| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x \left (-1+x \right ) y^{\prime }&=\cot \left (y\right ) \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
42.568 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} r y^{\prime }&=\frac {\left (a^{2}-r^{2}\right ) \tan \left (y\right )}{a^{2}+r^{2}} \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.606 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \sqrt {x^{2}+1}\, y^{\prime }+\sqrt {1+y^{2}}&=0 \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.375 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\frac {x \left (1+y^{2}\right )}{y \left (x^{2}+1\right )}\\ y \left (0\right )&=1\\ \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.694 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{2} y^{\prime }&=2+3 y^{6}\\ y \left (0\right )&=0\\ \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.136 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \cos \left (y\right )^{2}+\left (1+{\mathrm e}^{-x}\right ) \sin \left (y\right ) y^{\prime }&=0 \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
10.421 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\frac {x^{3} {\mathrm e}^{x^{2}}}{\ln \left (y\right ) y} \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
177.503 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x \cos \left (y\right )^{2}+{\mathrm e}^{x} \tan \left (y\right ) y^{\prime }&=0 \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
152.164 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x \left (1+y^{2}\right )+\left (1+2 y\right ) {\mathrm e}^{-x} y^{\prime }&=0 \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.217 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x y^{3}+{\mathrm e}^{x^{2}} y^{\prime }&=0 \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.981 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x \cos \left (y\right )^{2}+\tan \left (y\right ) y^{\prime }&=0 \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
59.637 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x y^{3}+\left (1+y\right ) {\mathrm e}^{-x} y^{\prime }&=0 \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.066 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }+\frac {x}{y}+2&=0 \end {array} \]
|
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
5.921 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} -y+y^{\prime } x&=x \cot \left (\frac {y}{x}\right ) \end {array} \]
|
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
259.918 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x \cos \left (\frac {y}{x}\right )^{2}-y+y^{\prime } x&=0 \end {array} \]
|
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
6.079 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime } x&=y \left (1+\ln \left (y\right )-\ln \left (x \right )\right ) \end {array} \]
|
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
6.403 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y x +\left (x^{2}+y^{2}\right ) y^{\prime }&=0 \end {array} \]
|
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
10.739 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (1-{\mathrm e}^{-\frac {y}{x}}\right ) y^{\prime }+1-\frac {y}{x}&=0 \end {array} \]
|
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
8.009 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2}-y x +y^{2}-y y^{\prime } x&=0 \end {array} \]
|
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
9.068 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (3+2 x +4 y\right ) y^{\prime }&=x +2 y+1 \end {array} \]
|
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
6.879 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\frac {2 x +y-1}{x -y-2} \end {array} \]
|
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
26.872 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y+2&=\left (2 x +y-4\right ) y^{\prime } \end {array} \]
|
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
9.540 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\sin \left (x -y\right )^{2} \end {array} \]
|
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
4.768 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\left (x +1\right )^{2}+\left (4 y+1\right )^{2}+8 y x +1 \end {array} \]
|
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
✓ |
✓ |
✓ |
19.849 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 3 x^{2}+6 x y^{2}+\left (6 x^{2} y+4 y^{3}\right ) y^{\prime }&=0 \end {array} \]
|
[_exact, _rational] |
✓ |
✓ |
✓ |
✗ |
2.352 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x^{2}-x y^{2}-2 y+3-\left (x^{2} y+2 x \right ) y^{\prime }&=0 \end {array} \]
|
[_exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
3.441 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x y^{2}+x -2 y+3+\left (x^{2} y-2 y-2 x \right ) y^{\prime }&=0 \end {array} \]
|
[_exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
3.538 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 3 \left (x^{2}-1\right ) y+\left (x^{3}+8 y-3 x \right ) y^{\prime }&=0 \end {array} \]
|
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.457 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2}+\ln \left (y\right )+\frac {x y^{\prime }}{y}&=0 \end {array} \]
|
[_exact, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
3.398 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x \left (3 x +y-y \,{\mathrm e}^{-x^{2}}\right )+\left (x^{2}+3 y^{2}+{\mathrm e}^{-x^{2}}\right ) y^{\prime }&=0 \end {array} \]
|
[_exact] |
✓ |
✓ |
✓ |
✗ |
26.139 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 3+y+2 y^{2} \sin \left (x \right )^{2}+\left (x +2 y x -y \sin \left (2 x \right )\right ) y^{\prime }&=0 \end {array} \]
|
[_exact, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
38.619 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 y x +\left (x^{2}+2 y x +y^{2}\right ) y^{\prime }&=0 \end {array} \]
|
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
135.585 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2}-\sin \left (y\right )^{2}+x \sin \left (2 y\right ) y^{\prime }&=0 \end {array} \]
|
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✓ |
✓ |
