| # |
ODE |
CAS classification |
Solved |
Maple |
Mma |
Sympy |
time(sec) |
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 3 x^{2} y^{3}+y^{4}+\left (3 x^{3} y^{2}+y^{4}+4 x y^{3}\right ) y^{\prime }&=0 \end {array} \]
|
[_exact, _rational] |
✓ |
✓ |
✓ |
✗ |
0.402 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 6 x y^{3}+2 y^{4}+\left (9 y^{2} x^{2}+8 x y^{3}\right ) y^{\prime }&=0 \end {array} \]
|
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
0.503 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x +y\right ) y^{\prime }&=0 \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.654 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 3 x^{2} y^{3}+y^{4}+\left (3 x^{3} y^{2}+y^{4}+4 x y^{3}\right ) y^{\prime }&=0 \end {array} \]
|
[_exact, _rational] |
✓ |
✓ |
✓ |
✗ |
2.231 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 6 x y^{3}+2 y^{4}+\left (9 y^{2} x^{2}+8 x y^{3}\right ) y^{\prime }&=0 \end {array} \]
|
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
0.922 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 y+2 x y^{2}+\left (2 x +2 x^{2} y\right ) y^{\prime }&=0 \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.338 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 6 y^{2} x^{2}+4 y y^{\prime } x^{3}&=0 \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.430 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 14 x^{2} y^{3}+21 x^{2} y^{2} y^{\prime }&=0 \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.669 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x +y\right )^{2}+\left (x +y\right )^{2} y^{\prime }&=0 \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
7.396 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 y^{3}+3 y^{2} y^{\prime }&=0 \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.549 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 27 x y^{2}+8 y^{3}+\left (18 x^{2} y+12 x y^{2}\right ) y^{\prime }&=0 \end {array} \]
|
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
8.059 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} a \cos \left (x \right ) y-\sin \left (x \right ) y^{2}+\left (b \cos \left (x \right ) y-x \sin \left (x \right ) y\right ) y^{\prime }&=0 \end {array} \]
|
[_linear] |
✓ |
✓ |
✓ |
✗ |
2.054 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{4} x^{4}+x^{5} y^{3} y^{\prime }&=0 \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.497 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 t y^{3}+3 t^{2} y^{2} y^{\prime }&=0\\ y \left (1\right )&=1\\ \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.557 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 t y^{3}+3 t^{2} y^{2} y^{\prime }&=0\\ y \left (1\right )&=1\\ \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.475 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 y^{2}&=x^{2} {y^{\prime }}^{2} \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.402 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x y {y^{\prime }}^{2}+\left (x +y\right ) y^{\prime }+1&=0 \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.341 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{2} {y^{\prime }}^{2}+y y^{\prime } x -2 x^{2}&=0 \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.631 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime }}^{3}+\left (x +y-2 y x \right ) {y^{\prime }}^{2}-2 y^{\prime } x y \left (x +y\right )&=0 \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.756 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y {y^{\prime }}^{2}+\left (y^{2}-x^{3}-x y^{2}\right ) y^{\prime }-x y \left (x^{2}+y^{2}\right )&=0 \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.711 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{2}-2 y y^{\prime } x +{y^{\prime }}^{2} \left (x^{2}-1\right )&=0 \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.447 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime }}^{2}-y^{2}&=0 \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.382 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime }}^{2}-3 y^{\prime }+2&=0 \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.699 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y \left (x^{2}-y^{2}\right )-x \left (x^{2}-y^{2}\right ) y^{\prime }&=0 \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.309 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x +\left (2-x +2 y\right ) y^{\prime }&=x y \left (y^{\prime }-1\right ) \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.253 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y+y \cos \left (y x \right )+\left (x +x \cos \left (y x \right )\right ) y^{\prime }&=0 \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.253 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \cos \left (x \right ) \cos \left (y\right )^{2}+2 \sin \left (x \right ) \sin \left (y\right ) \cos \left (y\right ) y^{\prime }&=0 \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
50.708 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (\sin \left (y\right )^{2}+x \cot \left (y\right )\right ) y^{\prime }&=0 \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
6.362 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (1-y^{2} x^{2}\right ) y^{\prime }&=\left (y x +1\right ) y^{2} \end {array} \]
|
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
1.412 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x \left (-y x +1\right ) \left (1-y^{2} x^{2}\right ) y^{\prime }+\left (y x +1\right ) \left (1+y^{2} x^{2}\right ) y&=0 \end {array} \]
|
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
0.870 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime }}^{2}&=y^{2} a^{2} \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.391 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime }}^{2}&=y^{2} x^{2} \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.663 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime }}^{2}-5 y^{\prime }+6&=0 \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
4.420 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime }}^{2}-7 y^{\prime }+12&=0 \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
4.526 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime }}^{2}+2 y^{\prime } x -3 x^{2}&=0 \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.458 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime }}^{2}-2 x^{2} y^{\prime }+2 y^{\prime } x&=0 \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.884 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y y^{\prime }+{y^{\prime }}^{2}&=x \left (x +y\right ) \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.545 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime }}^{2}+\left (x +y\right ) y^{\prime }+y x&=0 \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.996 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime }}^{2}-2 \left (x -y\right ) y^{\prime }-4 y x&=0 \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.066 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime }}^{2}+\left (a x +b y\right ) y^{\prime }+a b x y&=0 \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.931 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime }}^{2}-\left (2 y x +1\right ) y^{\prime }+2 y x&=0 \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
