Number of problems in this table is 498
Column notations: A is ODE degree. B is Program Number of solutions generated. C is CAS Number of solutions generated.
|
# |
ODE |
A |
B |
C |
CAS classification |
Solved? |
Verified? |
time (sec) |
|
\[ {}y y^{\prime } = x \left (1+y^{2}\right ) \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
1.931 |
|
|
\[ {}2 x y y^{\prime } = x^{2}+y^{2} \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.878 |
|
|
\[ {}x y^{2} y^{\prime } = x^{3}+y^{3} \] |
1 |
1 |
3 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.965 |
|
|
\[ {}x^{2} y^{\prime } = x y+y^{2} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.517 |
|
|
\[ {}x y y^{\prime } = x^{2}+3 y^{2} \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
2.107 |
|
|
\[ {}2 x y+x^{2} y^{\prime } = 5 y^{3} \] |
1 |
2 |
2 |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
0.892 |
|
|
\[ {}2 x y^{3}+y^{2} y^{\prime } = 6 x \] |
1 |
1 |
3 |
[_separable] |
✓ |
✓ |
2.352 |
|
|
\[ {}2 x y+x^{2} y^{\prime } = 5 y^{4} \] |
1 |
3 |
3 |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
1.335 |
|
|
\[ {}6 y+x y^{\prime } = 3 x y^{\frac {4}{3}} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
1.531 |
|
|
\[ {}y^{3} {\mathrm e}^{-2 x}+2 x y^{\prime } = 2 x y \] |
1 |
2 |
2 |
[_Bernoulli] |
✓ |
✓ |
1.37 |
|
|
\[ {}\sqrt {x^{4}+1}\, y^{2} \left (x y^{\prime }+y\right ) = x \] |
1 |
1 |
3 |
[_Bernoulli] |
✓ |
✓ |
10.416 |
|
|
\[ {}y^{3}+3 y^{2} y^{\prime } = {\mathrm e}^{-x} \] |
1 |
1 |
3 |
[[_1st_order, _with_linear_symmetries], _Bernoulli] |
✓ |
✓ |
1.696 |
|
|
\[ {}3 x y^{2} y^{\prime } = 3 x^{4}+y^{3} \] |
1 |
1 |
3 |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
1.539 |
|
|
\[ {}x y+y^{2}-x^{2} y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.591 |
|
|
\[ {}2 x y+x^{2} y^{\prime } = y^{2} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
0.942 |
|
|
\[ {}2 y+x y^{\prime } = 6 x^{2} \sqrt {y} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
1.185 |
|
|
\[ {}x^{2} y^{\prime } = x y+3 y^{2} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.075 |
|
|
\[ {}x^{3} y^{\prime } = x^{2} y-y^{3} \] |
1 |
2 |
2 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.033 |
|
|
\[ {}2 x^{2} y-x^{3} y^{\prime } = y^{3} \] |
1 |
2 |
2 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.299 |
|
|
\[ {}x y^{\prime } = 12 x^{4} y^{\frac {2}{3}}+6 y \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
1.676 |
|
|
\[ {}3 y+x^{3} y^{4}+3 x y^{\prime } = 0 \] |
1 |
1 |
3 |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
1.399 |
|
|
\[ {}y^{\prime } = -x y+x y^{3} \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
2.451 |
|
|
\[ {}y^{\prime } = \frac {-3 x^{2}-2 y^{2}}{4 x y} \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.454 |
|
|
\[ {}y^{\prime } = \cot \left (x \right ) \left (\sqrt {y}-y\right ) \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
7.763 |
|
|
\[ {}y^{\prime } = \frac {t \left (4-y\right ) y}{3} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.697 |
|
|
\[ {}y^{\prime } = \frac {t y \left (4-y\right )}{t +1} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.964 |
|
|
\[ {}y^{\prime } = \frac {x^{2}+3 y^{2}}{2 x y} \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.633 |
|
|
\[ {}y^{\prime } = \frac {x^{2}-3 y^{2}}{2 x y} \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.742 |
|
|
\[ {}y^{\prime } = \frac {3 y^{2}-x^{2}}{2 x y} \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.518 |
|
|
\[ {}y^{\prime } = t \left (3-y\right ) y \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.431 |
|
|
\[ {}y^{\prime } = y \left (3-t y\right ) \] |
1 |
1 |
1 |
[_Bernoulli] |
✓ |
✓ |
0.845 |
|
|
\[ {}y^{\prime } = -y \left (3-t y\right ) \] |
1 |
1 |
1 |
[_Bernoulli] |
✓ |
✓ |
0.822 |
|
|
\[ {}y^{\prime } = -\frac {y \left (y+1\right )}{x} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.308 |
|
|
\[ {}x y^{\prime }+y^{2}+y = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.447 |
|
|
\[ {}y^{\prime }+x \left (y^{2}+y\right ) = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.972 |
|
|
\[ {}y^{\prime } = 2 x y \left (1+y^{2}\right ) \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
10.752 |
|
|
\[ {}y^{\prime }-y = x y^{2} \] |
1 |
1 |
1 |
[_Bernoulli] |
✓ |
✓ |
0.945 |
|
|
