|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}x y y^{\prime }+x^{2}+y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
5.978 |
|
|
\[
{}\cos \left (y\right )+\left (1+{\mathrm e}^{-x}\right ) \sin \left (y\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
2.711 |
|
|
\[
{}y^{2}+x y-x y^{\prime } = 0
\] |
[_rational, _Bernoulli] |
✓ |
1.271 |
|
|
\[
{}y^{\prime } = -2 \left (2 x +3 y\right )^{2}
\] |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
10.519 |
|
|
\[
{}x -2 \sin \left (y\right )+3+\left (2 x -4 \sin \left (y\right )-3\right ) \cos \left (y\right ) y^{\prime } = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✗ |
6.904 |
|
|
\[
{}x^{2}-y-x y^{\prime } = 0
\] |
[_linear] |
✓ |
0.185 |
|
|
\[
{}x^{2}+y^{2}+2 x y y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
0.341 |
|
|
\[
{}x +y \cos \left (x \right )+\sin \left (x \right ) y^{\prime } = 0
\] |
[_linear] |
✓ |
0.211 |
|
|
\[
{}2 x +3 y+4+\left (3 x +4 y+5\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
0.333 |
|
|
\[
{}4 x^{3} y^{3}+\frac {1}{x}+\left (3 x^{4} y^{2}-\frac {1}{y}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _exact, _rational] |
✓ |
0.467 |
|
|
\[
{}2 u^{2}+2 u v+\left (u^{2}+v^{2}\right ) v^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
0.263 |
|
|
\[
{}x \sqrt {y^{2}+x^{2}}-y+\left (y \sqrt {y^{2}+x^{2}}-x \right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
0.319 |
|
|
\[
{}x +y+1-\left (y-x +3\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
0.308 |
|
|
\[
{}y^{2}-\frac {y}{\left (x +y\right ) x}+2+\left (\frac {1}{x +y}+2 \left (x +1\right ) y\right ) y^{\prime } = 0
\] |
[_exact, _rational] |
✓ |
0.350 |
|
|
\[
{}2 x y \,{\mathrm e}^{x^{2} y}+y^{2} {\mathrm e}^{x y^{2}}+1+\left (x^{2} {\mathrm e}^{x^{2} y}+2 x y \,{\mathrm e}^{x y^{2}}-2 y\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
0.319 |
|
|
\[
{}y \left (x -2 y\right )-x^{2} y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
1.815 |
|
|
\[
{}x y y^{\prime }+x^{2}+y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
4.644 |
|
|
\[
{}x^{2}+y^{2}+2 x y y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
3.918 |
|
|
\[
{}1-\sqrt {a^{2}-x^{2}}\, y^{\prime } = 0
\] |
[_quadrature] |
✓ |
0.524 |
|
|
\[
{}x +y+1-\left (x -y-3\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.842 |
|
|
\[
{}x -x^{2}-y^{2}+y^{\prime } y = 0
\] |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
0.405 |
|
|
\[
{}2 y-3 x +x y^{\prime } = 0
\] |
[_linear] |
✓ |
0.211 |
|
|
\[
{}x -y^{2}+2 x y y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
0.351 |
|
|
\[
{}-y-3 x^{2} \left (y^{2}+x^{2}\right )+x y^{\prime } = 0
\] |
[[_homogeneous, ‘class D‘], _rational, _Riccati] |
✓ |
0.395 |
|
|
\[
{}y-\ln \left (x \right )-x y^{\prime } = 0
\] |
[_linear] |
✓ |
0.217 |
|
|
\[
{}3 x^{2}+y^{2}-2 x y y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
0.339 |
|
|
\[
{}x y-2 y^{2}-\left (x^{2}-3 x y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
0.470 |
|
|
\[
{}x +y-\left (x -y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
0.399 |
|
|
\[
{}2 y-3 x y^{2}-x y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
0.744 |
|
|
\[
{}y+x \left (x^{2} y-1\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
0.310 |
|
|
\[
{}y+x^{3} y+2 x^{2}+\left (x +4 x y^{4}+8 y^{3}\right ) y^{\prime } = 0
\] |
[_rational] |
✓ |
0.344 |
|
|
\[
{}-y-x^{2} {\mathrm e}^{x}+x y^{\prime } = 0
\] |
[_linear] |
✓ |
0.222 |
|
|
\[
{}1+y^{2} = \left (x^{2}+x \right ) y^{\prime }
\] |
[_separable] |
✓ |
2.090 |
|
|
\[
{}2 y-x^{3}+x y^{\prime } = 0
\] |
[_linear] |
✓ |
0.214 |
|
|
\[
{}y+\left (y^{2}-x \right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