5.046 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime }}^{2}-\left (x -y\right ) y y^{\prime }-x y^{3}&=0 \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.695 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime }}^{2}-x y \left (x^{2}+y^{2}\right ) y^{\prime }+y^{4} x^{4}&=0 \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.742 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x {y^{\prime }}^{2}-\left (x^{2}+1\right ) y^{\prime }+x&=0 \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.734 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x {y^{\prime }}^{2}-\left (2 x +3 y\right ) y^{\prime }+6 y&=0 \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.099 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x {y^{\prime }}^{2}-\left (y x +1\right ) y^{\prime }+y&=0 \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.570 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x {y^{\prime }}^{2}+y \left (1-x \right ) y^{\prime }-y^{2}&=0 \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.526 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x {y^{\prime }}^{2}+\left (1-x^{2} y\right ) y^{\prime }-y x&=0 \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.530 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} {y^{\prime }}^{2}&=a^{2} \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
5.218 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} {y^{\prime }}^{2}&=y^{2} \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.687 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} {y^{\prime }}^{2}&=\left (x -y\right )^{2} \end {array} \]
|
[_linear] |
✓ |
✓ |
✓ |
✓ |
0.775 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} {y^{\prime }}^{2}-y^{\prime } x +y \left (1-y\right )&=0 \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.730 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} {y^{\prime }}^{2}+3 y y^{\prime } x +2 y^{2}&=0 \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.756 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} {y^{\prime }}^{2}+4 y y^{\prime } x -5 y^{2}&=0 \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.727 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} {y^{\prime }}^{2}-5 y y^{\prime } x +6 y^{2}&=0 \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.726 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} {y^{\prime }}^{2}+\left (a +b \,x^{2} y^{3}\right ) y^{\prime }+a b y^{3}&=0 \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
3.066 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (a^{2}-x^{2}\right ) {y^{\prime }}^{2}-2 y y^{\prime } x -y^{2}&=0 \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.296 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y {y^{\prime }}^{2}+\left (x -y\right ) y^{\prime }-x&=0 \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.208 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y {y^{\prime }}^{2}-\left (y x +1\right ) y^{\prime }+x&=0 \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.131 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y {y^{\prime }}^{2}+\left (x -y^{2}\right ) y^{\prime }-y x&=0 \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.143 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x y {y^{\prime }}^{2}+\left (x +y\right ) y^{\prime }+1&=0 \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.185 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x y {y^{\prime }}^{2}+\left (x^{2}+y^{2}\right ) y^{\prime }+y x&=0 \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.166 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x y {y^{\prime }}^{2}+\left (x^{2}-y^{2}\right ) y^{\prime }-y x&=0 \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.507 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x y {y^{\prime }}^{2}-\left (x^{2}-y^{2}\right ) y^{\prime }-y x&=0 \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.187 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x y {y^{\prime }}^{2}+\left (3 x^{2}-2 y^{2}\right ) y^{\prime }-6 y x&=0 \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.267 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{2} {y^{\prime }}^{2}&=a^{2} \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.615 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{2} {y^{\prime }}^{2}-\left (x +1\right ) y y^{\prime }+x&=0 \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.217 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x +y\right )^{2} {y^{\prime }}^{2}&=y^{2} \end {array} \]
|
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
0.579 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x +y\right )^{2} {y^{\prime }}^{2}-\left (x^{2}-y x -2 y^{2}\right ) y^{\prime }-y \left (x -y\right )&=0 \end {array} \]
|
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.140 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 y^{2} {y^{\prime }}^{2}+2 \left (1+3 x \right ) x y y^{\prime }+3 x^{3}&=0 \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.297 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x^{2}-4 y^{2}\right ) {y^{\prime }}^{2}+6 y y^{\prime } x -4 x^{2}+y^{2}&=0 \end {array} \]
|
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
4.247 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 {y^{\prime }}^{2} y^{2} x^{2}&=\left (x^{2}+y^{2}\right )^{2} \end {array} \]
|
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
1.191 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime }}^{3}-7 y^{\prime }+6&=0 \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.101 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime }}^{3}+\left (\cos \left (x \right ) \cot \left (x \right )-y\right ) {y^{\prime }}^{2}-\left (1+y \cos \left (x \right ) \cot \left (x \right )\right ) y^{\prime }+y&=0 \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.616 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime }}^{3}+\left (2 x -y^{2}\right ) {y^{\prime }}^{2}-2 y^{2} y^{\prime } x&=0 \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.135 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime }}^{3}-\left (y^{2}+2 x \right ) {y^{\prime }}^{2}+\left (x^{2}-y^{2}+2 x y^{2}\right ) y^{\prime }-\left (x^{2}-y^{2}\right ) y^{2}&=0 \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.017 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime }}^{3}-\left (x^{2}+y x +y^{2}\right ) {y^{\prime }}^{2}+x y \left (x^{2}+y x +y^{2}\right ) y^{\prime }-x^{3} y^{3}&=0 \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.160 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime }}^{3}-\left (y^{4}+x y^{2}+x^{2}\right ) {y^{\prime }}^{2}+x y^{2} \left (y^{4}+x y^{2}+x^{2}\right ) y^{\prime }-x^{3} y^{6}&=0 \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.568 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime }}^{3} x -\left (x +x^{2}+y\right ) {y^{\prime }}^{2}+\left (x^{2}+y+y x \right ) y^{\prime }-y x&=0 \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.144 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (a^{2}-x^{2}\right ) {y^{\prime }}^{3}+b x \left (a^{2}-x^{2}\right ) {y^{\prime }}^{2}-y^{\prime }-b x&=0 \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.549 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x +2 y\right ) {y^{\prime }}^{3}+3 \left (x +y\right ) {y^{\prime }}^{2}+\left (2 x +y\right ) y^{\prime }&=0 \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.642 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (y^{2} x^{2}+y x \right ) y+\left (y^{2} x^{2}-1\right ) x y^{\prime }&=0 \end {array} \]