\[ {}y+y^{\prime } = y^{2} \] |
1 |
1 |
1 |
[_quadrature] |
✓ |
✓ |
0.643 |
|
|
\[ {}7 x y^{\prime }-2 y = -\frac {x^{2}}{y^{6}} \] |
1 |
7 |
7 |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
2.708 |
|
|
\[ {}x^{2} y^{\prime }+2 y = 2 \,{\mathrm e}^{\frac {1}{x}} \sqrt {y} \] |
1 |
1 |
1 |
[_Bernoulli] |
✓ |
✓ |
0.326 |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime }+2 x y = \frac {1}{\left (x^{2}+1\right ) y} \] |
1 |
2 |
2 |
[_rational, _Bernoulli] |
✓ |
✓ |
0.718 |
|
|
\[ {}y^{\prime }-x y = x^{3} y^{3} \] |
1 |
2 |
2 |
[_Bernoulli] |
✓ |
✓ |
0.669 |
|
|
\[ {}y^{\prime }-\frac {\left (1+x \right ) y}{3 x} = y^{4} \] |
1 |
3 |
3 |
[_rational, _Bernoulli] |
✓ |
✓ |
1.426 |
|
|
\[ {}y^{\prime }-2 y = x y^{3} \] |
1 |
1 |
1 |
[_Bernoulli] |
✓ |
✓ |
0.796 |
|
|
\[ {}y^{\prime }-x y = x y^{\frac {3}{2}} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
6.904 |
|
|
\[ {}x y^{\prime }+y = x^{4} y^{4} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
0.791 |
|
|
\[ {}y^{\prime }-2 y = 2 \sqrt {y} \] |
1 |
1 |
1 |
[_quadrature] |
✓ |
✓ |
1.489 |
|
|
\[ {}y^{\prime }-4 y = \frac {48 x}{y^{2}} \] |
1 |
1 |
1 |
[_rational, _Bernoulli] |
✓ |
✓ |
0.758 |
|
|
\[ {}2 x y+x^{2} y^{\prime } = y^{3} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
0.911 |
|
|
\[ {}y^{\prime }-y = x \sqrt {y} \] |
1 |
1 |
1 |
[_Bernoulli] |
✓ |
✓ |
1.49 |
|
|
\[ {}y^{\prime } = \frac {y^{2}+2 x y}{x^{2}} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.347 |
|
|
\[ {}x y^{3} y^{\prime } = y^{4}+x^{4} \] |
1 |
1 |
4 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.851 |
|
|
\[ {}x y y^{\prime } = x^{2}+2 y^{2} \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.96 |
|
|
\[ {}y^{\prime } = \frac {x y+y^{2}}{x^{2}} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.893 |
|
|
\[ {}y^{\prime } = \frac {x^{3}+y^{3}}{x y^{2}} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.781 |
|
|
\[ {}x y y^{\prime }+x^{2}+y^{2} = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
2.448 |
|
|
\[ {}x y y^{\prime } = 3 x^{2}+4 y^{2} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
2.984 |
|
|
\[ {}3 x y^{2} y^{\prime } = x +y^{3} \] |
1 |
1 |
3 |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
1.648 |
|
|
\[ {}x y y^{\prime } = 3 x^{6}+6 y^{2} \] |
1 |
1 |
2 |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
1.386 |
|
|
\[ {}\left (y^{3}-1\right ) {\mathrm e}^{x}+3 y^{2} \left (1+{\mathrm e}^{x}\right ) y^{\prime } = 0 \] |
1 |
1 |
3 |
[_separable] |
✓ |
✓ |
5.071 |
|
|
\[ {}{\mathrm e}^{x} \left (x^{4} y^{2}+4 x^{3} y^{2}+1\right )+\left (2 x^{4} y \,{\mathrm e}^{x}+2 y\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[_exact, _Bernoulli] |
✓ |
✓ |
2.301 |
|
|
\[ {}x^{2}+y^{2}+2 x y y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
2.431 |
|
|
\[ {}3 x^{2} y^{2}+2 y+2 x y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
1.291 |
|
|
\[ {}t^{2} \left (1+y^{2}\right )+2 y y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
4.361 |
|
|
\[ {}2 t y y^{\prime } = 3 y^{2}-t^{2} \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
2.518 |
|
|
\[ {}y^{\prime } = \frac {\left (1+\cos \left (4 t \right )\right ) y}{4}-\frac {\left (1-\cos \left (4 t \right )\right ) y^{2}}{800} \] |
1 |
1 |
1 |
[_Bernoulli] |
✓ |
✓ |
14.143 |
|
|
\[ {}x y^{2}+x +\left (y-x^{2} y\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
6.561 |
|
|
\[ {}x y^{2}+x +\left (x^{2} y-y\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
4.193 |
|
|
\[ {}x y^{\prime }+y = y^{2} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
3.193 |
|
|
\[ {}y^{2}+y y^{\prime }+x^{2} y y^{\prime }-1 = 0 \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
3.517 |
|
|
\[ {}x^{2}+y^{2} = x y y^{\prime } \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.809 |
|
|
\[ {}x^{2}+y^{2} = 2 x y y^{\prime } \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
2.511 |
|
|
\[ {}x^{2} y+y^{2}+x^{3} y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
1.413 |
|
|
\[ {}x y^{3}-1+x^{2} y^{2} y^{\prime } = 0 \] |
1 |
1 |
3 |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
2.648 |
|
|
\[ {}y \left (y-x^{2}\right )+x^{3} y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
1.716 |
|
|
\[ {}{\mathrm e}^{x} y^{\prime } = 2 x y^{2}+{\mathrm e}^{x} y \] |
1 |
1 |
1 |
