| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=2 x y^{2}+3 y^{2} x^{2}\\ y \left (1\right )&=-1\\ \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
9.987 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=6 \,{\mathrm e}^{2 x -y}\\ y \left (0\right )&=0\\ \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
674.479 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 \sqrt {x}\, y^{\prime }&=\cos \left (y\right )^{2}\\ y \left (4\right )&=\frac {\pi }{4}\\ \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
8.437 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }+y&=2\\ y \left (0\right )&=0\\ \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
3.273 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }-2 y&=3 \,{\mathrm e}^{2 x}\\ y \left (0\right )&=0\\ \end {array} \]
|
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
10.585 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }+3 y&=2 x \,{\mathrm e}^{-3 x} \end {array} \]
|
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
13.999 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }-2 y x&={\mathrm e}^{x^{2}} \end {array} \]
|
[_linear] |
✓ |
✓ |
✓ |
✓ |
811.061 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime } x +2 y&=3 x\\ y \left (1\right )&=5\\ \end {array} \]
|
[_linear] |
✓ |
✓ |
✓ |
✓ |
15.904 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 y^{\prime } x +y&=10 \sqrt {x}\\ y \left (2\right )&=5\\ \end {array} \]
|
[_linear] |
✓ |
✓ |
✓ |
✓ |
13.474 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 y^{\prime } x +y&=10 \sqrt {x} \end {array} \]
|
[_linear] |
✓ |
✓ |
✓ |
✓ |
11.247 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y+3 y^{\prime } x&=12 x \end {array} \]
|
[_linear] |
✓ |
✓ |
✓ |
✓ |
12.320 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} -y+y^{\prime } x&=x\\ y \left (1\right )&=7\\ \end {array} \]
|
[_linear] |
✓ |
✓ |
✓ |
✓ |
10.476 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 y^{\prime } x -3 y&=9 x^{3} \end {array} \]
|
[_linear] |
✓ |
✓ |
✓ |
✓ |
9.042 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime } x +y&=3 y x\\ y \left (1\right )&=0\\ \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
14.955 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime } x +3 y&=2 x^{5}\\ y \left (2\right )&=1\\ \end {array} \]
|
[_linear] |
✓ |
✓ |
✓ |
✓ |
11.299 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }+y&={\mathrm e}^{x}\\ y \left (0\right )&=1\\ \end {array} \]
|
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
5.429 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime } x -3 y&=x^{3}\\ y \left (1\right )&=10\\ \end {array} \]
|
[_linear] |
✓ |
✓ |
✓ |
✓ |
8.775 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }+2 y x&=x\\ y \left (0\right )&=-2\\ \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.481 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\left (1-y\right ) \cos \left (x \right )\\ y \left (\pi \right )&=2\\ \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
9.095 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x +1\right ) y^{\prime }+y&=\cos \left (x \right )\\ y \left (0\right )&=1\\ \end {array} \]
|
[_linear] |
✓ |
✓ |
✓ |
✓ |
6.618 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime } x&=2 y+\cos \left (x \right ) x^{3} \end {array} \]
|
[_linear] |
✓ |
✓ |
✓ |
✓ |
10.593 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }+\cot \left (x \right ) y&=\cos \left (x \right ) \end {array} \]
|
[_linear] |
✓ |
✓ |
✓ |
✓ |
753.282 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=1+x +y+y x\\ y \left (0\right )&=0\\ \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.663 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime } x&=3 y+x^{4} \cos \left (x \right )\\ y \left (2 \pi \right )&=0\\ \end {array} \]
|
[_linear] |
✓ |
✓ |
✓ |
✓ |
12.093 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=2 y x +3 x^{2} {\mathrm e}^{x^{2}}\\ y \left (0\right )&=5\\ \end {array} \]
|
[_linear] |
✓ |
✓ |
✓ |
✓ |
836.664 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime } x +\left (2 x -3\right ) y&=4 x^{4} \end {array} \]
|
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.091 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x^{2}+4\right ) y^{\prime }+3 y x&=x\\ y \left (0\right )&=1\\ \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.156 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x^{2}+1\right ) y^{\prime }+3 x^{3} y&=6 x \,{\mathrm e}^{-\frac {3 x^{2}}{2}}\\ y \left (0\right )&=1\\ \end {array} \]
|
[_linear] |
✓ |
✓ |
✓ |
✗ |
7.139 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x +y\right ) y^{\prime }&=x -y \end {array} \]
|
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
867.979 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 y y^{\prime } x&=x^{2}+y^{2} \end {array} \]
|
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
23.739 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime } x&=y+2 \sqrt {y x} \end {array} \]
|
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
21.467 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x -y\right ) y^{\prime }&=x +y \end {array} \]
|
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
29.995 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x \left (x +y\right ) y^{\prime }&=y \left (x -y\right ) \end {array} \]
|
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
525.905 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x +2 y\right ) y^{\prime }&=y \end {array} \]
|
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
26.774 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{2} y^{\prime } x&=x^{3}+y^{3} \end {array} \]
|
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