0.439 |
|
|
\[
{}3 y^{3}-x y-\left (x^{2}+6 x y^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
0.550 |
|
|
\[
{}3 x^{2} y^{2}+4 \left (x^{3} y-3\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
0.251 |
|
|
\[
{}y \left (x +y\right )-x^{2} y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
0.274 |
|
|
\[
{}2 y+3 x y^{2}+\left (x +2 x^{2} y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
0.447 |
|
|
\[
{}y \left (y^{2}-2 x^{2}\right )+x \left (2 y^{2}-x^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
0.739 |
|
|
\[
{}-y+x y^{\prime } = 0
\] |
[_separable] |
✓ |
0.201 |
|
|
\[
{}y^{\prime }+y = 2 x +2
\] |
[[_linear, ‘class A‘]] |
✓ |
1.114 |
|
|
\[
{}y^{\prime }-y = x y
\] |
[_separable] |
✓ |
1.223 |
|
|
\[
{}-3 y-\left (-2+x \right ) {\mathrm e}^{x}+x y^{\prime } = 0
\] |
[_linear] |
✓ |
2.369 |
|
|
\[
{}i^{\prime }-6 i = 10 \sin \left (2 t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
1.306 |
|
|
\[
{}y^{\prime }+y = y^{2} {\mathrm e}^{x}
\] |
[[_1st_order, _with_linear_symmetries], _Bernoulli] |
✓ |
1.005 |
|
|
\[
{}y+\left (x y+x -3 y\right ) y^{\prime } = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
1.032 |
|
|
\[
{}\left (2 s-{\mathrm e}^{2 t}\right ) s^{\prime } = 2 s \,{\mathrm e}^{2 t}-2 \cos \left (2 t \right )
\] |
[_exact, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
6.635 |
|
|
\[
{}x y^{\prime }+y-x^{3} y^{6} = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
2.242 |
|
|
\[
{}r^{\prime }+2 r \cos \left (\theta \right )+\sin \left (2 \theta \right ) = 0
\] |
[_linear] |
✓ |
1.666 |
|
|
\[
{}y \left (1+y^{2}\right ) = 2 \left (1-2 x y^{2}\right ) y^{\prime }
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
1.599 |
|
|
\[
{}y^{\prime } y-x y^{2}+x = 0
\] |
[_separable] |
✓ |
1.695 |
|
|
\[
{}\left (x -x \sqrt {x^{2}-y^{2}}\right ) y^{\prime }-y = 0
\] |
[‘y=_G(x,y’)‘] |
✗ |
4.088 |
|
|
\[
{}2 x^{\prime }-\frac {x}{y}+x^{3} \cos \left (y \right ) = 0
\] |
[_Bernoulli] |
✓ |
5.803 |
|
|
\[
{}x y^{\prime } = y \left (1-x \tan \left (x \right )\right )+x^{2} \cos \left (x \right )
\] |
[_linear] |
✓ |
13.980 |
|
|
\[
{}2+y^{2}-\left (x y+2 y+y^{3}\right ) y^{\prime } = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
6.098 |
|
|
\[
{}1+y^{2} = \left (\arctan \left (y\right )-x \right ) y^{\prime }
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
5.541 |
|
|
\[
{}2 y^{5} x -y+2 x y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
2.764 |
|
|
\[
{}1+\sin \left (y\right ) = \left (2 y \cos \left (y\right )-x \left (\sec \left (y\right )+\tan \left (y\right )\right )\right ) y^{\prime }
\] |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
37.596 |
|
|
\[
{}x y^{\prime } = 2 y+x^{3} {\mathrm e}^{x}
\] |
[_linear] |
✓ |
1.644 |
|
|
\[
{}L i^{\prime }+R i = E \sin \left (2 t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
1.557 |
|
|
\[
{}x^{2} \cos \left (y\right ) y^{\prime } = 2 x \sin \left (y\right )-1
\] |
[‘y=_G(x,y’)‘] |
✓ |
2.094 |
|
|
\[
{}4 x^{2} y y^{\prime } = 3 x \left (3 y^{2}+2\right )+2 \left (3 y^{2}+2\right )^{3}
\] |
[_rational] |
✗ |
2.467 |
|
|
\[
{}x y^{3}-y^{3}-x^{2} {\mathrm e}^{x}+3 x y^{2} y^{\prime } = 0
\] |
[_Bernoulli] |
✓ |
2.227 |
|
|
\[
{}y^{\prime }+\left (x +y\right ) x = x^{3} \left (x +y\right )^{3}-1
\] |
[_Abel] |
✓ |
1.809 |
|
|
\[
{}y+{\mathrm e}^{y}-{\mathrm e}^{-x}+\left (1+{\mathrm e}^{y}\right ) y^{\prime } = 0
\] |
[‘y=_G(x,y’)‘] |
✓ |
1.710 |
|
|
\[
{}x^{2} {y^{\prime }}^{2}+x y y^{\prime }-6 y^{2} = 0
\] |
[_separable] |
✓ |
3.034 |
|
|
\[
{}x {y^{\prime }}^{2}+\left (y-1-x^{2}\right ) y^{\prime }-x \left (y-1\right ) = 0
\] |
[_quadrature] |
✓ |
1.729 |
|
|
\[