[_Bernoulli] |
✓ |
✓ |
1.677 |
|
|
\[ {}2 x^{2} y y^{\prime }+x^{4} {\mathrm e}^{x}-2 x y^{2} = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class D‘], _Bernoulli] |
✓ |
✓ |
2.105 |
|
|
\[ {}y \left (1-x^{4} y^{2}\right )+x y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
1.967 |
|
|
\[ {}3 y^{2} y^{\prime }-x y^{3} = {\mathrm e}^{\frac {x^{2}}{2}} \cos \left (x \right ) \] |
1 |
1 |
3 |
[_Bernoulli] |
✓ |
✓ |
3.883 |
|
|
\[ {}y^{3} y^{\prime }+y^{4} x = x \,{\mathrm e}^{-x^{2}} \] |
1 |
1 |
4 |
[_Bernoulli] |
✓ |
✓ |
2.7 |
|
|
\[ {}x y y^{\prime } = x^{2}-y^{2} \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
2.55 |
|
|
\[ {}y^{\prime }-x y = \sqrt {y}\, x \,{\mathrm e}^{x^{2}} \] |
1 |
1 |
1 |
[_Bernoulli] |
✓ |
✓ |
3.466 |
|
|
\[ {}t x^{\prime }+x \left (1-x^{2} t^{4}\right ) = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
2.024 |
|
|
\[ {}x^{2} y^{\prime }+y^{2} = x y \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.638 |
|
|
\[ {}y^{\prime }-x y = \frac {x}{y} \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
2.956 |
|
|
\[ {}x y^{\prime }+y = y^{2} x^{2} \cos \left (x \right ) \] |
1 |
1 |
1 |
[_Bernoulli] |
✓ |
✓ |
3.555 |
|
|
\[ {}r^{\prime }+\left (r-\frac {1}{r}\right ) \theta = 0 \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
4.374 |
|
|
\[ {}2 y+x y^{\prime } = 3 x^{3} y^{\frac {4}{3}} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
3.454 |
|
|
\[ {}3 y^{\prime }+\frac {2 y}{1+x} = \frac {x}{y^{2}} \] |
1 |
1 |
3 |
[_rational, _Bernoulli] |
✓ |
✓ |
3.15 |
|
|
\[ {}y^{\prime }+y \cos \left (x \right ) = y^{3} \sin \left (x \right ) \] |
1 |
2 |
2 |
[_Bernoulli] |
✓ |
✓ |
5.372 |
|
|
\[ {}y^{\prime }+y = y^{2} {\mathrm e}^{-t} \] |
1 |
1 |
1 |
[[_1st_order, _with_linear_symmetries], _Bernoulli] |
✓ |
✓ |
1.988 |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime }+x y = x \left (-x^{2}+1\right ) \sqrt {y} \] |
1 |
1 |
1 |
[_rational, _Bernoulli] |
✓ |
✓ |
19.409 |
|
|
\[ {}y-x y^{\prime } = 2 y^{2}+2 y^{\prime } \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
4.532 |
|
|
\[ {}2 x^{3}-y^{3}-3 x +3 x y^{2} y^{\prime } = 0 \] |
1 |
1 |
3 |
[_rational, _Bernoulli] |
✓ |
✓ |
2.457 |
|
|
\[ {}2 x y^{\prime }-y+\frac {x^{2}}{y^{2}} = 0 \] |
1 |
1 |
3 |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
2.127 |
|
|
\[ {}x y^{\prime }+y \left (1+y^{2}\right ) = 0 \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
5.533 |
|
|
\[ {}x y^{\prime }-5 y-x \sqrt {y} = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
2.575 |
|
|
\[ {}x y-y^{2}-x^{2} y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
2.412 |
|
|
\[ {}x y^{\prime }-2 y-2 x^{4} y^{3} = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
1.782 |
|
|
\[ {}x y^{\prime }+y = x^{3} y^{6} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
2.024 |
|
|
\[ {}x^{\prime } = x+x^{2} {\mathrm e}^{\theta } \] |
1 |
1 |
1 |
[[_1st_order, _with_linear_symmetries], _Bernoulli] |
✓ |
✓ |
2.016 |
|
|
\[ {}x^{2}+y^{2} = 2 x y y^{\prime } \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
3.538 |
|
|
\[ {}2 \left (x^{2}+1\right ) y^{\prime } = \left (2 y^{2}-1\right ) x y \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
12.092 |
|
|
\[ {}y^{\prime } = -\frac {2 x^{2}+y^{2}+x}{x y} \] |
1 |
1 |
2 |
[_rational, _Bernoulli] |
✓ |
✓ |
0.653 |
|
|
\[ {}x y^{\prime }+y-\frac {y^{2}}{x^{\frac {3}{2}}} = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
1.586 |
|
|
\[ {}y^{\prime } = \frac {\cos \left (x \right )-2 x y^{2}}{2 x^{2} y} \] |
1 |
1 |
1 |
[_Bernoulli] |
✓ |
✓ |
33.947 |
|
|
\[ {}y^{\prime }-\frac {y}{x} = \frac {4 x^{2} \cos \left (x \right )}{y} \] |
1 |
1 |
2 |
[[_homogeneous, ‘class D‘], _Bernoulli] |
✓ |
✓ |
2.286 |
|
|
\[ {}y^{\prime }+\frac {y \tan \left (x \right )}{2} = 2 y^{3} \sin \left (x \right ) \] |
1 |
2 |
2 |
[_Bernoulli] |
✓ |
✓ |
8.359 |
|
|
\[ {}y^{\prime }-\frac {3 y}{2 x} = 6 y^{\frac {1}{3}} x^{2} \ln \left (x \right ) \] |
1 |
1 |
1 |
[_Bernoulli] |
✓ |
✓ |
2.007 |
|
|
\[ {}y^{\prime }+\frac {2 y}{x} = 6 \sqrt {x^{2}+1}\, \sqrt {y} \] |
1 |
1 |
1 |
[_Bernoulli] |
✓ |
✓ |
1.845 |
|
|
\[ {}y^{\prime }+\frac {2 y}{x} = 6 x^{4} y^{2} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
0.689 |
|
|
\[ {}2 x \left (y^{\prime }+y^{3} x^{2}\right )+y = 0 \] |
1 |
2 |
2 |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
