| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y \left (y \,{\mathrm e}^{y x}+1\right )+\left (x y \,{\mathrm e}^{y x}+{\mathrm e}^{y x}+x \right ) y^{\prime }&=0 \end {array} \]
|
[_exact] |
✓ |
✓ |
✓ |
✗ |
18.442 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{2}-\left (y x +2\right ) y^{\prime }&=0 \end {array} \]
|
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
99.026 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2}-2 y x -y^{2}-\left (x^{2}+2 y x -y^{2}\right ) y^{\prime }&=0 \end {array} \]
|
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
63.845 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{2}+\left (y x +y^{2}-1\right ) y^{\prime }&=0\\ y \left (-1\right )&=1\\ \end {array} \]
|
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
✓ |
✓ |
✓ |
8.523 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y \left (y^{2}-3 x^{2}\right )+x^{3} y^{\prime }&=0 \end {array} \]
|
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
47.503 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\cos \left (x \right )-y \sec \left (x \right )\\ y \left (0\right )&=1\\ \end {array} \]
|
[_linear] |
✓ |
✓ |
✓ |
✓ |
6.964 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=3 x +y\\ y \left (-1\right )&=0\\ \end {array} \]
|
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
5.278 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=3 x +y\\ y \left (-1\right )&=1\\ \end {array} \]
|
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.286 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\cos \left (x \right )+\tan \left (x \right ) y \end {array} \]
|
[_linear] |
✓ |
✓ |
✓ |
✓ |
6.268 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2}-1+2 y+\left (-x^{2}+1\right ) y^{\prime }&=0\\ y \left (2\right )&=1\\ \end {array} \]
|
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.548 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{3}-3 x y^{2}+\left (y^{3}-3 x^{2} y\right ) y^{\prime }&=0 \end {array} \]
|
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
54.332 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (-x^{2}+1\right ) y^{\prime }&=1-y x -3 x^{2}+2 x^{4} \end {array} \]
|
[_linear] |
✓ |
✓ |
✓ |
✓ |
12.393 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{2}+y-\left (y^{2}+2 y x +x \right ) y^{\prime }&=0\\ y \left (3\right )&=1\\ \end {array} \]
|
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
✓ |
✓ |
✓ |
11.720 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{3}-x^{3}&=x y \left (x +y y^{\prime }\right ) \end {array} \]
|
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
28.908 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y \left (y^{2} x^{2}+x^{2}+y^{2}\right )+x \left (x^{2}+y^{2}-y^{2} x^{2}\right ) y^{\prime }&=0 \end {array} \]
|
[_rational] |
✓ |
✓ |
✓ |
✗ |
9.353 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 3 x -2 y+1+\left (3 x -2 y+3\right ) y^{\prime }&=0 \end {array} \]
|
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
19.193 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \sin \left (y\right ) \left (x +\sin \left (y\right )\right )+2 x^{2} \cos \left (y\right ) y^{\prime }&=0 \end {array} \]
|
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✓ |
✓ |
1792.518 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\left (9 x +4 y+1\right )^{2} \end {array} \]
|
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
✓ |
✓ |
✓ |
42.098 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=y-x y^{3} {\mathrm e}^{-2 x} \end {array} \]
|
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
15.206 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\sin \left (x +y\right ) \end {array} \]
|
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
3.151 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y x +\left (x^{2}-3 y\right ) y^{\prime }&=0 \end {array} \]
|
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
111.159 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (3 \tan \left (x \right )-2 \cos \left (y\right )\right ) \sec \left (x \right )^{2}+\tan \left (x \right ) \sin \left (y\right ) y^{\prime }&=0 \end {array} \]
|
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✓ |
✗ |
218.245 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x +2 y-1+\left (2 x +4 y-3\right ) y^{\prime }&=0 \end {array} \]
|
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
6.092 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 6 y^{2}-x \left (2 x^{3}+y\right ) y^{\prime }&=0 \end {array} \]
|
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
84.489 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x^{3} y^{\prime }&=y \left (3 x^{2}+y^{2}\right ) \end {array} \]
|
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
23.227 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 3 \sin \left (y\right )-5 x +2 x^{2} \cot \left (y\right ) y^{\prime }&=0 \end {array} \]
|
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
✓ |
✓ |
179.489 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=1+6 x \,{\mathrm e}^{x -y} \end {array} \]
|
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
129.383 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y+x \left (3 y x -2\right ) y^{\prime }&=0 \end {array} \]
|
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
138.721 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime } x&=y-y^{3} \cos \left (x \right ) \end {array} \]
|
[[_homogeneous, ‘class D‘], _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
14.135 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 y+x \left (x^{2} \ln \left (y\right )-1\right ) y^{\prime }&=0 \end {array} \]
|
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
✓ |
✓ |
17.076 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \cos \left (y\right ) \sin \left (2 x \right )+\left (\cos \left (y\right )^{2}-\cos \left (x \right )^{2}\right ) y^{\prime }&=0 \end {array} \]
|
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
✓ |
✗ |
37.504 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} k \,{\mathrm e}^{2 v}-u -2 \,{\mathrm e}^{2 v} \left ({\mathrm e}^{2 v}+k u \right ) v^{\prime }&=0 \end {array} \]
|
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
8.607 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime } \tan \left (x \right ) \sin \left (2 y\right )&=\sin \left (x \right )^{2}+\cos \left (y\right )^{2} \end {array} \]