|
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
1.726 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x^{3} y^{3}+y^{2} x^{2}+y x +1\right ) y+\left (x^{3} y^{3}-y^{2} x^{2}-y x +1\right ) x y^{\prime }&=0 \end {array} \]
|
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
1.124 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime }}^{2}-5 y^{\prime }+6&=0 \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
8.941 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime }}^{2}-\frac {a^{2}}{x^{2}}&=0 \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.453 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x +y+1+\left (2 x +2 y+2\right ) y^{\prime }&=0 \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.842 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y y^{\prime } x -y x&=y\\ y \left (1\right )&=1\\ \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.273 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 y^{3}+2 y^{2}+\left (3 x y^{2}+2 y x \right ) y^{\prime }&=0 \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✗ |
0.368 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{3}-x y^{2}+2 x^{2} y y^{\prime }&=0 \end {array} \]
|
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
0.470 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 x y^{3}-9 y^{2}+4 x y^{2}+\left (3 y^{2} x^{2}-6 y x +2 x^{2} y\right ) y^{\prime }&=0 \end {array} \]
|
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
125.143 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} {y^{\prime }}^{2}+y y^{\prime } x -6 y^{2}&=0 \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.802 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x {y^{\prime }}^{2}+\left (y-1-x^{2}\right ) y^{\prime }-\left (-1+y\right ) x&=0 \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.132 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x {y^{\prime }}^{5}-y {y^{\prime }}^{4}+\left (x^{2}+1\right ) {y^{\prime }}^{3}-2 x y {y^{\prime }}^{2}+\left (x +y^{2}\right ) y^{\prime }-y&=0 \end {array} \]
|
[[_homogeneous, ‘class G‘], _rational, _Clairaut] |
✓ |
✓ |
✓ |
✗ |
0.336 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (y-x \right ) y^{\prime }&=y-x \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
6.020 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime }}^{2}&=4 x^{2} \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.432 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime } \left (y^{\prime }+y\right )&=x \left (x +y\right )\\ y \left (0\right )&=0\\ \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.804 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} {y^{\prime }}^{2}-3 y y^{\prime } x +2 y^{2}&=0 \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.769 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime }}^{2}-y^{2} a^{2}&=0 \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
3.896 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime }}^{2}&=4 x^{2} \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.371 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y \,{\mathrm e}^{y x}+x \,{\mathrm e}^{y x} y^{\prime }&=0 \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.454 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y+y \cos \left (y x \right )+\left (x +x \cos \left (y x \right )\right ) y^{\prime }&=0 \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.336 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \cos \left (x \right ) \cos \left (y\right )^{2}+2 \sin \left (x \right ) \sin \left (y\right ) \cos \left (y\right ) y^{\prime }&=0 \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
189.157 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} -y^{2}+x^{2} {y^{\prime }}^{2}&=0 \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.761 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x {y^{\prime }}^{2}-\left (2 x +3 y\right ) y^{\prime }+6 y&=0 \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.032 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} {y^{\prime }}^{2}-5 y y^{\prime } x +6 y^{2}&=0 \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.740 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} {y^{\prime }}^{2}+y^{\prime } x -y^{2}-y&=0 \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.681 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x {y^{\prime }}^{2}+\left (1-x^{2} y\right ) y^{\prime }-y x&=0 \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.680 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime }}^{2}-\left (x^{2} y+3\right ) y^{\prime }+3 x^{2} y&=0 \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
11.046 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x {y^{\prime }}^{2}-\left (y x +1\right ) y^{\prime }+y&=0 \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.644 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime }}^{2}-y^{2} x^{2}&=0 \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.734 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x +y\right )^{2} {y^{\prime }}^{2}&=y^{2} \end {array} \]
|
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
68.615 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y {y^{\prime }}^{2}+\left (x -y^{2}\right ) y^{\prime }-y x&=0 \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
3.326 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime }}^{2}-y^{\prime } x y \left (x +y\right )+x^{3} y^{3}&=0 \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
1.599 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (4 x -y\right ) {y^{\prime }}^{2}+6 \left (x -y\right ) y^{\prime }+2 x -5 y&=0 \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
35.302 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x -y\right )^{2} {y^{\prime }}^{2}&=y^{2} \end {array} \]
|
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
6.706 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x y {y^{\prime }}^{2}+\left (x y^{2}-1\right ) y^{\prime }-y&=0 \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.812 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x^{2}+y^{2}\right )^{2} {y^{\prime }}^{2}&=4 y^{2} x^{2} \end {array} \]
|
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
320.513 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x +y\right )^{2} {y^{\prime }}^{2}+\left (2 y^{2}+y x -x^{2}\right ) y^{\prime }+y \left (y-x \right )&=0 \end {array} \]
|
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
140.115 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x y \left (x^{2}+y^{2}\right ) \left (-1+{y^{\prime }}^{2}\right )&=y^{\prime } \left (x^{4}+y^{2} x^{2}+y^{4}\right ) \end {array} \]