0.687 |
|
|
\[ {}\left (x -a \right ) \left (x -b \right ) \left (y^{\prime }-\sqrt {y}\right ) = 2 \left (-a +b \right ) y \] |
1 |
1 |
1 |
[_rational, _Bernoulli] |
✓ |
✓ |
2.076 |
|
|
\[ {}y^{\prime }+\frac {6 y}{x} = \frac {3 y^{\frac {2}{3}} \cos \left (x \right )}{x} \] |
1 |
1 |
1 |
[_Bernoulli] |
✓ |
✓ |
82.877 |
|
|
\[ {}y^{\prime }+4 x y = 4 x^{3} \sqrt {y} \] |
1 |
1 |
1 |
[_Bernoulli] |
✓ |
✓ |
1.561 |
|
|
\[ {}y^{\prime }-\frac {y}{2 x \ln \left (x \right )} = 2 x y^{3} \] |
1 |
2 |
2 |
[_Bernoulli] |
✓ |
✓ |
0.931 |
|
|
\[ {}y^{\prime }-\frac {y}{\left (\pi -1\right ) x} = \frac {3 x y^{\pi }}{1-\pi } \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
0.887 |
|
|
\[ {}2 y^{\prime }+\cot \left (x \right ) y = \frac {8 \cos \left (x \right )^{3}}{y} \] |
1 |
1 |
2 |
[_Bernoulli] |
✓ |
✓ |
14.635 |
|
|
\[ {}\left (1-\sqrt {3}\right ) y^{\prime }+y \sec \left (x \right ) = y^{\sqrt {3}} \sec \left (x \right ) \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
187.417 |
|
|
\[ {}y^{\prime }+\frac {2 x y}{x^{2}+1} = x y^{2} \] |
1 |
1 |
1 |
[_rational, _Bernoulli] |
✓ |
✓ |
1.042 |
|
|
\[ {}y^{\prime }+\cot \left (x \right ) y = y^{3} \sin \left (x \right )^{3} \] |
1 |
1 |
1 |
[_Bernoulli] |
✓ |
✓ |
1.64 |
|
|
\[ {}x^{3}+y^{3}-x y^{2} y^{\prime } = 0 \] |
1 |
1 |
3 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.392 |
|
|
\[ {}x y^{\prime } = 2 y \left (y-1\right ) \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
3.056 |
|
|
\[ {}x y y^{\prime } = 2 x^{2}-y^{2} \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.446 |
|
|
\[ {}x^{2}-y^{2}+x y y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.035 |
|
|
\[ {}x^{2} y^{\prime }-2 x y-2 y^{2} = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
0.959 |
|
|
\[ {}2+y^{2}+2 x +2 y y^{\prime } = 0 \] |
1 |
1 |
2 |
[_rational, _Bernoulli] |
✓ |
✓ |
1.158 |
|
|
\[ {}3 x y^{\prime }-3 x y^{4} \ln \left (x \right )-y = 0 \] |
1 |
3 |
3 |
[_Bernoulli] |
✓ |
✓ |
1.372 |
|
|
\[ {}y \left (6 y^{2}-x -1\right )+2 x y^{\prime } = 0 \] |
1 |
2 |
2 |
[_rational, _Bernoulli] |
✓ |
✓ |
0.606 |
|
|
\[ {}\left (1+x \right ) \left (y^{\prime }+y^{2}\right )-y = 0 \] |
1 |
1 |
1 |
[[_1st_order, _with_linear_symmetries], _rational, _Bernoulli] |
✓ |
✓ |
0.238 |
|
|
\[ {}x y y^{\prime }+y^{2}-\sin \left (x \right ) = 0 \] |
1 |
2 |
2 |
[_Bernoulli] |
✓ |
✓ |
0.791 |
|
|
\[ {}2 x^{3}-y^{4}+x y^{3} y^{\prime } = 0 \] |
1 |
4 |
4 |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
0.724 |
|
|
\[ {}y^{\prime }-y \tan \left (x \right )+y^{2} \cos \left (x \right ) = 0 \] |
1 |
1 |
1 |
[_Bernoulli] |
✓ |
✓ |
0.339 |
|
|
\[ {}x y^{2} \left (x y^{\prime }+y\right ) = 1 \] |
1 |
1 |
3 |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
2.256 |
|
|
\[ {}1+\sin \left (2 x \right ) y^{2}-2 y \cos \left (x \right )^{2} y^{\prime } = 0 \] |
1 |
1 |
2 |
[_exact, _Bernoulli] |
✓ |
✓ |
11.411 |
|
|
\[ {}y^{\prime } = x y \left (3+y\right ) \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.513 |
|
|
\[ {}y^{\prime } = \left (a +b y \cos \left (k x \right )\right ) y \] |
1 |
1 |
1 |
[_Bernoulli] |
✓ |
✓ |
1.233 |
|
|
\[ {}y^{\prime }+y \left (1-x y^{2}\right ) = 0 \] |
1 |
2 |
2 |
[_Bernoulli] |
✓ |
✓ |
0.682 |
|
|
\[ {}y^{\prime }+2 x y \left (1+a x y^{2}\right ) = 0 \] |
1 |
2 |
2 |
[_Bernoulli] |
✓ |
✓ |
0.995 |
|
|
\[ {}y^{\prime }+\left (\tan \left (x \right )+y^{2} \sec \left (x \right )\right ) y = 0 \] |
1 |
2 |
2 |
[_Bernoulli] |
✓ |
✓ |
1.552 |
|
|
\[ {}y^{\prime } = f \left (x \right ) y+g \left (x \right ) y^{k} \] |
1 |
1 |
1 |
[_Bernoulli] |
✓ |
✓ |
0.525 |
|
|
\[ {}y^{\prime }+2 y \left (1-x \sqrt {y}\right ) = 0 \] |
1 |
1 |
1 |
[_Bernoulli] |
✓ |
✓ |
1.003 |
|
|
\[ {}x y^{\prime }+\left (1-x y\right ) y = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
0.727 |
|
|
\[ {}x y^{\prime } = \left (1-x y\right ) y \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
0.707 |
|
|
\[ {}x y^{\prime } = \left (1+x y\right ) y \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
0.716 |
|
|
\[ {}x y^{\prime } = a \,x^{3} \left (1-x y\right ) y \] |
1 |
1 |
1 |
[_Bernoulli] |
✓ |
✓ |
1.191 |
|
|
\[ {}x y^{\prime } = y \left (1+2 x y\right ) \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
0.711 |
|
|