|
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✓ |
✓ |
273.765 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x +2 y-1-\left (x +2 y-5\right ) y^{\prime }&=0 \end {array} \]
|
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
15.713 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y \left (x \tan \left (x \right )+\ln \left (y\right )\right )+\tan \left (x \right ) y^{\prime }&=0 \end {array} \]
|
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✗ |
✓ |
✓ |
✓ |
86.959 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} -y+y^{\prime } x&=x^{k} y^{n} \end {array} \]
|
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
23.398 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} -y+y^{\prime } x&=x^{k} y \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
15.299 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} -y+y^{\prime } x&=y \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
13.488 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 12 x +4 y-8-\left (3 x +y\right ) y^{\prime }&=0\\ y \left (1\right )&=0\\ \end {array} \]
|
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
31.060 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=2 \left (3 x +y\right )^{2}-1\\ y \left (0\right )&=1\\ \end {array} \]
|
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
✓ |
✓ |
✓ |
214.870 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 y y^{\prime } x&=y^{2}-2 x^{3}\\ y \left (1\right )&=2\\ \end {array} \]
|
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
18.497 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{4}-2 y x +3 x^{2} y^{\prime }&=0\\ y \left (2\right )&=1\\ \end {array} \]
|
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
16.290 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 y^{3}-x^{3}+3 y^{2} y^{\prime } x&=0\\ y \left (1\right )&=1\\ \end {array} \]
|
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
138.396 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2}+6 y^{2}-4 y y^{\prime } x&=0\\ y \left (1\right )&=1\\ \end {array} \]
|
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
40.022 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y-2-\left (x -y-1\right ) y^{\prime }&=0 \end {array} \]
|
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
122.661 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x -4 y-9+\left (4 x +y-2\right ) y^{\prime }&=0 \end {array} \]
|
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
284.691 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x -y+\left (-6+4 x +y\right ) y^{\prime }&=0 \end {array} \]
|
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
61.508 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x -4 y-3-\left (x -6 y-5\right ) y^{\prime }&=0 \end {array} \]
|
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
77.195 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x +3 y-5+\left (3 x -y-2\right ) y^{\prime }&=0 \end {array} \]
|
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
375.115 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (2 x -y+3\right ) y^{\prime }+2&=0 \end {array} \]
|
[[_homogeneous, ‘class C‘], [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
11.137 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x -y+2+3 y^{\prime }&=0 \end {array} \]
|
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.555 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x +y-1+\left (2 x +2 y+1\right ) y^{\prime }&=0 \end {array} \]
|
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
100.370 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 3 x +2 y+7+\left (2 x -y\right ) y^{\prime }&=0 \end {array} \]
|
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
24.878 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x -2+4 \left (x +y-1\right ) y^{\prime }&=0 \end {array} \]
|
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
65.027 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x -3 y+2+3 \left (x +3 y-4\right ) y^{\prime }&=0 \end {array} \]
|
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
210.192 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 6 x -3 y+2-\left (2 x -y-1\right ) y^{\prime }&=0 \end {array} \]
|
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
20.260 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 9 x -4 y+4-\left (1+2 x -y\right ) y^{\prime }&=0 \end {array} \]
|
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
33.538 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x +3 y-4+\left (x +4 y-5\right ) y^{\prime }&=0 \end {array} \]
|
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
119.778 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x +2 y-1-\left (-5+2 x +y\right ) y^{\prime }&=0 \end {array} \]
|
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
60.506 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x -1-\left (3 x -2 y-5\right ) y^{\prime }&=0 \end {array} \]
|
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
55.000 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x -3 y+4+3 \left (-1+x \right ) y^{\prime }&=0\\ y \left (3\right )&=2\\ \end {array} \]
|
[_linear] |
✓ |
✓ |
✓ |
✓ |
7.631 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x -3 y+4+3 \left (-1+x \right ) y^{\prime }&=0\\ y \left (-1\right )&=2\\ \end {array} \]
|
[_linear] |
✓ |
✓ |
✓ |
✓ |
7.364 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x +y-4-\left (3 x -y-4\right ) y^{\prime }&=0\\ y \left (4\right )&=1\\ \end {array} \]
|
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
16.569 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x +y-4-\left (3 x -y-4\right ) y^{\prime }&=0\\ y \left (3\right )&=7\\ \end {array} \]
|
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
20.207 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2}+y^{2}+1+x \left (x -2 y\right ) y^{\prime }&=0 \end {array} \]
|
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
64.465 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 y \left (x^{2}-y+x \right )+\left (x^{2}-2 y\right ) y^{\prime }&=0 \end {array} \]
|
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
8.519 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y \left (1+2 x -y\right )+x \left (3 x -4 y+3\right ) y^{\prime }&=0 \end {array} \]
|
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
