| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime } x +x y^{2}-y&=0 \end {array} \]
|
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
11.902 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime } x +x y^{2}-y-a \,x^{3}&=0 \end {array} \]
|
[[_homogeneous, ‘class D‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✗ |
9.276 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime } x +x y^{2}-\left (2 x^{2}+1\right ) y-x^{3}&=0 \end {array} \]
|
[[_homogeneous, ‘class D‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
12.242 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime } x +a x y^{2}+2 y+b x&=0 \end {array} \]
|
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
✓ |
✓ |
✗ |
6.227 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime } x +a x y^{2}+b y+c x +d&=0 \end {array} \]
|
[_rational, _Riccati] |
✓ |
✓ |
✓ |
✗ |
133.898 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime } x +x^{a} y^{2}+\frac {\left (a -b \right ) y}{2}+x^{b}&=0 \end {array} \]
|
[_rational, _Riccati] |
✓ |
✓ |
✓ |
✗ |
7.425 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime } x +a \,x^{\alpha } y^{2}+b y-c \,x^{\beta }&=0 \end {array} \]
|
[_rational, _Riccati] |
✓ |
✓ |
✓ |
✗ |
1.623 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime } x -y^{2} \ln \left (x \right )+y&=0 \end {array} \]
|
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
10.921 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime } x -y \left (2 y \ln \left (x \right )-1\right )&=0 \end {array} \]
|
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
9.657 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime } x +f \left (x \right ) \left (y^{2}-x^{2}\right )-y&=0 \end {array} \]
|
[[_homogeneous, ‘class D‘], _Riccati] |
✓ |
✓ |
✓ |
✗ |
8.231 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime } x +y^{3}+3 x y^{2}&=0 \end {array} \]
|
[_rational, _Abel] |
✗ |
✓ |
✓ |
✗ |
32.703 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime } x -y-\sqrt {x^{2}+y^{2}}&=0 \end {array} \]
|
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
15.139 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime } x +a \sqrt {x^{2}+y^{2}}-y&=0 \end {array} \]
|
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
21.098 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime } x -x \sqrt {x^{2}+y^{2}}-y&=0 \end {array} \]
|
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
6.165 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime } x -x \left (y-x \right ) \sqrt {x^{2}+y^{2}}-y&=0 \end {array} \]
|
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
115.302 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime } x -{\mathrm e}^{\frac {y}{x}} x -y-x&=0 \end {array} \]
|
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
319.384 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime } x -\ln \left (y\right ) y&=0 \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
8.390 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime } x -y \left (\ln \left (y x \right )-1\right )&=0 \end {array} \]
|
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✓ |
8.711 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime } x -y \left (x \ln \left (\frac {x^{2}}{y}\right )+2\right )&=0 \end {array} \]
|
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
✓ |
✗ |
4.722 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime } x -\sin \left (x -y\right )&=0 \end {array} \]
|
[‘y=_G(x,y’)‘] |
✓ |
✗ |
✗ |
✗ |
39.642 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime } x +\left (\sin \left (y\right )-3 x^{2} \cos \left (y\right )\right ) \cos \left (y\right )&=0 \end {array} \]
|
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✓ |
✗ |
7.289 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime } x -y-x \sin \left (\frac {y}{x}\right )&=0 \end {array} \]
|
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
11.756 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime } x +x -y+x \cos \left (\frac {y}{x}\right )&=0 \end {array} \]
|
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
10.900 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime } x +x \tan \left (\frac {y}{x}\right )-y&=0 \end {array} \]
|
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
20.456 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime } x -y f \left (y x \right )&=0 \end {array} \]
|
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✓ |
4.671 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime } x -y f \left (x^{a} y^{b}\right )&=0 \end {array} \]