27.809 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime }&=y x +x^{2} {\mathrm e}^{\frac {y}{x}} \end {array} \]
|
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
874.768 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime }&=y x +y^{2} \end {array} \]
|
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
9.794 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y y^{\prime } x&=x^{2}+3 y^{2} \end {array} \]
|
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
16.483 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x^{2}-y^{2}\right ) y^{\prime }&=2 y x \end {array} \]
|
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
35.354 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y y^{\prime } x&=y^{2}+x \sqrt {4 x^{2}+y^{2}} \end {array} \]
|
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
26.243 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime } x&=y+\sqrt {x^{2}+y^{2}} \end {array} \]
|
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
14.789 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x +y y^{\prime }&=\sqrt {x^{2}+y^{2}} \end {array} \]
|
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
16.494 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x \left (x +y\right ) y^{\prime }+y \left (3 x +y\right )&=0 \end {array} \]
|
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
74.485 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\sqrt {x +y+1} \end {array} \]
|
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
6.855 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\left (4 x +y\right )^{2} \end {array} \]
|
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
✓ |
✓ |
✓ |
3.668 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x +y\right ) y^{\prime }&=0 \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.654 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime }+2 y x&=5 y^{3} \end {array} \]
|
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
14.858 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{2} y^{\prime }+2 x y^{3}&=6 x \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.940 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=y+y^{3} \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
7.449 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime }+2 y x&=5 y^{4} \end {array} \]
|
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
17.602 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime } x +6 y&=3 x y^{{4}/{3}} \end {array} \]
|
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
109.841 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 y^{\prime } x +y^{3} {\mathrm e}^{-2 x}&=2 y x \end {array} \]
|
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
9.615 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{2} \left (y^{\prime } x +y\right ) \sqrt {x^{4}+1}&=x \end {array} \]
|
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
13.982 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 3 y^{2} y^{\prime }+y^{3}&={\mathrm e}^{-x} \end {array} \]
|
[[_1st_order, _with_linear_symmetries], _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.481 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 3 y^{2} y^{\prime } x&=3 x^{4}+y^{3} \end {array} \]
|
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
12.279 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x \,{\mathrm e}^{y} y^{\prime }&=2 \,{\mathrm e}^{y}+2 x^{3} {\mathrm e}^{2 x} \end {array} \]
|
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
88.649 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x \sin \left (y\right ) \cos \left (y\right ) y^{\prime }&=4 x^{2}+\sin \left (y\right )^{2} \end {array} \]
|
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✓ |
✓ |
34.935 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left ({\mathrm e}^{y}+x \right ) y^{\prime }&=x \,{\mathrm e}^{-y}-1 \end {array} \]
|
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
81.014 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x +3 y+\left (3 x +2 y\right ) y^{\prime }&=0 \end {array} \]
|
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
26.701 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 x -y+\left (6 y-x \right ) y^{\prime }&=0 \end {array} \]
|
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
23.899 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 3 x^{2}+2 y^{2}+\left (4 y x +6 y^{2}\right ) y^{\prime }&=0 \end {array} \]
|
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
2651.476 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x y^{2}+3 x^{2}+\left (2 x^{2} y+4 y^{3}\right ) y^{\prime }&=0 \end {array} \]
|
[_exact, _rational] |
✓ |
✓ |
✓ |
✗ |
7.366 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{3}+\frac {y}{x}+\left (y^{2}+\ln \left (x \right )\right ) y^{\prime }&=0 \end {array} \]
|
[_exact] |
✓ |
✓ |
✓ |
✗ |
378.496 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 1+y \,{\mathrm e}^{y x}+\left (2 y+x \,{\mathrm e}^{y x}\right ) y^{\prime }&=0 \end {array} \]
|
[_exact] |
✓ |
✓ |
✓ |
✗ |
56.839 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \cos \left (x \right )+\ln \left (y\right )+\left (\frac {x}{y}+{\mathrm e}^{y}\right ) y^{\prime }&=0 \end {array} \]
|
[_exact] |
✓ |
✓ |
✓ |
✗ |
12.413 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x +\arctan \left (y\right )+\frac {\left (x +y\right ) y^{\prime }}{1+y^{2}}&=0 \end {array} \]
|
[_exact] |
✓ |
✓ |
✓ |
✗ |
7.372 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 3 x^{2} y^{3}+y^{4}+\left (3 x^{3} y^{2}+y^{4}+4 x y^{3}\right ) y^{\prime }&=0 \end {array} \]
|
[_exact, _rational] |
✓ |
✓ |
✓ |
✗ |