|
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
8.981 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime }}^{3} x -\left (x +x^{2}+y\right ) {y^{\prime }}^{2}+\left (x^{2}+y+y x \right ) y^{\prime }-y x&=0 \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.333 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x y {y^{\prime }}^{2}+\left (x +y\right ) y^{\prime }+1&=0 \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
3.185 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 6 x {y^{\prime }}^{2}-\left (3 x +2 y\right ) y^{\prime }+y&=0 \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.176 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{2} {y^{\prime }}^{2}-\left (x +1\right ) y y^{\prime }+x&=0 \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
3.789 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x {y^{\prime }}^{2}-\left (x^{2}+1\right ) y^{\prime }+x&=0 \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.724 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} {y^{\prime }}^{2}&=\left (x -y\right )^{2} \end {array} \]
|
[_linear] |
✓ |
✓ |
✓ |
✓ |
0.919 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x {y^{\prime }}^{2}+y \left (1-x \right ) y^{\prime }-y^{2}&=0 \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.700 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x +y\right ) y^{\prime }&=0 \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.446 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {y^{\prime }}{x +y}&=0 \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.451 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y y^{\prime \prime }&=0 \end {array} \]
|
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.046 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{2} y^{\prime \prime }&=0 \end {array} \]
|
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.057 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} a y y^{\prime \prime }+b y&=0 \end {array} \]
|
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.098 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} a \sin \left (x \right ) y x y^{\prime }&=0 \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.469 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} f \left (x \right ) \sin \left (x \right ) y x y^{\prime } \pi& =0 \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.450 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y y^{\prime }&=0 \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.421 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y y^{\prime } x&=0 \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.425 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x y \sin \left (x \right ) y^{\prime }&=0 \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.427 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \pi y \sin \left (x \right ) y^{\prime }&=0 \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.425 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y {y^{\prime }}^{2}&=0 \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.825 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime \prime }}^{2}&=1 \end {array} \]
|
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.067 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{3} {y^{\prime \prime }}^{2}+y y^{\prime }&=0 \end {array} \]
|
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
✓ |
✓ |
34.926 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y {y^{\prime \prime }}^{3}+y^{3} y^{\prime }&=0 \end {array} \]
|
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
16.557 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y {y^{\prime \prime }}^{3}+y^{3} {y^{\prime }}^{5}&=0 \end {array} \]
|
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
42.038 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 y^{3} y^{\prime }+x y^{2}&=0 \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
1.079 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (2 x y^{3}+y\right ) y^{\prime }+2 y^{2}&=0 \end {array} \]
|
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
✓ |
✓ |
0.773 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (3 x y^{3}-4 y x +y\right ) y^{\prime }+y^{2} \left (y^{2}-2\right )&=0 \end {array} \]
|
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
✓ |
✗ |
5.524 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime }}^{2}+\left (a y+b x \right ) y^{\prime }+a b x y&=0 \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.401 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime }}^{2}+y \left (y-x \right ) y^{\prime }-x y^{3}&=0 \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.728 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} {y^{\prime }}^{2}+3 y y^{\prime } x +2 y^{2}&=0 \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.860 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} {y^{\prime }}^{2}+4 y y^{\prime } x -5 y^{2}&=0 \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.767 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} {y^{\prime }}^{2}+\left (x^{2} y-2 y x +x^{3}\right ) y^{\prime }+\left (y^{2}-x^{2} y\right ) \left (1-x \right )&=0 \end {array} \]
|
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.079 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} {y^{\prime }}^{2}+\left (y^{3} a \,x^{2}+b \right ) y^{\prime }+a b y^{3}&=0 \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.132 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (-a^{2}+x^{2}\right ) {y^{\prime }}^{2}+2 y y^{\prime } x +y^{2}&=0 \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.302 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y {y^{\prime }}^{2}-\left (y-x \right ) y^{\prime }-x&=0 \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
8.767 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x y {y^{\prime }}^{2}+\left (x^{2}+y^{2}\right ) y^{\prime }+y x&=0 \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
1.793 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x y^{2} {y^{\prime }}^{2}-2 y^{3} y^{\prime }+2 x y^{2}-x^{3}&=0 \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.315 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime }}^{3}-\left (x^{2}+y x +y^{2}\right ) {y^{\prime }}^{2}+\left (x y^{3}+y^{2} x^{2}+x^{3} y\right ) y^{\prime }-x^{3} y^{3}&=0 \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.050 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (-a^{2}+x^{2}\right ) {y^{\prime }}^{3}+b x \left (-a^{2}+x^{2}\right ) {y^{\prime }}^{2}+y^{\prime }+b x&=0 \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.141 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime }}^{3} \sin \left (x \right )-\left (\sin \left (x \right ) y-\cos \left (x \right )^{2}\right ) {y^{\prime }}^{2}-\left (y \cos \left (x \right )^{2}+\sin \left (x \right )\right ) y^{\prime }+\sin \left (x \right ) y&=0 \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
2.546 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 y {y^{\prime }}^{3}-y {y^{\prime }}^{2}+2 y^{\prime } x -x&=0 \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
