| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {y \cos \left (\frac {y}{x}\right )}{x}-\left (\frac {x \sin \left (\frac {y}{x}\right )}{y}+\cos \left (\frac {y}{x}\right )\right ) y^{\prime }&=0 \end {array} \]
|
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
50.207 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y+x \ln \left (\frac {y}{x}\right ) y^{\prime }-2 y^{\prime } x&=0 \end {array} \]
|
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
109.092 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 \,{\mathrm e}^{\frac {x}{y}} y+\left (y-2 x \,{\mathrm e}^{\frac {x}{y}}\right ) y^{\prime }&=0 \end {array} \]
|
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
38.503 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {\mathrm e}^{\frac {y}{x}} x -y \sin \left (\frac {y}{x}\right )+x \sin \left (\frac {y}{x}\right ) y^{\prime }&=0 \end {array} \]
|
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
2329.042 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2}+y^{2}&=2 y y^{\prime } x\\ y \left (-1\right )&=0\\ \end {array} \]
|
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
99.387 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {\mathrm e}^{\frac {y}{x}} x +y&=y^{\prime } x\\ y \left (1\right )&=0\\ \end {array} \]
|
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
921.575 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }-\frac {y}{x}+\csc \left (\frac {y}{x}\right )&=0\\ y \left (1\right )&=0\\ \end {array} \]
|
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1655.545 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y x -y^{2}-x^{2} y^{\prime }&=0\\ y \left (1\right )&=1\\ \end {array} \]
|
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
24.074 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x +2 y-4-\left (2 x -4 y\right ) y^{\prime }&=0 \end {array} \]
|
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
82.978 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 3 x +2 y+1-\left (3 x +2 y-1\right ) y^{\prime }&=0 \end {array} \]
|
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
34.442 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x +y+1+\left (2 x +2 y+2\right ) y^{\prime }&=0 \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.842 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x +y-1+\left (2 x +2 y-3\right ) y^{\prime }&=0 \end {array} \]
|
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
139.205 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x +y-1-\left (x -y-1\right ) y^{\prime }&=0 \end {array} \]
|
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
67.275 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x +y+\left (2 x +2 y-1\right ) y^{\prime }&=0 \end {array} \]
|
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
31.917 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 7 y-3+\left (2 x +1\right ) y^{\prime }&=0 \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
12.346 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x +2 y+\left (3 x +6 y+3\right ) y^{\prime }&=0 \end {array} \]
|
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
58.273 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x +2 y+\left (-1+y\right ) y^{\prime }&=0 \end {array} \]
|
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
70.798 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 3 x -2 y+4-\left (2 x +7 y-1\right ) y^{\prime }&=0 \end {array} \]
|
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
69.467 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x +y+\left (3 x +3 y-4\right ) y^{\prime }&=0\\ y \left (1\right )&=0\\ \end {array} \]
|
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✗ |
✗ |
66.651 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 3 x +2 y+3-\left (x +2 y-1\right ) y^{\prime }&=0 \end {array} \]
|
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
388.277 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y+7+\left (2 x +y+3\right ) y^{\prime }&=0\\ y \left (0\right )&=1\\ \end {array} \]
|
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
34.877 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x +y+2-\left (x -y-4\right ) y^{\prime }&=0 \end {array} \]
|
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
348.019 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 3 x^{2} y+8 x y^{2}+\left (x^{3}+8 x^{2} y+12 y^{2}\right ) y^{\prime }&=0 \end {array} \]
|
[_exact, _rational] |
✓ |
✓ |
✓ |
✗ |
64.745 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {2 y x +1}{y}+\frac {\left (y-x \right ) y^{\prime }}{y^{2}}&=0 \end {array} \]
|
[[_homogeneous, ‘class D‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