\[ {}x y^{\prime }+\left (a +b \,x^{n} y\right ) y = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
0.899 |
|
|
\[ {}x y^{\prime }+\left (1-a y \ln \left (x \right )\right ) y = 0 \] |
1 |
1 |
1 |
[_Bernoulli] |
✓ |
✓ |
0.99 |
|
|
\[ {}x y^{\prime } = y \left (1+y^{2}\right ) \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
1.431 |
|
|
\[ {}x y^{\prime }+y \left (1-x y^{2}\right ) = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
0.803 |
|
|
\[ {}x y^{\prime }+y = a \left (x^{2}+1\right ) y^{3} \] |
1 |
1 |
2 |
[_rational, _Bernoulli] |
✓ |
✓ |
0.915 |
|
|
\[ {}x y^{\prime } = a y+b \left (x^{2}+1\right ) y^{3} \] |
1 |
2 |
2 |
[_rational, _Bernoulli] |
✓ |
✓ |
1.003 |
|
|
\[ {}2 y+x y^{\prime } = a \,x^{2 k} y^{k} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
1.387 |
|
|
\[ {}x y^{\prime } = 4 y-4 \sqrt {y} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.38 |
|
|
\[ {}\left (1+x \right ) y^{\prime } = a y+b x y^{2} \] |
1 |
1 |
1 |
[_rational, _Bernoulli] |
✓ |
✓ |
0.895 |
|
|
\[ {}\left (1+x \right ) y^{\prime }+y+\left (1+x \right )^{4} y^{3} = 0 \] |
1 |
2 |
2 |
[[_1st_order, _with_linear_symmetries], _rational, _Bernoulli] |
✓ |
✓ |
0.829 |
|
|
\[ {}\left (1+x \right ) y^{\prime } = \left (1-x y^{3}\right ) y \] |
1 |
3 |
3 |
[_rational, _Bernoulli] |
✓ |
✓ |
1.029 |
|
|
\[ {}\left (x +a \right ) y^{\prime } = y \left (1-a y\right ) \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.45 |
|
|
\[ {}\left (a -x \right ) y^{\prime } = y+\left (c x +b \right ) y^{3} \] |
1 |
2 |
2 |
[_rational, _Bernoulli] |
✓ |
✓ |
0.899 |
|
|
\[ {}2 x y^{\prime } = y \left (1+y^{2}\right ) \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
1.427 |
|
|
\[ {}2 x y^{\prime }+y \left (1+y^{2}\right ) = 0 \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
1.734 |
|
|
\[ {}2 x y^{\prime } = \left (1+x -6 y^{2}\right ) y \] |
1 |
2 |
2 |
[_rational, _Bernoulli] |
✓ |
✓ |
0.672 |
|
|
\[ {}2 \left (1+x \right ) y^{\prime }+2 y+\left (1+x \right )^{4} y^{3} = 0 \] |
1 |
2 |
2 |
[[_1st_order, _with_linear_symmetries], _rational, _Bernoulli] |
✓ |
✓ |
0.63 |
|
|
\[ {}3 x y^{\prime } = \left (2+x y^{3}\right ) y \] |
1 |
3 |
3 |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
0.784 |
|
|
\[ {}3 x y^{\prime } = \left (1+3 x y^{3} \ln \left (x \right )\right ) y \] |
1 |
1 |
3 |
[_Bernoulli] |
✓ |
✓ |
1.441 |
|
|
\[ {}x^{2} y^{\prime } = \left (a y+x \right ) y \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
0.651 |
|
|
\[ {}x^{2} y^{\prime } = \left (x a +b y\right ) y \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
0.786 |
|
|
\[ {}x^{2} y^{\prime }+\left (x^{2}+y^{2}-x \right ) y = 0 \] |
1 |
2 |
2 |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
0.843 |
|
|
\[ {}x^{2} y^{\prime } = 2 y \left (x -y^{2}\right ) \] |
1 |
2 |
2 |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
0.528 |
|
|
\[ {}x^{2} y^{\prime } = \left (x a +b y^{3}\right ) y \] |
1 |
3 |
3 |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
1.39 |
|
|
\[ {}x^{2} y^{\prime }+x y+\sqrt {y} = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
0.869 |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime }+x y \left (1-y\right ) = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.104 |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime } = x y \left (1+a y\right ) \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.698 |
|
|
\[ {}\left (-x^{2}+4\right ) y^{\prime }+4 y = \left (2+x \right ) y^{2} \] |
1 |
1 |
1 |
[_rational, _Bernoulli] |
✓ |
✓ |
0.651 |
|
|
\[ {}\left (a^{2}+x^{2}\right ) y^{\prime }+y \left (x -y\right ) = 0 \] |
1 |
1 |
1 |
[_rational, _Bernoulli] |
✓ |
✓ |
0.622 |
|
|
\[ {}\left (a^{2}+x^{2}\right ) y^{\prime }+x y+b x y^{2} = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.346 |
|
|
\[ {}x \left (x +a \right ) y^{\prime } = \left (b +c y\right ) y \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
3.375 |
|
|
\[ {}x^{3} y^{\prime } = y \left (y+x^{2}\right ) \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
0.691 |
|
|
\[ {}x^{3} y^{\prime } = \left (2 x^{2}+y^{2}\right ) y \] |
1 |
2 |
2 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
0.748 |
|
|
\[ {}x^{2} \left (1-x \right ) y^{\prime } = \left (2-x \right ) x y-y^{2} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
0.813 |
|
|
\[ {}2 x^{3} y^{\prime } = \left (x^{2}-y^{2}\right ) y \] |