18.066 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x \left (a y^{\prime }+b y^{\prime \prime }+c y^{\prime \prime \prime }+e y^{\prime \prime \prime \prime }\right ) y&=0 \end {array} \]
|
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✗ |
0.468 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 y^{\prime \prime \prime } y^{\prime }-3 {y^{\prime }}^{2}&=0 \end {array} \]
|
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
7.167 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (A x y+B \,x^{2}+k x \right ) y^{\prime }&=A y^{2}+B y x +\left (A b +k \right ) y+B b x +b k \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.298 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y+2 x y^{2}-x^{2} y^{3}+2 x^{2} y y^{\prime }&=0 \end {array} \]
|
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
1.339 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{2} \left (3 y-6 y^{\prime } x \right )-x \left (y-2 y^{\prime } x \right )&=0 \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.581 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{3} y-y^{4}+\left (x y^{3}-x^{4}\right ) y^{\prime }&=0 \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.332 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime }}^{2}+\left (x +y\right ) y^{\prime }+y x&=0 \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.469 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime }}^{3}-\left (y^{2}+2 x \right ) {y^{\prime }}^{2}+\left (x^{2}-y^{2}+2 x y^{2}\right ) y^{\prime }-\left (x^{2}-y^{2}\right ) y^{2}&=0 \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.305 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} {y^{\prime }}^{2}-2 \left (y x +2 y^{\prime }\right ) y^{\prime }+y^{2}&=0 \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.670 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} {y^{\prime }}^{2}-\left (-1+x \right )^{2}&=0 \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.464 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{3}+3 t x^{2} x^{\prime }&=0 \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.359 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x+3 t x^{2} x^{\prime }&=0 \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
1.210 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{2} {\mathrm e}^{2 x}+\left ({\mathrm e}^{2 x} y-2 y\right ) y^{\prime }&=0 \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.720 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 8 x^{2} y^{3}-2 y^{4}+\left (5 x^{3} y^{2}-8 x y^{3}\right ) y^{\prime }&=0 \end {array} \]
|
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
4.606 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x y {y^{\prime }}^{2}-\left (x^{2}+y^{2}\right ) y^{\prime }+y x&=0 \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
1.694 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime }}^{2}&=9 y^{4} \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.559 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime }}^{3}-{\mathrm e}^{2 x} y^{\prime }&=0 \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
12.626 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y&=y y^{\prime }+y^{\prime }-{y^{\prime }}^{2} \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
13.756 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime }}^{2}&=x^{6} \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.475 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {\mathrm e}^{x y^{2}-x^{2}} \left (y^{2}-2 x \right )+2 \,{\mathrm e}^{x y^{2}-x^{2}} x y y^{\prime }&=0 \end {array} \]
|
[[_homogeneous, ‘class G‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.151 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 y^{3}+\left (4 x^{3} y^{3}-3 x y^{2}\right ) y^{\prime }&=0 \end {array} \]
|
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
5.096 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x y^{2}+\left (x^{2} y+10 y^{4}\right ) y^{\prime }&=0 \end {array} \]
|
[[_homogeneous, ‘class G‘], _exact, _rational] |
✓ |
✓ |
✓ |
✓ |
0.918 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y \cos \left (t y\right )+t \cos \left (t y\right ) y^{\prime }&=0 \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.432 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 3 t y^{2}+y^{3} y^{\prime }&=0 \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.572 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{2}+2 t y y^{\prime }&=0 \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.428 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} -2 t y^{2} \sin \left (t^{2}\right )+2 y \cos \left (t^{2}\right ) y^{\prime }&=0 \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.939 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 t y^{2}+2 t^{2} y y^{\prime }&=0\\ y \left (1\right )&=1\\ \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.548 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 t +2 y+\left (2 t +2 y\right ) y^{\prime }&=0 \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.683 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (t^{2}-y^{2}\right ) y^{\prime }+y^{2}+t y&=0 \end {array} \]
|
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.637 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime }}^{2}-2 y^{\prime } x -8 x^{2}&=0 \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.111 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} {y^{\prime }}^{2}+3 y y^{\prime } x +2 y^{2}&=0 \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
1.516 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime }}^{2}-\left (2 x +y\right ) y^{\prime }+x^{2}+y x&=0 \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.177 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime }}^{3}&=y {y^{\prime }}^{2}-x^{2} y^{\prime }+x^{2} y \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
4.415 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime }}^{2}-y^{2}&=0 \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.246 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (y^{\prime }-1\right )^{2}&=y^{2} \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.393 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime }}^{4}&=1 \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
4.448 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 y+2 x y^{2}+\left (2 x +2 x^{2} y\right ) y^{\prime }&=0 \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.096 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {y^{\prime }}{-\sin \left (y\right )+\frac {x}{y}}&=0 \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.064 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 5 x y^{2}+5 y+\left (5 x^{2} y+5 x \right ) y^{\prime }&=0 \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.093 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y {y^{\prime }}^{2}+\left (x -y\right ) y^{\prime }-x&=0 \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.070 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime }}^{3}-\left (x^{2}+y x +y^{2}\right ) {y^{\prime }}^{2}+\left (x y^{3}+y^{2} x^{2}+x^{3} y\right ) y^{\prime }-x^{3} y^{3}&=0 \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.930 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y+y \cos \left (y x \right )+\left (x +x \cos \left (y x \right )\right ) y^{\prime }&=0 \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.453 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \cos \left (x \right ) \cos \left (y\right )^{2}+2 \sin \left (x \right ) \sin \left (y\right ) \cos \left (y\right ) y^{\prime }&=0 \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