2.231 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {\mathrm e}^{x} \sin \left (y\right )+\tan \left (y\right )+\left ({\mathrm e}^{x} \cos \left (y\right )+x \sec \left (y\right )^{2}\right ) y^{\prime }&=0 \end {array} \]
|
[_exact] |
✓ |
✓ |
✓ |
✗ |
19.168 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {2 x}{y}-\frac {3 y^{2}}{x^{4}}+\left (\frac {2 y}{x^{3}}-\frac {x^{2}}{y^{2}}+\frac {1}{\sqrt {y}}\right ) y^{\prime }&=0 \end {array} \]
|
[_exact, _rational] |
✓ |
✓ |
✗ |
✗ |
20.189 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {2 x^{{5}/{2}}-3 y^{{5}/{3}}}{2 x^{{5}/{2}} y^{{2}/{3}}}+\frac {\left (3 y^{{5}/{3}}-2 x^{{5}/{2}}\right ) y^{\prime }}{3 x^{{3}/{2}} y^{{5}/{3}}}&=0 \end {array} \]
|
[[_1st_order, _with_linear_symmetries], _exact, _rational] |
✓ |
✓ |
✓ |
✗ |
18.119 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{3}+3 y-y^{\prime } x&=0 \end {array} \]
|
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.276 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x y^{2}+3 y^{2}-x^{2} y^{\prime }&=0 \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.740 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y x +y^{2}-x^{2} y^{\prime }&=0 \end {array} \]
|
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
11.645 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x y^{3}+{\mathrm e}^{x}+\left (3 y^{2} x^{2}+\sin \left (y\right )\right ) y^{\prime }&=0 \end {array} \]
|
[_exact] |
✓ |
✓ |
✓ |
✗ |
7.997 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 3 y+x^{4} y^{\prime }&=2 y x \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.959 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x y^{2}+x^{2} y^{\prime }&=y^{2} \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.756 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x^{2} y+x^{3} y^{\prime }&=1 \end {array} \]
|
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.803 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime }+2 y x&=y^{2} \end {array} \]
|
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
22.290 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime } x +2 y&=6 \sqrt {y}\, x^{2} \end {array} \]
|
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
20.394 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=1+x^{2}+y^{2}+y^{2} x^{2} \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.914 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime }&=y x +3 y^{2} \end {array} \]
|
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
10.365 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 6 x y^{3}+2 y^{4}+\left (9 y^{2} x^{2}+8 x y^{3}\right ) y^{\prime }&=0 \end {array} \]
|
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
0.922 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=1+x^{2}+y^{2}+x^{2} y^{4} \end {array} \]
|
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
✗ |
3.467 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{3} y^{\prime }&=x^{2} y-y^{3} \end {array} \]
|
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
23.681 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }+3 y&=3 x^{2} {\mathrm e}^{-3 x} \end {array} \]
|
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
6.922 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=x^{2}-2 y x +y^{2} \end {array} \]
|
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
✓ |
✓ |
✓ |
3.116 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {\mathrm e}^{x}+y \,{\mathrm e}^{y x}+\left ({\mathrm e}^{y}+x \,{\mathrm e}^{y x}\right ) y^{\prime }&=0 \end {array} \]
|
[_exact] |
✓ |
✓ |
✓ |
✗ |
108.712 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x^{2} y-x^{3} y^{\prime }&=y^{3} \end {array} \]
|
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
82.404 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 3 x^{5} y^{2}+x^{3} y^{\prime }&=2 y^{2} \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.428 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime } x +3 y&=\frac {3}{x^{{3}/{2}}} \end {array} \]
|
[_linear] |
✓ |
✓ |
✓ |
✓ |
9.701 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x^{2}-1\right ) y^{\prime }+\left (-1+x \right ) y&=1 \end {array} \]
|
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.898 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime } x&=6 y+12 x^{4} y^{{2}/{3}} \end {array} \]
|
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
35.905 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {\mathrm e}^{y}+\cos \left (x \right ) y+\left (x \,{\mathrm e}^{y}+\sin \left (x \right )\right ) y^{\prime }&=0 \end {array} \]
|
[_exact] |
✓ |
✓ |
✓ |
✗ |
69.684 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 9 y^{2} x^{2}+x^{{3}/{2}} y^{\prime }&=y^{2} \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.306 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 y+\left (x +1\right ) y^{\prime }&=3 x +3 \end {array} \]
|
[_linear] |
✓ |
✓ |
✓ |
✓ |
9.299 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 9 \sqrt {x}\, y^{{4}/{3}}-12 x^{{1}/{5}} y^{{3}/{2}}+\left (8 x^{{3}/{2}} y^{{1}/{3}}-15 x^{{6}/{5}} \sqrt {y}\right ) y^{\prime }&=0 \end {array} \]
|
[[_homogeneous, ‘class G‘], _exact, _rational] |
✓ |
✓ |
✗ |
✗ |
0.787 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 3 y+x^{3} y^{4}+3 y^{\prime } x&=0 \end {array} \]
|
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
11.816 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime } x +y&=2 \,{\mathrm e}^{2 x} \end {array} \]
|
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.524 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (2 x +1\right ) y^{\prime }+y&=\left (2 x +1\right )^{{3}/{2}} \end {array} \]
|
[_linear] |
✓ |
✓ |
✓ |
✓ |
86.335 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=3 \left (y+7\right ) x^{2} \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.849 |
|