1 |
2 |
2 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
0.756 |
|
|
\[ {}2 x^{3} y^{\prime } = \left (3 x^{2}+a y^{2}\right ) y \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
0.921 |
|
|
\[ {}6 x^{3} y^{\prime } = 4 x^{2} y+\left (1-3 x \right ) y^{4} \] |
1 |
3 |
3 |
[_rational, _Bernoulli] |
✓ |
✓ |
0.968 |
|
|
\[ {}x^{4} y^{\prime } = \left (x^{3}+y\right ) y \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
0.574 |
|
|
\[ {}x^{2} \left (-x^{2}+1\right ) y^{\prime } = \left (x -3 x^{3} y\right ) y \] |
1 |
1 |
1 |
[_rational, _Bernoulli] |
✓ |
✓ |
0.868 |
|
|
\[ {}y^{\prime } \left (a +\cos \left (\frac {x}{2}\right )^{2}\right ) = y \tan \left (\frac {x}{2}\right ) \left (1+a +\cos \left (\frac {x}{2}\right )^{2}-y\right ) \] |
1 |
1 |
1 |
[_Bernoulli] |
✓ |
✓ |
10.263 |
|
|
\[ {}y y^{\prime }+4 \left (1+x \right ) x +y^{2} = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
1.223 |
|
|
\[ {}y y^{\prime } = x a +b y^{2} \] |
1 |
1 |
2 |
[_rational, _Bernoulli] |
✓ |
✓ |
0.854 |
|
|
\[ {}y y^{\prime } = b \cos \left (x +c \right )+a y^{2} \] |
1 |
1 |
2 |
[_Bernoulli] |
✓ |
✓ |
1.502 |
|
|
\[ {}y y^{\prime } = x a +b x y^{2} \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
1.19 |
|
|
\[ {}y y^{\prime } = \csc \left (x \right )^{2}-y^{2} \cot \left (x \right ) \] |
1 |
1 |
2 |
[_Bernoulli] |
✓ |
✓ |
21.66 |
|
|
\[ {}x^{2}+y^{2}+2 x +2 y y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
1.248 |
|
|
\[ {}2 y y^{\prime } = x y^{2}+x^{3} \] |
1 |
1 |
2 |
[_rational, _Bernoulli] |
✓ |
✓ |
0.678 |
|
|
\[ {}x y y^{\prime }+1+y^{2} = 0 \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
1.368 |
|
|
\[ {}x y y^{\prime } = x +y^{2} \] |
1 |
1 |
2 |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
0.72 |
|
|
\[ {}x y y^{\prime }+x^{2}+y^{2} = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
0.955 |
|
|
\[ {}x y y^{\prime }+x^{4}-y^{2} = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
0.75 |
|
|
\[ {}x y y^{\prime } = a \,x^{3} \cos \left (x \right )+y^{2} \] |
1 |
1 |
2 |
[[_homogeneous, ‘class D‘], _Bernoulli] |
✓ |
✓ |
0.971 |
|
|
\[ {}x y y^{\prime } = a +b y^{2} \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
1.295 |
|
|
\[ {}x y y^{\prime } = a \,x^{n}+b y^{2} \] |
1 |
1 |
2 |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
1.063 |
|
|
\[ {}x y y^{\prime } = \left (x^{2}+1\right ) \left (1-y^{2}\right ) \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
12.514 |
|
|
\[ {}2 x y y^{\prime }+1-2 x^{3}-y^{2} = 0 \] |
1 |
1 |
2 |
[_rational, _Bernoulli] |
✓ |
✓ |
0.704 |
|
|
\[ {}2 x y y^{\prime }+a +y^{2} = 0 \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
1.216 |
|
|
\[ {}2 x y y^{\prime } = x a +y^{2} \] |
1 |
1 |
2 |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
0.686 |
|
|
\[ {}x^{2}+y^{2}+2 x y y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
1.293 |
|
|
\[ {}2 x y y^{\prime } = x^{2}+y^{2} \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
0.924 |
|
|
\[ {}2 x y y^{\prime } = 4 x^{2} \left (2 x +1\right )+y^{2} \] |
1 |
1 |
2 |
[_rational, _Bernoulli] |
✓ |
✓ |
0.618 |
|
|
\[ {}2 x y y^{\prime }+x^{2} \left (a \,x^{3}+1\right ) = 6 y^{2} \] |
1 |
1 |
2 |
[_rational, _Bernoulli] |
✓ |
✓ |
0.755 |
|
|
\[ {}2 \left (1+x \right ) y y^{\prime }+2 x -3 x^{2}+y^{2} = 0 \] |
1 |
1 |
2 |
[_exact, _rational, _Bernoulli] |
✓ |
✓ |
0.92 |
|
|
\[ {}a x y y^{\prime } = x^{2}+y^{2} \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.403 |
|
|
\[ {}a x y y^{\prime }+x^{2}-y^{2} = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.078 |
|
|
\[ {}\left (x^{2}+1\right ) y y^{\prime }+x \left (1-y^{2}\right ) = 0 \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
3.071 |
|
|
\[ {}\left (-x^{2}+1\right ) y y^{\prime }+2 x^{2}+x y^{2} = 0 \] |
1 |
1 |
2 |
[_rational, _Bernoulli] |
✓ |
✓ |
0.832 |
|
|
\[ {}2 x^{2} y y^{\prime } = x^{2} \left (2 x +1\right )-y^{2} \] |
1 |
1 |
2 |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
1.65 |
|
|
\[ {}2 \left (1+x \right ) x y y^{\prime } = 1+y^{2} \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
1.658 |
|
|
\[ {}3 x^{2} y y^{\prime }+1+2 x y^{2} = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
0.836 |
|
|