18.981 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y \left (2 x -y+2\right )+2 \left (x -y\right ) y^{\prime }&=0 \end {array} \]
|
[[_homogeneous, ‘class D‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.822 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 y x +3 y^{2}-x +x \left (x +2 y\right ) y^{\prime }&=0 \end {array} \]
|
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
22.978 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y+x \left (y^{2}+\ln \left (x \right )\right ) y^{\prime }&=0 \end {array} \]
|
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
✓ |
✓ |
51.218 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2}+2 x +y+\left (3 x^{2} y-x \right ) y^{\prime }&=0 \end {array} \]
|
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
2.941 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{2}+\left (y x +y^{2}-1\right ) y^{\prime }&=0 \end {array} \]
|
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
✓ |
✓ |
✓ |
3.189 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 3 x^{2}+3 y^{2}+x \left (x^{2}+3 y^{2}+6 y\right ) y^{\prime }&=0 \end {array} \]
|
[_rational] |
✓ |
✓ |
✓ |
✗ |
2.043 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 y \left (x +y+2\right )+\left (y^{2}-x^{2}-4 x -1\right ) y^{\prime }&=0 \end {array} \]
|
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
✓ |
✓ |
✓ |
5.072 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2+y^{2}+2 x +2 y y^{\prime }&=0 \end {array} \]
|
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
2.251 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x y^{2}-y+\left (y^{2}+x +y\right ) y^{\prime }&=0 \end {array} \]
|
[_rational] |
✓ |
✓ |
✓ |
✗ |
49.333 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y \left (x +y\right )+\left (x +2 y-1\right ) y^{\prime }&=0 \end {array} \]
|
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
10.045 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x \left (x^{2}-\sin \left (y\right )+1\right )+\left (x^{2}+1\right ) \cos \left (y\right ) y^{\prime }&=0 \end {array} \]
|
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✓ |
✓ |
5.298 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2}+y+y^{2}-y^{\prime } x&=0 \end {array} \]
|
[[_homogeneous, ‘class D‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
1.863 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x -\sqrt {x^{2}+y^{2}}+\left (y-\sqrt {x^{2}+y^{2}}\right ) y^{\prime }&=0 \end {array} \]
|
[[_homogeneous, ‘class G‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
10.334 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y \sqrt {1+y^{2}}+\left (x \sqrt {1+y^{2}}-y\right ) y^{\prime }&=0 \end {array} \]
|
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
✓ |
✓ |
4.031 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{2}-\left (y x +x^{3}\right ) y^{\prime }&=0 \end {array} \]
|
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
16.498 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y-2 x^{3} \tan \left (\frac {y}{x}\right )-y^{\prime } x&=0 \end {array} \]
|
[[_homogeneous, ‘class D‘]] |
✓ |
✓ |
✓ |
✗ |
7.475 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 y^{2} x^{2}+y+\left (x^{3} y-x \right ) y^{\prime }&=0 \end {array} \]
|
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
16.831 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{2}+\left (y x +\tan \left (y x \right )\right ) y^{\prime }&=0 \end {array} \]
|
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✓ |
18.240 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x^{2} y^{4}-y+\left (4 x^{3} y^{3}-x \right ) y^{\prime }&=0 \end {array} \]
|
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✗ |
8.526 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2}+y^{3}+y+\left (x^{3}+y^{2}-x \right ) y^{\prime }&=0 \end {array} \]
|
[_rational] |
✗ |
✗ |
✗ |
✗ |
2.049 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y \left (1+y^{2}\right )+x \left (y^{2}-x +1\right ) y^{\prime }&=0 \end {array} \]
|
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
✓ |
✓ |
4.746 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{2}+\left (-y+{\mathrm e}^{x}\right ) y^{\prime }&=0 \end {array} \]
|
[[_1st_order, _with_linear_symmetries], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.691 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{2} x^{2}-2 y+\left (x^{3} y-x \right ) y^{\prime }&=0 \end {array} \]
|
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
16.469 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x^{3} y+y^{3}-\left (x^{4}+2 x y^{2}\right ) y^{\prime }&=0 \end {array} \]
|
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✗ |
5.609 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 1+\cos \left (x \right ) y-\sin \left (x \right ) y^{\prime }&=0 \end {array} \]
|
[_linear] |
✓ |
✓ |
✓ |
✓ |
34.913 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (\sin \left (y\right )^{2}+x \cot \left (y\right )\right ) y^{\prime }&=0 \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
6.362 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 1-\left (y-2 y x \right ) y^{\prime }&=0 \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.523 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 1-\left (1+2 x \tan \left (y\right )\right ) y^{\prime }&=0 \end {array} \]
|
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
✓ |
✓ |
2.412 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (y^{3}+\frac {x}{y}\right ) y^{\prime }&=1 \end {array} \]
|
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
5.204 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 1+\left (x -y^{2}\right ) y^{\prime }&=0 \end {array} \]
|
[[_1st_order, _with_exponential_symmetries]] |
✓ |
✓ |
✓ |
✓ |
2.918 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{2}+\left (y x +y^{2}-1\right ) y^{\prime }&=0 \end {array} \]
|
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
✓ |
✓ |
✓ |
3.257 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y&=\left ({\mathrm e}^{y}+2 y x -2 x \right ) y^{\prime } \end {array} \]
|
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
✓ |
✗ |
2.088 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (2 x +3\right ) y^{\prime }&=y+\sqrt {2 x +3} \end {array} \]