|
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✗ |
5.823 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime } x +a y-f \left (x \right ) g \left (x^{a} y\right )&=0 \end {array} \]
|
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✗ |
✓ |
✓ |
✗ |
8.803 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x +1\right ) y^{\prime }+y \left (y-x \right )&=0 \end {array} \]
|
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.898 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 y^{\prime } x -y-2 x^{3}&=0 \end {array} \]
|
[_linear] |
✓ |
✓ |
✓ |
✓ |
9.256 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (2 x +1\right ) y^{\prime }-4 \,{\mathrm e}^{-y}+2&=0 \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.911 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 3 y^{\prime } x -3 x y^{4} \ln \left (x \right )-y&=0 \end {array} \]
|
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
11.191 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime }+y-x&=0 \end {array} \]
|
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.105 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime }-y+x^{2} {\mathrm e}^{x -\frac {1}{x}}&=0 \end {array} \]
|
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.318 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime }-\left (-1+x \right ) y&=0 \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.855 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime }+x^{2}+y x +y^{2}&=0 \end {array} \]
|
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
10.522 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime }-y^{2}-y x&=0 \end {array} \]
|
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
10.597 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime }-y^{2}-y x -x^{2}&=0 \end {array} \]
|
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
11.066 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} \left (y^{\prime }+y^{2}\right )+a \,x^{k}-b \left (b -1\right )&=0 \end {array} \]
|
[_rational, _Riccati] |
✓ |
✓ |
✓ |
✗ |
0.526 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} \left (y^{\prime }+y^{2}\right )+4 y x +2&=0 \end {array} \]
|
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
10.302 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} \left (y^{\prime }+y^{2}\right )+a x y+b&=0 \end {array} \]
|
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
7.388 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} \left (y^{\prime }-y^{2}\right )-a \,x^{2} y+a x +2&=0 \end {array} \]
|
[_rational, _Riccati] |
✓ |
✓ |
✓ |
✗ |
5.697 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} \left (y^{\prime }+a y^{2}\right )-b&=0 \end {array} \]
|
[[_homogeneous, ‘class G‘], _rational, [_Riccati, _special]] |
✓ |
✓ |
✓ |
✓ |
8.904 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} \left (y^{\prime }+a y^{2}\right )+b \,x^{\alpha }+c&=0 \end {array} \]
|
[_rational, _Riccati] |
✓ |
✓ |
✓ |
✗ |
136.295 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime }+a y^{3}-a \,x^{2} y^{2}&=0 \end {array} \]
|
[_rational, _Abel] |
✗ |
✓ |
✓ |
✗ |
8.376 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime }+x y^{3}+a y^{2}&=0 \end {array} \]
|
[_rational, _Abel] |
✗ |
✓ |
✓ |
✗ |
15.167 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime }+y^{3} a \,x^{2}+b y^{2}&=0 \end {array} \]
|
[_rational, _Abel] |
✗ |
✓ |
✓ |
✗ |
10.655 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x^{2}+1\right ) y^{\prime }+y x -1&=0 \end {array} \]
|
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.548 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x^{2}+1\right ) y^{\prime }+y x -x \left (x^{2}+1\right )&=0 \end {array} \]
|
[_linear] |
✓ |
✓ |
✓ |
✓ |
13.191 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x^{2}+1\right ) y^{\prime }+2 y x -2 x^{2}&=0 \end {array} \]
|
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.728 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x^{2}+1\right ) y^{\prime }+\left (1+y^{2}\right ) \left (2 y x -1\right )&=0 \end {array} \]
|
[_rational, _Abel] |
✗ |
✓ |
✓ |
✗ |
59.748 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x^{2}+1\right ) y^{\prime }+x \sin \left (y\right ) \cos \left (y\right )-x \left (x^{2}+1\right ) \cos \left (y\right )^{2}&=0 \end {array} \]
|
[‘y=_G(x,y’)‘] |
✗ |
✓ |
✓ |
✗ |
27.069 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x^{2}-1\right ) y^{\prime }-y x +a&=0 \end {array} \]
|
[_linear] |
✓ |
✓ |
✓ |
✓ |
8.020 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x^{2}-1\right ) y^{\prime }+2 y x -\cos \left (x \right )&=0 \end {array} \]