1.658 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 y x +\left (x^{2}+y^{2}\right ) y^{\prime }&=0 \end {array} \]
|
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
66.638 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {\mathrm e}^{x} \sin \left (y\right )+{\mathrm e}^{-y}-\left (x \,{\mathrm e}^{-y}-{\mathrm e}^{x} \cos \left (y\right )\right ) y^{\prime }&=0 \end {array} \]
|
[_exact] |
✓ |
✓ |
✓ |
✗ |
1.360 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \cos \left (y\right )-\left (x \sin \left (y\right )-y^{2}\right ) y^{\prime }&=0 \end {array} \]
|
[_exact, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
✓ |
✓ |
1.159 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x -2 y x +{\mathrm e}^{y}+\left (x \,{\mathrm e}^{y}+y-x^{2}\right ) y^{\prime }&=0 \end {array} \]
|
[_exact] |
✓ |
✓ |
✓ |
✗ |
6.864 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2}-x +y^{2}-\left ({\mathrm e}^{y}-2 y x \right ) y^{\prime }&=0 \end {array} \]
|
[_exact] |
✓ |
✓ |
✓ |
✗ |
8.059 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x +\cos \left (x \right ) y+\left (2 y+\sin \left (x \right )-\sin \left (y\right )\right ) y^{\prime }&=0 \end {array} \]
|
[_exact] |
✓ |
✓ |
✓ |
✗ |
0.970 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x \sqrt {x^{2}+y^{2}}-\frac {x^{2} y y^{\prime }}{y-\sqrt {x^{2}+y^{2}}}&=0 \end {array} \]
|
[[_homogeneous, ‘class A‘], _exact, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
1.398 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 x^{3}-\sin \left (x \right )+y^{3}-\left (y^{2}+1-3 x y^{2}\right ) y^{\prime }&=0 \end {array} \]
|
[_exact] |
✓ |
✓ |
✓ |
✗ |
0.832 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {\mathrm e}^{x} \left (y^{3}+x y^{3}+1\right )+3 y^{2} \left (x \,{\mathrm e}^{x}-6\right ) y^{\prime }&=0\\ y \left (0\right )&=1\\ \end {array} \]
|
[_exact, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
15.368 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \cos \left (y\right ) \sin \left (x \right )+\cos \left (x \right ) \sin \left (y\right ) y^{\prime }&=0\\ y \left (\frac {\pi }{4}\right )&=\frac {\pi }{4}\\ \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
292.485 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{2} {\mathrm e}^{x y^{2}}+4 x^{3}+\left (2 x y \,{\mathrm e}^{x y^{2}}-3 y^{2}\right ) y^{\prime }&=0\\ y \left (1\right )&=0\\ \end {array} \]
|
[_exact] |
✓ |
✓ |
✓ |
✗ |
48.406 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{2}+y-y^{\prime } x&=0 \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.467 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y \sec \left (x \right )+\sin \left (x \right ) y^{\prime }&=0 \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
73.065 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {\mathrm e}^{x}-\sin \left (y\right )+y^{\prime } \cos \left (y\right )&=0 \end {array} \]
|
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✓ |
✓ |
1.004 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x^{2}+1\right ) y^{\prime }+y x&=0 \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.480 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{3}+x y^{2}+y+\left (x^{3}+x^{2} y+x \right ) y^{\prime }&=0 \end {array} \]
|
[_rational, [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
✓ |
✗ |
2.528 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 3 y-y^{\prime } x&=0 \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.411 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y-3 y^{\prime } x&=0 \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.467 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y \left (2 x^{2} y^{3}+3\right )+x \left (x^{2} y^{3}-1\right ) y^{\prime }&=0 \end {array} \]
|
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
67.737 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 y x +x^{2}+\left (x^{2}+y^{2}\right ) y^{\prime }&=0 \end {array} \]
|
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
65.504 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2}+\cos \left (x \right ) y+\left (y^{3}+\sin \left (x \right )\right ) y^{\prime }&=0 \end {array} \]
|
[_exact] |
✓ |
✓ |
✓ |
✗ |
0.860 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2}+y^{2}+x +y y^{\prime } x&=0 \end {array} \]
|
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
1.126 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x -2 y x +{\mathrm e}^{y}+\left (x \,{\mathrm e}^{y}+y-x^{2}\right ) y^{\prime }&=0 \end {array} \]
|
[_exact] |
✓ |
✓ |
✓ |
✗ |
1.326 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {\mathrm e}^{x} \sin \left (y\right )+{\mathrm e}^{-y}-\left (x \,{\mathrm e}^{-y}-{\mathrm e}^{x} \cos \left (y\right )\right ) y^{\prime }&=0 \end {array} \]
|
[_exact] |
✓ |
✓ |