|
[_linear] |
✓ |
✓ |
✓ |
✓ |
0.227 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y+\left (y^{2} {\mathrm e}^{y}-x \right ) y^{\prime }&=0 \end {array} \]
|
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
3.845 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=1+3 \tan \left (x \right ) y \end {array} \]
|
[_linear] |
✓ |
✓ |
✓ |
✓ |
0.629 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (\cos \left (x \right )+1\right ) y^{\prime }&=\sin \left (x \right ) \left (\sin \left (x \right )+\cos \left (x \right ) \sin \left (x \right )-y\right ) \end {array} \]
|
[_linear] |
✓ |
✓ |
✓ |
✓ |
0.439 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\left (\sin \left (x \right )^{2}-y\right ) \cos \left (x \right ) \end {array} \]
|
[_linear] |
✓ |
✓ |
✓ |
✓ |
0.369 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x +1\right ) y^{\prime }-y&=x \left (x +1\right )^{2} \end {array} \]
|
[_linear] |
✓ |
✓ |
✓ |
✓ |
0.247 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 1+y+\left (x -y \left (1+y\right )^{2}\right ) y^{\prime }&=0 \end {array} \]
|
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
✓ |
✓ |
5.505 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }+y^{2}&=x^{2}+1 \end {array} \]
|
[_Riccati] |
✓ |
✓ |
✓ |
✗ |
0.508 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 3 y^{\prime } x -3 x y^{4} \ln \left (x \right )-y&=0 \end {array} \]
|
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
0.978 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\frac {4 x^{3} y^{2}}{x^{4} y+2} \end {array} \]
|
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
25.034 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y \left (6 y^{2}-x -1\right )+2 y^{\prime } x&=0 \end {array} \]
|
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
0.638 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x +1\right ) \left (y^{\prime }+y^{2}\right )-y&=0 \end {array} \]
|
[[_1st_order, _with_linear_symmetries], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
0.465 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y y^{\prime } x +y^{2}-\sin \left (x \right )&=0 \end {array} \]
|
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
0.674 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x^{3}-y^{4}+x y^{3} y^{\prime }&=0 \end {array} \]
|
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
0.987 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }-\tan \left (x \right ) y+\cos \left (x \right ) y^{2}&=0 \end {array} \]
|
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
0.967 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 6 y^{2}-x \left (2 x^{3}+y\right ) y^{\prime }&=0 \end {array} \]
|
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
29.872 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime }}^{3} x -y {y^{\prime }}^{2}+1&=0 \end {array} \]
|
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✗ |
6.535 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y&=y^{\prime } x +{y^{\prime }}^{3} \end {array} \]
|
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✗ |
1.961 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x \left (-1+{y^{\prime }}^{2}\right )&=2 y^{\prime } \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.168 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x y^{\prime } \left (y^{\prime }+2\right )&=y \end {array} \]
|
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
2.767 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x&=y^{\prime } \sqrt {1+{y^{\prime }}^{2}} \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.763 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 {y^{\prime }}^{2} \left (y-y^{\prime } x \right )&=1 \end {array} \]
|
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✗ |
2.113 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y&=2 y^{\prime } x +y^{2} {y^{\prime }}^{3} \end {array} \]
|
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.855 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime }}^{3}+y^{2}&=y y^{\prime } x \end {array} \]
|
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
✗ |
3.687 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 y^{\prime } x -y&=y^{\prime } \ln \left (y y^{\prime }\right ) \end {array} \]
|
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
2.850 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y&=y^{\prime } x -x^{2} {y^{\prime }}^{3} \end {array} \]
|
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
✗ |
20.003 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y \left (y-2 y^{\prime } x \right )^{3}&={y^{\prime }}^{2} \end {array} \]
|
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✗ |
✗ |
4.536 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime } x +y&=4 \sqrt {y^{\prime }} \end {array} \]
|
[[_homogeneous, ‘class G‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
8.952 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 y^{\prime } x -y&=\ln \left (y^{\prime }\right ) \end {array} \]
|
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
7.082 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x y^{2} \left (y^{\prime } x +y\right )&=1 \end {array} \]
|
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.185 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 5 y+{y^{\prime }}^{2}&=x \left (x +y^{\prime }\right ) \end {array} \]
|
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✓ |
3.147 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\frac {y+2}{x +1} \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.862 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime } x&=y-{\mathrm e}^{\frac {y}{x}} x \end {array} \]
|
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
484.599 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 1+y^{2} \sin \left (2 x \right )-2 y \cos \left (x \right )^{2} y^{\prime }&=0 \end {array} \]
|
[_exact, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
14.481 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 \sqrt {y x}-y-y^{\prime } x&=0 \end {array} \]
|
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
9.246 |
|