|
[_linear] |
✓ |
✓ |
✓ |
✓ |
7.770 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x^{2}-1\right ) y^{\prime }+y^{2}-2 y x +1&=0 \end {array} \]
|
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
✓ |
✓ |
✓ |
7.210 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x^{2}-1\right ) y^{\prime }-y \left (y-x \right )&=0 \end {array} \]
|
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
11.013 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x^{2}-1\right ) y^{\prime }+a \left (y^{2}-2 y x +1\right )&=0 \end {array} \]
|
[_rational, _Riccati] |
✓ |
✓ |
✓ |
✗ |
5.102 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x^{2}-1\right ) y^{\prime }+a x y^{2}+y x&=0 \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
9.840 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x^{2}-1\right ) y^{\prime }-2 x y \ln \left (y\right )&=0 \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
11.604 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x^{2}-4\right ) y^{\prime }+\left (2+x \right ) y^{2}-4 y&=0 \end {array} \]
|
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.091 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x^{2}-5 x +6\right ) y^{\prime }+3 y x -8 y+x^{2}&=0 \end {array} \]
|
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.799 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x -a \right ) \left (x -b \right ) y^{\prime }+k \left (x +y-a \right ) \left (x +y-b \right )+y^{2}&=0 \end {array} \]
|
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
✓ |
✓ |
✓ |
17.968 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x^{2} y^{\prime }-2 y^{2}-y x +2 a^{2} x&=0 \end {array} \]
|
[_rational, _Riccati] |
✓ |
✓ |
✓ |
✗ |
3.148 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x^{2} y^{\prime }-2 y^{2}-3 y x +2 a^{2} x&=0 \end {array} \]
|
[_rational, _Riccati] |
✓ |
✓ |
✓ |
✗ |
7.933 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x \left (2 x -1\right ) y^{\prime }+y^{2}-\left (4 x +1\right ) y+4 x&=0 \end {array} \]
|
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
✓ |
✓ |
✓ |
11.978 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x \left (-1+x \right ) y^{\prime }+y^{2} \left (-1+x \right )-x&=0 \end {array} \]
|
[_rational, _Riccati] |
✓ |
✓ |
✓ |
✗ |
13.997 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 3 x^{2} y^{\prime }-7 y^{2}-3 y x -x^{2}&=0 \end {array} \]
|
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
10.470 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 3 \left (x^{2}-4\right ) y^{\prime }+y^{2}-y x -3&=0 \end {array} \]
|
[_rational, _Riccati] |
✓ |
✓ |
✓ |
✗ |
187.329 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (a x +b \right )^{2} y^{\prime }+\left (a x +b \right ) y^{3}+c y^{2}&=0 \end {array} \]
|
[_rational, _Abel] |
✗ |
✓ |
✓ |
✗ |
12.076 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{3} y^{\prime }-y^{2}-x^{4}&=0 \end {array} \]
|
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
5.270 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{3} y^{\prime }-y^{2}-x^{2} y&=0 \end {array} \]
|
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
9.621 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{3} y^{\prime }-y^{2} x^{4}+x^{2} y+20&=0 \end {array} \]
|
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
8.657 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{3} y^{\prime }-x^{6} y^{2}-\left (2 x -3\right ) x^{2} y+3&=0 \end {array} \]
|
[_rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
2.870 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x \left (x^{2}+1\right ) y^{\prime }+x^{2} y&=0 \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.601 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x \left (x^{2}-1\right ) y^{\prime }-\left (2 x^{2}-1\right ) y+a \,x^{3}&=0 \end {array} \]
|
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.266 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x \left (x^{2}-1\right ) y^{\prime }+\left (x^{2}-1\right ) y^{2}-x^{2}&=0 \end {array} \]
|
[_rational, _Riccati] |
✓ |
✓ |
✓ |
✗ |
191.873 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} \left (-1+x \right ) y^{\prime }-y^{2}-x \left (x -2\right ) y&=0 \end {array} \]
|
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
7.407 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x \left (x^{2}-1\right ) y^{\prime }+2 \left (x^{2}-1\right ) y^{2}-\left (3 x^{2}-5\right ) y+x^{2}-3&=0 \end {array} \]
|
[_rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