{}x {y^{\prime }}^{2}-2 y^{\prime } y+4 x = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
1.517 |
|
|
\[
{}3 x^{4} {y^{\prime }}^{2}-x y^{\prime }-y = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
1.914 |
|
|
\[
{}8 y {y^{\prime }}^{2}-2 x y^{\prime }+y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
1.725 |
|
|
\[
{}y^{2} {y^{\prime }}^{2}+3 x y^{\prime }-y = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
3.639 |
|
|
\[
{}{y^{\prime }}^{2}-x y^{\prime }+y = 0
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
0.341 |
|
|
\[
{}16 y^{3} {y^{\prime }}^{2}-4 x y^{\prime }+y = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
3.420 |
|
|
\[
{}x {y^{\prime }}^{5}-y {y^{\prime }}^{4}+\left (x^{2}+1\right ) {y^{\prime }}^{3}-2 x y {y^{\prime }}^{2}+\left (y^{2}+x \right ) y^{\prime }-y = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Clairaut] |
✓ |
0.753 |
|
|
\[
{}x {y^{\prime }}^{2}-y^{\prime } y-y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
2.127 |
|
|
\[
{}y = 2 x y^{\prime }+y^{2} {y^{\prime }}^{3}
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
106.514 |
|
|
\[
{}{y^{\prime }}^{2}-x y^{\prime }-y = 0
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
0.440 |
|
|
\[
{}y = \left (1+y^{\prime }\right ) x +{y^{\prime }}^{2}
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
0.492 |
|
|
\[
{}y = 2 y^{\prime }+\sqrt {1+{y^{\prime }}^{2}}
\] |
[_quadrature] |
✓ |
2.766 |
|
|
\[
{}y {y^{\prime }}^{2}-x y^{\prime }+3 y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
2.277 |
|
|
\[
{}y = x y^{\prime }-2 {y^{\prime }}^{2}
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
0.333 |
|
|
\[
{}y^{2} {y^{\prime }}^{2}+3 x y^{\prime }-y = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
3.628 |
|
|
\[
{}x {y^{\prime }}^{2}-2 y^{\prime } y+4 x = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
1.514 |
|
|
\[
{}x {y^{\prime }}^{2}-2 y^{\prime } y+x +2 y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
1.698 |
|
|
\[
{}\left (3 y-1\right )^{2} {y^{\prime }}^{2} = 4 y
\] |
[_quadrature] |
✓ |
76.214 |
|
|
\[
{}y = -x y^{\prime }+x^{4} {y^{\prime }}^{2}
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
1.924 |
|
|
\[
{}2 y = {y^{\prime }}^{2}+4 x y^{\prime }
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
0.439 |
|
|
\[
{}y \left (3-4 y\right )^{2} {y^{\prime }}^{2} = 4-4 y
\] |
[_quadrature] |
✓ |
12.471 |
|
|
\[
{}{y^{\prime }}^{3}-4 x^{4} y^{\prime }+8 x^{3} y = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
76.833 |
|
|
\[
{}\left (1+{y^{\prime }}^{2}\right ) \left (x -y\right )^{2} = \left (x +y^{\prime } y\right )^{2}
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
4.260 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }-6 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.838 |
|
|
\[
{}y^{\prime \prime \prime }-6 y^{\prime \prime }+12 y^{\prime }-8 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.069 |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime }+2 y = {\mathrm e}^{5 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.981 |
|
|
\[
{}y^{\prime \prime }+9 y = x \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
7.902 |
|
|
\[
{}x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.147 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+x y^{\prime }-y = 3 x^{4}
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.262 |
|
|
\[
{}x y^{\prime \prime }-y^{\prime }+4 x^{3} y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.342 |
|
|
\[
{}y^{\prime \prime }+{y^{\prime }}^{2}+1 = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.381 |
|
|
\[
{}y y^{\prime \prime }+{y^{\prime }}^{2} = 2
\] |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
1.301 |
|