410.361 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y \left (4 x +y\right )-2 \left (x^{2}-y\right ) y^{\prime }&=0 \end {array} \]
|
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
198.005 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y x +1+x \left (x +4 y-2\right ) y^{\prime }&=0 \end {array} \]
|
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
41.747 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 y^{2}+3 y x -2 y+6 x +x \left (x +2 y-1\right ) y^{\prime }&=0 \end {array} \]
|
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
6.041 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y \left (y+2 x -2\right )-2 \left (x +y\right ) y^{\prime }&=0 \end {array} \]
|
[[_homogeneous, ‘class D‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
25.896 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{2}+\left (3 y x +y^{2}-1\right ) y^{\prime }&=0 \end {array} \]
|
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
✓ |
✓ |
✓ |
8.784 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 y \left (x +y+2\right )+\left (y^{2}-x^{2}-4 x -1\right ) y^{\prime }&=0 \end {array} \]
|
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
✓ |
✓ |
✓ |
7.770 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 y^{2}+10 y x -4 y+8+x \left (2 x +2 y-1\right ) y^{\prime }&=0 \end {array} \]
|
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
6.324 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 3 x^{2}+3 y^{2}+x \left (x^{2}+3 y^{2}+6 y\right ) y^{\prime }&=0 \end {array} \]
|
[_rational] |
✓ |
✓ |
✓ |
✗ |
3.144 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y \left (8 x -9 y\right )+2 x \left (x -3 y\right ) y^{\prime }&=0 \end {array} \]
|
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
93.732 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y \left (2 x^{2}-y x +1\right )+\left (x -y\right ) y^{\prime }&=0 \end {array} \]
|
[[_homogeneous, ‘class D‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
15.722 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{2}-3 y-x +\left (2 y-3\right ) y^{\prime }&=0 \end {array} \]
|
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
5.052 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{3}+y+1+x \left (x -3 y^{2}-1\right ) y^{\prime }&=0 \end {array} \]
|
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
✓ |
✗ |
78.438 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x +3 y-5-\left (x -y-1\right ) y^{\prime }&=0 \end {array} \]
|
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
314.329 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x -2 y+3+2 \left (x +2 y-1\right ) y^{\prime }&=0 \end {array} \]
|
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
25.532 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x +y-4+\left (x -3 y+12\right ) y^{\prime }&=0 \end {array} \]
|
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
798.218 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=a x +b y+c \end {array} \]
|
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.708 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{3} \sec \left (x \right )^{2}-\left (1-2 \tan \left (x \right ) y^{2}\right ) y^{\prime }&=0 \end {array} \]
|
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
✓ |
✗ |
21.461 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{3} y+\left (3 x^{4}-y^{3}\right ) y^{\prime }&=0 \end {array} \]
|
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✗ |
13.168 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} a_{1} x +k y+c_{1} +\left (k x +b_{2} y+c_{2} \right ) y^{\prime }&=0 \end {array} \]
|
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
17.742 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x +2 y+1\right ) y^{\prime }+7+x -4 y&=0 \end {array} \]
|
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
35.303 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime } x&=x^{3} y^{3}-2 y \end {array} \]
|
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
8.168 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (2 x -1\right ) y+2 \left (x^{2}+y^{2}-x \right ) y^{\prime }&=0 \end {array} \]
|
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
✓ |
✓ |
47.900 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 5 x +3 \,{\mathrm e}^{y}+2 x \,{\mathrm e}^{y} y^{\prime }&=0 \end {array} \]
|
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
357.423 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 3 x +y-2+\left (3 x +y+4\right ) y^{\prime }&=0 \end {array} \]
|
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
10.786 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 6 y x -3 y^{2}+2 y+2 \left (x -y\right ) y^{\prime }&=0 \end {array} \]
|
[[_homogeneous, ‘class D‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
6.921 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=x -y+2 \end {array} \]
|
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.330 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x +y-2-\left (x -4 y-2\right ) y^{\prime }&=0 \end {array} \]
|
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
288.966 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4+\left (x -y+2\right )^{2} y^{\prime }&=0 \end {array} \]
|
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
4.033 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x +4 y-1-\left (x +2 y-3\right ) y^{\prime }&=0 \end {array} \]
|
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
11.672 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 y+3 \left (2 x -1\right ) \left (y^{\prime }+y^{4}\right )&=0\\ y \left (1\right )&=1\\ \end {array} \]
|
[[_1st_order, _with_linear_symmetries], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
7.036 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (-1+x \right ) y-\left (x^{2}-2 x -2 y\right ) y^{\prime }&=0 \end {array} \]
|
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
452.485 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\tan \left (y\right ) \cot \left (x \right )-\sec \left (y\right ) \cos \left (x \right ) \end {array} \]
|
[‘y=_G(x,y’)‘] |
✗ |
✓ |
✓ |
✓ |
325.100 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 1+\left (x +y\right )^{2}+\left (1+x \left (x +y\right )\right ) y^{\prime }&=0 \end {array} \]
|
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
18.367 |
|