98.509 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 3 x \left (x^{2}-1\right ) y^{\prime }+x y^{2}-\left (x^{2}+1\right ) y-3 x&=0 \end {array} \]
|
[_rational, _Riccati] |
✓ |
✓ |
✓ |
✗ |
114.214 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (a \,x^{2}+b x +c \right ) \left (-y+y^{\prime } x \right )-y^{2}+x^{2}&=0 \end {array} \]
|
[[_homogeneous, ‘class D‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✗ |
6.522 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{4} \left (y^{\prime }+y^{2}\right )+a&=0 \end {array} \]
|
[_rational, [_Riccati, _special]] |
✓ |
✓ |
✓ |
✓ |
6.954 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x \left (x^{3}-1\right ) y^{\prime }-2 x y^{2}+y+x^{2}&=0 \end {array} \]
|
[_rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
6.051 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (2 x^{4}-x \right ) y^{\prime }-2 \left (x^{3}-1\right ) y&=0 \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.288 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (a \,x^{2}+b x +c \right )^{2} \left (y^{\prime }+y^{2}\right )+A&=0 \end {array} \]
|
[_rational, _Riccati] |
✓ |
✓ |
✓ |
✗ |
7.674 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{7} y^{\prime }+5 x^{3} y^{2}+2 \left (x^{2}+1\right ) y^{3}&=0 \end {array} \]
|
[_rational, _Abel] |
✗ |
✓ |
✓ |
✗ |
27.595 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{n} y^{\prime }+y^{2}-\left (n -1\right ) x^{n -1} y+x^{2 n -2}&=0 \end {array} \]
|
[[_homogeneous, ‘class G‘], _Riccati] |
✓ |
✓ |
✓ |
✗ |
7.254 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{n} y^{\prime }-a y^{2}-b \,x^{2 n -2}&=0 \end {array} \]
|
[[_homogeneous, ‘class G‘], _Riccati] |
✓ |
✓ |
✓ |
✗ |
12.343 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2 n +1} y^{\prime }-a y^{3}-b \,x^{3 n}&=0 \end {array} \]
|
[[_homogeneous, ‘class G‘], _Abel] |
✓ |
✓ |
✓ |
✗ |
13.070 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{m \left (n -1\right )+n} y^{\prime }-a y^{n}-b \,x^{n \left (m +1\right )}&=0 \end {array} \]
|
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✗ |
7.998 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \sqrt {x^{2}-1}\, y^{\prime }-\sqrt {-1+y^{2}}&=0 \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
16.151 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime } \sqrt {-x^{2}+1}-y \sqrt {-1+y^{2}}&=0 \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
18.894 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime } \sqrt {a^{2}+x^{2}}+y-\sqrt {a^{2}+x^{2}}+x&=0 \end {array} \]
|
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.934 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x \ln \left (x \right ) y^{\prime }+y-a x \left (1+\ln \left (x \right )\right )&=0 \end {array} \]
|
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.468 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x \ln \left (x \right ) y^{\prime }-y^{2} \ln \left (x \right )-\left (2 \ln \left (x \right )^{2}+1\right ) y-\ln \left (x \right )^{3}&=0 \end {array} \]
|
[_Riccati] |
✓ |
✓ |
✓ |
✗ |
10.546 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \sin \left (x \right ) y^{\prime }-y^{2} \sin \left (x \right )^{2}+\left (\cos \left (x \right )-3 \sin \left (x \right )\right ) y+4&=0 \end {array} \]
|
[_Riccati] |
✓ |
✓ |
✓ |
✗ |
25.897 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \cos \left (x \right ) y^{\prime }+y+\left (1+\sin \left (x \right )\right ) \cos \left (x \right )&=0 \end {array} \]
|
[_linear] |
✓ |
✓ |
✓ |
✓ |
7.201 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \cos \left (x \right ) y^{\prime }-y^{4}-\sin \left (x \right ) y&=0 \end {array} \]
|
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
75.415 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \cos \left (x \right ) \sin \left (x \right ) y^{\prime }-y-\sin \left (x \right )^{3}&=0 \end {array} \]
|
[_linear] |
✓ |
✓ |
✓ |
✗ |
91.087 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime } \sin \left (2 x \right )+\sin \left (2 y\right )&=0 \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
34.287 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (a \sin \left (x \right )^{2}+b \right ) y^{\prime }+a y \sin \left (2 x \right )+A x \left (a \sin \left (x \right )^{2}+c \right )&=0 \end {array} \]
|
[_linear] |
✓ |
✓ |
✓ |
✗ |
26.858 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 f \left (x \right ) y^{\prime }+2 f \left (x \right ) y^{2}-y f^{\prime }\left (x \right )-2 f \left (x \right )^{2}&=0 \end {array} \]
|
[_Riccati] |
✓ |
✓ |
✓ |
✗ |
7.397 |
|