\[ {}2 x^{3} y y^{\prime }+a +3 x^{2} y^{2} = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class G‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
0.829 |
|
|
\[ {}x y \left (b \,x^{2}+a \right ) y^{\prime } = A +B y^{2} \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
3.143 |
|
|
\[ {}3 x^{4} y y^{\prime } = 1-2 x^{3} y^{2} \] |
1 |
1 |
2 |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
0.97 |
|
|
\[ {}3 y^{2} y^{\prime } = 1+x +a y^{3} \] |
1 |
1 |
3 |
[_rational, _Bernoulli] |
✓ |
✓ |
1.469 |
|
|
\[ {}3 x y^{2} y^{\prime } = 2 x -y^{3} \] |
1 |
1 |
3 |
[[_homogeneous, ‘class G‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
1.135 |
|
|
\[ {}6 x y^{2} y^{\prime }+x +2 y^{3} = 0 \] |
1 |
1 |
3 |
[[_homogeneous, ‘class G‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
0.997 |
|
|
\[ {}y^{\prime }+x y = x^{3} y^{3} \] |
1 |
2 |
2 |
[_Bernoulli] |
✓ |
✓ |
0.822 |
|
|
\[ {}y+x y^{2}-x y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
0.744 |
|
|
\[ {}x y \left (x^{2}+1\right ) y^{\prime }-1-y^{2} = 0 \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
6.803 |
|
|
\[ {}\left (-x^{2}+1\right ) z^{\prime }-x z = a x z^{2} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
3.239 |
|
|
\[ {}3 z^{2} z^{\prime }-a z^{3} = 1+x \] |
1 |
1 |
3 |
[_rational, _Bernoulli] |
✓ |
✓ |
1.86 |
|
|
\[ {}z^{\prime }+2 x z = 2 a \,x^{3} z^{3} \] |
1 |
2 |
2 |
[_Bernoulli] |
✓ |
✓ |
0.997 |
|
|
\[ {}z^{\prime }+z \cos \left (x \right ) = z^{n} \sin \left (2 x \right ) \] |
1 |
1 |
1 |
[_Bernoulli] |
✓ |
✓ |
32.015 |
|
|
\[ {}x y^{\prime }+y = y^{2} \ln \left (x \right ) \] |
1 |
1 |
1 |
[_Bernoulli] |
✓ |
✓ |
1.004 |
|
|
\[ {}y = x y^{\prime }+x \sqrt {1+{y^{\prime }}^{2}} \] |
1 |
2 |
2 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
5.283 |
|
|
\[ {}x^{2}+y^{2} = 2 x y y^{\prime } \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.574 |
|
|
\[ {}x y-y^{2}-x^{2} y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.472 |
|
|
\[ {}x y^{\prime }+y = y^{2} \ln \left (x \right ) \] |
1 |
1 |
1 |
[_Bernoulli] |
✓ |
✓ |
1.133 |
|
|
\[ {}y+y^{\prime } = x y^{3} \] |
1 |
2 |
2 |
[_Bernoulli] |
✓ |
✓ |
0.512 |
|
|
\[ {}\left (-x^{3}+1\right ) y^{\prime }-2 \left (1+x \right ) y = y^{\frac {5}{2}} \] |
1 |
3 |
1 |
[_rational, _Bernoulli] |
✓ |
✓ |
19.07 |
|
|
\[ {}x y^{\prime }+x y^{2}-y = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
0.94 |
|
|
\[ {}x y^{\prime }-y \left (2 y \ln \left (x \right )-1\right ) = 0 \] |
1 |
1 |
1 |
[_Bernoulli] |
✓ |
✓ |
1.199 |
|
|
\[ {}x^{2} \left (-1+x \right ) y^{\prime }-y^{2}-x \left (-2+x \right ) y = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
1.212 |
|
|
\[ {}y^{\prime }+\frac {y}{x} = \frac {y^{2}}{x} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.67 |
|
|
\[ {}2 \cos \left (x \right ) y^{\prime } = y \sin \left (x \right )-y^{3} \] |
1 |
1 |
1 |
[_Bernoulli] |
✓ |
✓ |
7.613 |
|
|
\[ {}2 x y y^{\prime }+\left (1+x \right ) y^{2} = {\mathrm e}^{x} \] |
1 |
1 |
2 |
[_Bernoulli] |
✓ |
✓ |
1.655 |
|
|
\[ {}x^{2} y+y^{2}+x^{3} y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
0.845 |
|
|
\[ {}x y^{\prime }+y = x^{2} \left (1+{\mathrm e}^{x}\right ) y^{2} \] |
1 |
1 |
1 |
[_Bernoulli] |
✓ |
✓ |
1.166 |
|
|
\[ {}y^{\prime }+8 x^{3} y^{3}+2 x y = 0 \] |
1 |
2 |
2 |
[_Bernoulli] |
✓ |
✓ |
0.96 |
|
|
\[ {}x^{3} y^{\prime }-y^{2}-x^{2} y = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
1.043 |
|
|
\[ {}\left (x^{2}-1\right ) y^{\prime }+x y-3 x y^{2} = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
6.486 |
|
|
\[ {}x y y^{\prime }+x^{2}+y^{2} = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
2.011 |
|
|
\[ {}2 x y y^{\prime }+3 x^{2}-y^{2} = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.442 |
|
|
\[ {}3 x y^{2} y^{\prime }+y^{3}-2 x = 0 \] |
1 |
1 |
3 |
[[_homogeneous, ‘class G‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
1.956 |
|
|
\[ {}x y \left (x^{2}+1\right ) y^{\prime } = 1+y^{2} \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
2.289 |
|
|
\[ {}y+y^{\prime } = x y^{\frac {2}{3}} \] |
1 |
1 |
1 |
[_Bernoulli] |
✓ |
✓ |
1.57 |
|
|
\[ {}y^{\prime }+\frac {y}{x} = 2 x^{\frac {3}{2}} \sqrt {y} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
3.696 |
|
|
\[ {}3 x y^{2} y^{\prime }+3 y^{3} = 1 \] |
1 |
1 |
3 |
[_separable] |
✓ |
✓ |
1.345 |
|
|