✓ |
✗ |
1.355 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2}-y^{2}-y-\left (x^{2}-y^{2}-x \right ) y^{\prime }&=0 \end {array} \]
|
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
✓ |
✓ |
✓ |
24.516 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{2} x^{4}-y+\left (x^{2} y^{4}-x \right ) y^{\prime }&=0 \end {array} \]
|
[_rational] |
✓ |
✓ |
✓ |
✗ |
1.042 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y \left (2 x +y^{3}\right )-x \left (2 x -y^{3}\right ) y^{\prime }&=0 \end {array} \]
|
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✗ |
0.859 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \arctan \left (y x \right )+\frac {y x -2 x y^{2}}{1+y^{2} x^{2}}+\frac {\left (x^{2}-2 x^{2} y\right ) y^{\prime }}{1+y^{2} x^{2}}&=0 \end {array} \]
|
[_exact] |
✓ |
✓ |
✓ |
✗ |
3.628 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {\mathrm e}^{x} \left (x +1\right )+\left ({\mathrm e}^{y} y-x \,{\mathrm e}^{x}\right ) y^{\prime }&=0 \end {array} \]
|
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✓ |
✓ |
1.108 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {y x +1}{y}+\frac {\left (-x +2 y\right ) y^{\prime }}{y^{2}}&=0 \end {array} \]
|
[[_homogeneous, ‘class D‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
2.521 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{2}-3 y x -2 x^{2}+\left (y x -x^{2}\right ) y^{\prime }&=0 \end {array} \]
|
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
2.639 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (2 x +y+1\right ) y-x \left (x +2 y-1\right ) y^{\prime }&=0 \end {array} \]
|
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
332.702 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y \left (2 x -y-1\right )+x \left (2 y-x -1\right ) y^{\prime }&=0 \end {array} \]
|
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
280.596 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{2}+12 x^{2} y+\left (2 y x +4 x^{3}\right ) y^{\prime }&=0 \end {array} \]
|
[[_homogeneous, ‘class G‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
2.569 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x \left (2 x +3 y\right ) y^{\prime }+3 \left (x +y\right )^{2}&=0 \end {array} \]
|
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
3.081 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y-\left (x^{2}+y^{2}+x \right ) y^{\prime }&=0 \end {array} \]
|
[_rational] |
✓ |
✓ |
✓ |
✗ |
6.406 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 y x +\left (a +x^{2}+y^{2}\right ) y^{\prime }&=0 \end {array} \]
|
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
✓ |
✓ |
53.741 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 y x +x^{2}+b +\left (a +x^{2}+y^{2}\right ) y^{\prime }&=0 \end {array} \]
|
[_exact, _rational] |
✓ |
✓ |
✓ |
✗ |
0.579 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime } x +y&=x^{3} \end {array} \]
|
[_linear] |
✓ |
✓ |
✓ |
✓ |
10.886 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }+a y&=b \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.901 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime } x +y&=y^{2} \ln \left (x \right ) \end {array} \]
|
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
45.751 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }+2 x y&={\mathrm e}^{-y^{2}} \end {array} \]
|
[_linear] |
✓ |
✓ |
✓ |
✓ |
17.454 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} r^{\prime }&=\left (r+{\mathrm e}^{-\theta }\right ) \tan \left (\theta \right ) \end {array} \]
|
[_linear] |
✓ |
✓ |
✓ |
✓ |
6.735 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }-\frac {2 x y}{x^{2}+1}&=1 \end {array} \]
|
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.816 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }+y&=x y^{3} \end {array} \]
|
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.611 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (-x^{3}+1\right ) y^{\prime }-2 \left (x +1\right ) y&=y^{{5}/{2}} \end {array} \]
|
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
5.436 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \tan \left (\theta \right ) r^{\prime }-r&=\tan \left (\theta \right )^{2} \end {array} \]
|
[_linear] |
✓ |
✓ |
✓ |
✓ |
395.832 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 y+y^{\prime }&=3 \,{\mathrm e}^{-2 x} \end {array} \]
|
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
16.170 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 y+y^{\prime }&=\frac {3 \,{\mathrm e}^{-2 x}}{4} \end {array} \]
|
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
4.655 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 y+y^{\prime }&=\sin \left (x \right ) \end {array} \]
|
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