181.373 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {\mathrm e}^{x^{2} y} \left (1+2 x^{2} y\right )+x^{3} {\mathrm e}^{x^{2} y} y^{\prime }&=0 \end {array} \]
|
[_linear] |
✓ |
✓ |
✓ |
✓ |
0.606 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 3 t^{2} x-t x+\left (3 t^{3} x^{2}+t^{3} x^{4}\right ) x^{\prime }&=0 \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.638 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (-2 y x +x^{2}\right ) y^{\prime }+x^{2}-3 y x +2 y^{2}&=0 \end {array} \]
|
[_linear] |
✓ |
✓ |
✓ |
✓ |
0.869 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y \left (y x +2 y^{2} x^{2}\right )+x \left (y x -y^{2} x^{2}\right ) y^{\prime }&=0 \end {array} \]
|
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
1.978 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x^{3} y^{3}+y^{2} x^{2}+y x +1\right ) y+\left (x^{3} y^{3}-y^{2} x^{2}-y x +1\right ) x y^{\prime }&=0 \end {array} \]
|
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
0.946 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime }}^{3}+2 x {y^{\prime }}^{2}-y^{2} {y^{\prime }}^{2}-2 y^{2} y^{\prime } x&=0 \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
3.269 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x +2 y\right ) {y^{\prime }}^{3}+3 \left (x +y\right ) {y^{\prime }}^{2}+\left (2 x +y\right ) y^{\prime }&=0 \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
4.819 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 y^{2} {y^{\prime }}^{2}+2 \left (1+3 x \right ) x y y^{\prime }+3 x^{3}&=0 \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.875 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime }}^{2}-7 y^{\prime }+12&=0 \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
3.476 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x y^{2} \left ({y^{\prime }}^{2}+2\right )&=2 y^{3} y^{\prime }+x^{3} \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.177 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime }}^{2}-9 y^{\prime }+18&=0 \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
3.552 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left ({y^{\prime }}^{2}-\frac {1}{a^{2}-x^{2}}\right ) \left (y^{\prime }-\sqrt {\frac {y}{x}}\right )&=0 \end {array} \]
|
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
11.494 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x y {y^{\prime }}^{2}+\left (3 x^{2}-2 y^{2}\right ) y^{\prime }-6 y x&=0 \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.893 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime }}^{3}-\left (x^{2}+y x +y^{2}\right ) {y^{\prime }}^{2}+\left (x y^{3}+y^{2} x^{2}+x^{3} y\right ) y^{\prime }-x^{3} y^{3}&=0 \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.754 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (y^{4} x^{4}+y^{2} x^{2}+y x \right ) y+\left (y^{4} x^{4}-y^{2} x^{2}+y x \right ) x y^{\prime }&=0 \end {array} \]
|
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
0.851 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y \left (y x +2 y^{2} x^{2}\right )+x \left (y x -y^{2} x^{2}\right ) y^{\prime }&=0 \end {array} \]
|
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
0.790 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime }}^{2}-7 y^{\prime }+12&=0 \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
4.205 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime }}^{2}-5 y^{\prime }+6&=0 \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
7.007 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime }}^{2}-9 y^{\prime }+18&=0 \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
3.796 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime }}^{2}+2 y^{\prime } x -3 x^{2}&=0 \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.413 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime } \left (y^{\prime }-y\right )&=x \left (x +y\right ) \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
4.090 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y {y^{\prime }}^{2}+\left (x -y\right ) y^{\prime }-x&=0 \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.310 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x +y {y^{\prime }}^{2}&=\left (y x +1\right ) y^{\prime } \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.527 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x {y^{\prime }}^{2}+\left (y-x \right ) y^{\prime }-y&=0 \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.735 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime }}^{2}+y^{\prime } x +y y^{\prime }+y x&=0 \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.666 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime }}^{3}-y^{\prime } \left (x^{2}+y x +y^{2}\right )+x y \left (x +y\right )&=0 \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.726 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (y^{\prime }+y+x \right ) \left (y^{\prime } x +x +y\right ) \left (y^{\prime }+2 x \right )&=0 \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.661 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} {y^{\prime }}^{3}+y \left (x^{2} y+1\right ) {y^{\prime }}^{2}+y^{2} y^{\prime }&=0 \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✗ |
✗ |
27.528 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} {y^{\prime }}^{2}+y y^{\prime } x -6 y^{2}&=0 \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.529 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime }}^{3}+2 x {y^{\prime }}^{2}-y^{2} {y^{\prime }}^{2}-2 y^{2} y^{\prime } x&=0 \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.911 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 {y^{\prime }}^{3}-\left (2 x +4 \sin \left (x \right )-\cos \left (x \right )\right ) {y^{\prime }}^{2}-\left (\cos \left (x \right ) x -4 x \sin \left (x \right )+\sin \left (2 x \right )\right ) y^{\prime }+\sin \left (2 x \right ) x&=0 \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
0.562 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left ({y^{\prime }}^{2}-\frac {1}{a^{2}-x^{2}}\right ) \left (y^{\prime }-\sqrt {\frac {y}{x}}\right )&=0 \end {array} \]
|
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
0.926 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x y {y^{\prime }}^{2}+\left (3 x^{2}-2 y^{2}\right ) y^{\prime }-6 y x&=0 \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.202 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime }}^{3}-\left (y+2 x -{\mathrm e}^{x -y}\right ) {y^{\prime }}^{2}+\left (2 y x -2 x \,{\mathrm e}^{x -y}-y \,{\mathrm e}^{x -y}\right ) y^{\prime }+2 x y \,{\mathrm e}^{x -y}&=0 \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.199 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x^{3} y^{3}+y^{2} x^{2}+y x +1\right ) y+\left (x^{3} y^{3}-y^{2} x^{2}-y x +1\right ) x y^{\prime }&=0 \end {array} \]
