424 |
|
|
\[
{}x {y^{\prime }}^{2}-2 y y^{\prime }+4 x = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
1.532 |
|
|
\[
{}3 x^{4} {y^{\prime }}^{2}-y^{\prime } x -y = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
1.954 |
|
|
\[
{}8 y {y^{\prime }}^{2}-2 y^{\prime } x +y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
1.701 |
|
|
\[
{}y^{2} {y^{\prime }}^{2}+3 y^{\prime } x -y = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
3.758 |
|
|
\[
{}{y^{\prime }}^{2}-y^{\prime } x +y = 0
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
0.342 |
|
|
\[
{}16 y^{3} {y^{\prime }}^{2}-4 y^{\prime } x +y = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
3.508 |
|
|
\[
{}x {y^{\prime }}^{5}-y {y^{\prime }}^{4}+\left (x^{2}+1\right ) {y^{\prime }}^{3}-2 x y {y^{\prime }}^{2}+\left (x +y^{2}\right ) y^{\prime }-y = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Clairaut] |
✓ |
0.807 |
|
|
\[
{}x {y^{\prime }}^{2}-y y^{\prime }-y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
2.148 |
|
|
\[
{}y = 2 y^{\prime } x +y^{2} {y^{\prime }}^{3}
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
107.009 |
|
|
\[
{}{y^{\prime }}^{2}-y^{\prime } x -y = 0
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
0.450 |
|
|
\[
{}y = \left (1+y^{\prime }\right ) x +{y^{\prime }}^{2}
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
0.503 |
|
|
\[
{}y = 2 y^{\prime }+\sqrt {1+{y^{\prime }}^{2}}
\] |
[_quadrature] |
✓ |
2.813 |
|
|
\[
{}y {y^{\prime }}^{2}-y^{\prime } x +3 y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
2.312 |
|
|
\[
{}y = y^{\prime } x -2 {y^{\prime }}^{2}
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
0.336 |
|
|
\[
{}y^{2} {y^{\prime }}^{2}+3 y^{\prime } x -y = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
3.760 |
|
|
\[
{}x {y^{\prime }}^{2}-2 y y^{\prime }+4 x = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
1.536 |
|
|
\[
{}x {y^{\prime }}^{2}-2 y y^{\prime }+x +2 y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
1.672 |
|
|
\[
{}\left (3 y-1\right )^{2} {y^{\prime }}^{2} = 4 y
\] |
[_quadrature] |
✓ |
77.250 |
|
|
\[
{}y = -y^{\prime } x +x^{4} {y^{\prime }}^{2}
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
1.948 |
|
|
\[
{}2 y = {y^{\prime }}^{2}+4 y^{\prime } x
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
0.441 |
|
|
\[
{}y \left (3-4 y\right )^{2} {y^{\prime }}^{2} = 4-4 y
\] |
[_quadrature] |
✓ |
12.316 |
|
|
\[
{}{y^{\prime }}^{3}-4 x^{4} y^{\prime }+8 x^{3} y = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
77.801 |
|
|
\[
{}\left (1+{y^{\prime }}^{2}\right ) \left (x -y\right )^{2} = \left (y y^{\prime }+x \right )^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
4.181 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }-6 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.123 |
|
|
\[
{}y^{\prime \prime \prime }-6 y^{\prime \prime }+12 y^{\prime }-8 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.083 |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime }+2 y = {\mathrm e}^{5 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.264 |
|
|
\[
{}y^{\prime \prime }+9 y = x \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
8.404 |
|
|
\[
{}x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.165 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+y^{\prime } x -y = 3 x^{4}
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.266 |
|
|
\[
{}x y^{\prime \prime }-y^{\prime }+4 x^{3} y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.358 |
|
|
\[
{}y^{\prime \prime }+{y^{\prime }}^{2}+1 = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] |
✓ |
4.221 |
|
|
\[
{}y y^{\prime \prime }+{y^{\prime }}^{2} = 2
\] |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
1.427 |
|
|
\[
{}y y^{\prime \prime }+{y^{\prime }}^{3} = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
0.532 |
|