17.023 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }+\cos \left (x \right ) y&={\mathrm e}^{2 x} \end {array} \]
|
[_linear] |
✓ |
✓ |
✓ |
✓ |
6.016 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }+\cos \left (x \right ) y&=\frac {\sin \left (2 x \right )}{2} \end {array} \]
|
[_linear] |
✓ |
✓ |
✓ |
✓ |
7.361 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime } x +y&=x \sin \left (x \right ) \end {array} \]
|
[_linear] |
✓ |
✓ |
✓ |
✓ |
6.145 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} -y+y^{\prime } x&=x^{2} \sin \left (x \right ) \end {array} \]
|
[_linear] |
✓ |
✓ |
✓ |
✓ |
21.930 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime } x +x y^{2}-y&=0 \end {array} \]
|
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
39.711 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime } x -y \left (2 y \ln \left (x \right )-1\right )&=0 \end {array} \]
|
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
32.524 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} \left (-1+x \right ) y^{\prime }-y^{2}-x \left (x -2\right ) y&=0 \end {array} \]
|
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
41.740 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }-y&={\mathrm e}^{x}\\ y \left (0\right )&=1\\ \end {array} \]
|
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
4.580 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }+\frac {y}{x}&=\frac {y^{2}}{x}\\ y \left (-1\right )&=1\\ \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
106.240 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 \cos \left (x \right ) y^{\prime }&=\sin \left (x \right ) y-y^{3}\\ y \left (0\right )&=1\\ \end {array} \]
|
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
24.424 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x -\cos \left (y\right )\right ) y^{\prime }+\tan \left (y\right )&=0\\ y \left (1\right )&=\frac {\pi }{6}\\ \end {array} \]
|
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
✓ |
✓ |
39.088 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=x^{3}+\frac {2 y}{x}-\frac {y^{2}}{x} \end {array} \]
|
[_rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
6.750 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=2 \sec \left (x \right ) \tan \left (x \right )-\sin \left (x \right ) y^{2} \end {array} \]
|
[_Riccati] |
✓ |
✓ |
✓ |
✗ |
1.811 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\frac {1}{x^{2}}-\frac {y}{x}-y^{2} \end {array} \]
|
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
26.058 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=1+\frac {y}{x}-\frac {y^{2}}{x^{2}} \end {array} \]
|
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
43.717 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 y y^{\prime } x +\left (x +1\right ) y^{2}&={\mathrm e}^{x} \end {array} \]
|
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
18.352 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime } \cos \left (y\right )+\sin \left (y\right )&=x^{2} \end {array} \]
|
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✓ |
✓ |
15.677 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x +1\right ) y^{\prime }-1-y&=\left (x +1\right ) \sqrt {1+y} \end {array} \]
|
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
28.809 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {\mathrm e}^{y} \left (1+y^{\prime }\right )&={\mathrm e}^{x} \end {array} \]
|
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
268.141 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime } \sin \left (y\right )+\cos \left (y\right ) \sin \left (x \right )&=\sin \left (x \right ) \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
44.673 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x -y\right )^{2} y^{\prime }&=4 \end {array} \]
|
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
8.301 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} -y+y^{\prime } x&=\sqrt {x^{2}+y^{2}} \end {array} \]
|
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
46.284 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (3 x +2 y+1\right ) y^{\prime }+4 x +3 y+2&=0 \end {array} \]
|
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
55.454 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x^{2}-y^{2}\right ) y^{\prime }&=2 y x \end {array} \]
|
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
111.600 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y+\left (1+y^{2} {\mathrm e}^{2 x}\right ) y^{\prime }&=0 \end {array} \]
|
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
5.503 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y+y^{2}+x^{3} y^{\prime }&=0 \end {array} \]
|
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
38.489 |
|