|
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
0.664 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime }}^{3}-\left (x^{2}+y x +y^{2}\right ) {y^{\prime }}^{2}+\left (x y^{3}+y^{2} x^{2}+x^{3} y\right ) y^{\prime }-x^{3} y^{3}&=0 \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.183 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (a^{2}-x^{2}\right ) {y^{\prime }}^{3}+b x \left (a^{2}-x^{2}\right ) {y^{\prime }}^{2}-y^{\prime }-b x&=0 \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.206 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x +2 y\right ) {y^{\prime }}^{3}+3 \left (x +y\right ) {y^{\prime }}^{2}+\left (2 x +y\right ) y^{\prime }&=0 \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.812 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x y^{2} \left ({y^{\prime }}^{2}+2\right )&=2 y^{3} y^{\prime }+x^{3} \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.562 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{2}+\left (y x +3 y^{3}\right ) y^{\prime }&=0 \end {array} \]
|
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✗ |
57.550 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{2}+y y^{\prime } x&=0 \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.083 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime } \left (y^{\prime }+y\right )&=x \left (x +y\right ) \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
0.121 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} {y^{\prime }}^{2}+4 y y^{\prime } x +3 y^{2}&=0 \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.121 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x y {y^{\prime }}^{2}+\left (x +y\right ) y^{\prime }+1&=0 \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.939 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y {y^{\prime }}^{2}-\left (y x +x +y^{2}\right ) y^{\prime }+x^{2}+y x&=0 \end {array} \]
|
[[_linear, ‘class A‘]] |
✓ |
✓ |
✗ |
✗ |
0.277 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left ({y^{\prime }}^{2}-y^{2}\right ) {\mathrm e}^{y^{\prime }}-x {y^{\prime }}^{2}+x y^{2}&=0 \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.865 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {\mathrm e}^{x} \sec \left (y\right )+\left ({\mathrm e}^{x}+1\right ) \sec \left (y\right ) \tan \left (y\right ) y^{\prime }&=0\\ y \left (3\right )&=\frac {\pi }{3}\\ \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✗ |
0.850 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x -y\right ) y^{\prime }&=y-x \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.060 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (y^{2} x^{2}-y x -2\right ) x y^{\prime }+y \left (y^{2} x^{2}-1\right )&=0 \end {array} \]
|
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
1.452 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x y^{2} {y^{\prime }}^{2}+\left (x^{3}+x y^{2}-y^{3}\right ) y^{\prime }+x^{3}-y^{3}&=0 \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.290 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (-2 y x +x^{2}\right ) {y^{\prime }}^{2}-\left (3 x^{2}+2 y\right ) \left (x -2 y\right ) y^{\prime }+6 x y \left (x -2 y\right )&=0 \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.144 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y y^{\prime }&=-x {y^{\prime }}^{2} \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.098 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x -x {y^{\prime }}^{2}&=0 \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.086 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime }}^{3}+y {y^{\prime }}^{2}-x^{2} y^{\prime }-x^{2} y&=0 \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.576 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x y^{2}-x^{2} y^{2} y^{\prime }&=0 \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.065 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y x +y^{2} y^{\prime }&=0 \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
1.261 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y \,{\mathrm e}^{y x}+x \,{\mathrm e}^{y x} y^{\prime }&=0 \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.377 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x \,{\mathrm e}^{y x}+y \,{\mathrm e}^{y x} y^{\prime }&=0 \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.211 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 3 y^{2} x^{2}+\left (2 x^{3} y+4 y^{3}\right ) y^{\prime }&=0 \end {array} \]
|
[[_homogeneous, ‘class G‘], _exact, _rational] |
✓ |
✓ |
✓ |
✓ |
3.254 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{2}+y y^{\prime } x&=0 \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.336 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 y x +y^{2} y^{\prime }&=0 \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.613 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x y^{2}+\left (y^{2} x^{2}+x^{2} y\right ) y^{\prime }&=0 \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
1.671 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x y^{2}+x^{2} y y^{\prime }&=0 \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.343 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 3 y^{2} x^{2}+\left (2 x^{3} y+x^{3} y^{4}\right ) y^{\prime }&=0 \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.775 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x y {y^{\prime }}^{2}-\left (x^{2}+y^{2}\right ) y^{\prime }+y x&=0 \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.969 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (y^{\prime }-2 x \right ) \left (y^{\prime }-3 x^{2}\right )&=0 \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.587 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (y^{2}+2 y x \right ) \left (x^{2}+2 y x \right ) y^{\prime }&=0 \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
6.164 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (y^{2}+2 y x \right ) \left (x^{2}+2 y x \right ) y^{\prime }&=0 \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
5.721 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y y^{\prime }&=x^{3} y^{2}+x y^{2} \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.513 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{2} y^{\prime }-y x&=0 \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.686 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{2} {y^{\prime }}^{2}-x^{2}&=0 \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.152 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} {y^{\prime }}^{2}+y^{\prime } x -y^{2}-y&=0 \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.751 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} {y^{\prime }}^{2}-7 y y^{\prime } x +12 y^{2}&=0 \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
1.833 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x {y^{\prime }}^{2}-2 \left (2 x +y\right ) y^{\prime }+8 y&=0 \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
15.783 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime }}^{2}-\left (x^{2} y+3\right ) y^{\prime }+3 x^{2} y&=0 \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
15.784 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x {y^{\prime }}^{2}-\left (y x +1\right ) y^{\prime }+y&=0 \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.663 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime }}^{2}-y^{2} x^{2}&=0 \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
1.618 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x +y\right )^{2} {y^{\prime }}^{2}&=y^{2} \end {array} \]
|
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
368.052 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x {y^{\prime }}^{2}+\left (1-x^{2} y\right ) y^{\prime }-y x&=0 \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.722 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y {y^{\prime }}^{2}+\left (x -y^{2}\right ) y^{\prime }-y x&=0 \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.954 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime }}^{2}-y^{\prime } x y \left (x +y\right )+x^{3} y^{3}&=0 \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
1.994 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (4 x -y\right ) {y^{\prime }}^{2}+6 \left (x -y\right ) y^{\prime }+2 x -5 y&=0 \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
24.229 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x -y\right )^{2} {y^{\prime }}^{2}&=y^{2} \end {array} \]
|
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.461 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x y {y^{\prime }}^{2}+\left (x y^{2}-1\right ) y^{\prime }-y&=0 \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.078 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x^{2}+y^{2}\right )^{2} {y^{\prime }}^{2}&=4 y^{2} x^{2} \end {array} \]
|
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
76.164 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x +y\right )^{2} {y^{\prime }}^{2}+\left (2 y^{2}+y x -x^{2}\right ) y^{\prime }+y \left (y-x \right )&=0 \end {array} \]
|
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
789.333 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x y \left (x^{2}+y^{2}\right ) \left (-1+{y^{\prime }}^{2}\right )&=y^{\prime } \left (x^{4}+y^{2} x^{2}+y^{4}\right ) \end {array} \]
|
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.188 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime }}^{3} x -\left (x +x^{2}+y\right ) {y^{\prime }}^{2}+\left (x^{2}+y+y x \right ) y^{\prime }-y x&=0 \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
16.751 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x y {y^{\prime }}^{2}+\left (x +y\right ) y^{\prime }+1&=0\\ y \left (1\right )&=1\\ \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
0.815 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 6 x {y^{\prime }}^{2}-\left (3 x +2 y\right ) y^{\prime }+y&=0 \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
3.083 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{2} {y^{\prime }}^{2}-\left (x +1\right ) y y^{\prime }+x&=0 \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.022 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x {y^{\prime }}^{2}-\left (x^{2}+1\right ) y^{\prime }+x&=0 \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.560 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} {y^{\prime }}^{2}-\left (x -y\right )^{2}&=0 \end {array} \]
|
[_linear] |
✓ |
✓ |
✓ |
✓ |
0.690 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x {y^{\prime }}^{2}+y \left (1-x \right ) y^{\prime }-y^{2}&=0 \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.276 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime }}^{2}&=4 x^{2} \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
5.368 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{3} \sin \left (2 x \right )-3 y^{2} \cos \left (x \right )^{2} y^{\prime }&=0 \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.944 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 y y^{\prime } x +y^{2}&=0 \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.383 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (y^{\prime } x +y\right )^{2}&=1 \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.501 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime }}^{3}-y^{\prime }&=0 \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
4.070 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime }}^{2}-y^{\prime }-6&=0 \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.898 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x +2 y\right ) {y^{\prime }}^{3}+3 \left (x +y\right ) {y^{\prime }}^{2}+2 y y^{\prime } x&=0 \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✗ |
✗ |
207.040 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x^{3} y^{3}+y^{2} x^{2}+y x +1\right ) y+\left (x^{3} y^{3}-y^{2} x^{2}-y x +1\right ) x y^{\prime }&=0 \end {array} \]
|
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
0.678 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime }}^{2}-\left (2 x +y\right ) y^{\prime }+x^{2}+y x&=0 \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.556 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} {y^{\prime }}^{2}+3 y y^{\prime } x +2 y^{2}&=0 \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.694 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime }}^{3}-y {y^{\prime }}^{2}-x^{2} y^{\prime }+x^{2} y&=0 \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.873 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime }}^{2}-y^{2}&=0 \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.190 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime }}^{3}+y^{2}&=y y^{\prime } \left (1+y^{\prime }\right ) \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.176 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime }}^{2}+y x&=y^{\prime } x +y^{2} \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.123 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x y^{\prime } \left (y^{\prime } x +y\right )&=2 y^{2} \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.137 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime }}^{2}-2 y^{\prime } x&=8 x^{2} \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.902 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime }}^{2}+4 y^{\prime } x -y^{2}-2 x^{2} y&=x^{4}-4 x^{2} \end {array} \]
|
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
0.209 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime }}^{3}-{\mathrm e}^{2 x} y^{\prime }&=0 \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.224 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{2}+x^{2} {y^{\prime }}^{5}&=x y \left ({y^{\prime }}^{2}+{y^{\prime }}^{3}\right ) \end {array} \]
|
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
2.084 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime } {y^{\prime }}^{2}&={y^{\prime \prime \prime }}^{3} \end {array} \]
|
[[_3rd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.132 |
|