\[ {}x^{2} y^{\prime }+y^{2}-x y = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.135 |
|
|
\[ {}3 x^{3} y^{2} y^{\prime }-y^{3} x^{2} = 1 \] |
1 |
1 |
3 |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
1.158 |
|
|
\[ {}y^{\prime }-2 y-y^{2} {\mathrm e}^{3 x} = 0 \] |
1 |
1 |
1 |
[[_1st_order, _with_linear_symmetries], _Bernoulli] |
✓ |
✓ |
0.631 |
|
|
\[ {}y^{\prime }+x y = \frac {x}{y} \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
1.196 |
|
|
\[ {}x v^{\prime } = \frac {1-4 v^{2}}{3 v} \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
2.539 |
|
|
\[ {}x +x y^{2}+{\mathrm e}^{x^{2}} y y^{\prime } = 0 \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
1.51 |
|
|
\[ {}y^{\prime }+2 y = \frac {x}{y^{2}} \] |
1 |
1 |
3 |
[_rational, _Bernoulli] |
✓ |
✓ |
1.266 |
|
|
\[ {}y^{\prime }+x y = x y^{2} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.536 |
|
|
\[ {}3 x y^{\prime }+y+x^{2} y^{4} = 0 \] |
1 |
3 |
3 |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
0.913 |
|
|
\[ {}y^{\prime }+\frac {y}{x} = y^{3} \] |
1 |
1 |
2 |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
1.257 |
|
|
\[ {}3 y+x y^{\prime } = x^{2} y^{2} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
0.606 |
|
|
\[ {}y+y^{\prime } = x y^{3} \] |
1 |
2 |
2 |
[_Bernoulli] |
✓ |
✓ |
0.39 |
|
|
\[ {}y+y^{\prime } = y^{4} {\mathrm e}^{x} \] |
1 |
3 |
3 |
[[_1st_order, _with_linear_symmetries], _Bernoulli] |
✓ |
✓ |
3.585 |
|
|
\[ {}2 y^{\prime }+y = y^{3} \left (-1+x \right ) \] |
1 |
2 |
2 |
[_Bernoulli] |
✓ |
✓ |
0.32 |
|
|
\[ {}y^{\prime }-2 y \tan \left (x \right ) = y^{2} \tan \left (x \right )^{2} \] |
1 |
1 |
1 |
[_Bernoulli] |
✓ |
✓ |
0.323 |
|
|
\[ {}y^{\prime }+y \tan \left (x \right ) = y^{3} \sec \left (x \right )^{4} \] |
1 |
2 |
2 |
[_Bernoulli] |
✓ |
✓ |
2.615 |
|
|
\[ {}y^{\prime }-\cot \left (x \right ) y = y^{2} \sec \left (x \right )^{2} \] |
1 |
1 |
1 |
[_Bernoulli] |
✓ |
✓ |
2.363 |
|
|
\[ {}2 x y y^{\prime } = x^{2}-y^{2} \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
1.6 |
|
|
\[ {}x \left (1+y^{2}\right )-\left (x^{2}+1\right ) y y^{\prime } = 0 \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
2.521 |
|
|
\[ {}\frac {r \tan \left (\theta \right ) r^{\prime }}{a^{2}-r^{2}} = 1 \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
7.163 |
|
|
\[ {}y^{\prime }+\frac {y}{x} = x y^{2} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
1.179 |
|
|
\[ {}2 x^{3} y^{\prime } = y \left (y^{2}+3 x^{2}\right ) \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.546 |
|
|
\[ {}y^{2}-x^{2}+x y y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.685 |
|
|
\[ {}x^{3}+y^{3}+3 x y^{2} y^{\prime } = 0 \] |
1 |
1 |
3 |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
2.03 |
|
|
\[ {}x y y^{\prime }+x^{2}+y^{2} = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
2.356 |
|
|
\[ {}y^{2}+x y-x y^{\prime } = 0 \] |
1 |
1 |
1 |
[_rational, _Bernoulli] |
✓ |
✓ |
28.431 |
|
|
\[ {}y \left (x -2 y\right )-x^{2} y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.345 |
|
|
\[ {}x y y^{\prime }+x^{2}+y^{2} = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.536 |
|
|
\[ {}x^{2}+y^{2}+2 x y y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
1.734 |
|
|
\[ {}y+y^{\prime } = y^{2} {\mathrm e}^{x} \] |
1 |
1 |
1 |
[[_1st_order, _with_linear_symmetries], _Bernoulli] |
✓ |
✓ |
0.582 |
|
|
\[ {}x y^{\prime }+y-x^{3} y^{6} = 0 \] |
1 |
1 |
5 |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
2.846 |
|
|
\[ {}y y^{\prime }-x y^{2}+x = 0 \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
2.288 |
|
|
\[ {}2 x^{\prime }-\frac {x}{y}+x^{3} \cos \left (y \right ) = 0 \] |
1 |
1 |
2 |
[_Bernoulli] |
✓ |
✓ |
4.125 |
|
|
\[ {}2 x y^{5}-y+2 x y^{\prime } = 0 \] |
1 |
4 |
4 |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
1.774 |
|
|
\[ {}x y^{3}-y^{3}-x^{2} {\mathrm e}^{x}+3 x y^{2} y^{\prime } = 0 \] |
1 |
1 |
3 |
[_Bernoulli] |
✓ |
✓ |
1.971 |
|
|
\[ {}2 x y^{\prime } = y \left (2 x^{2}-y^{2}\right ) \] |
1 |
2 |
2 |
[_rational, _Bernoulli] |
✓ |
✓ |
1.091 |
|
|
\[ {}2 x y^{\prime }+\left (x^{2} y^{4}+1\right ) y = 0 \] |
1 |
4 |
4 |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
1.036 |
|
|
\[ {}x^{2} y^{\prime }+y^{2}-x y = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
0.875 |
|
|
\[ {}y^{\prime } = \frac {y}{2 x}+\frac {x^{2}}{2 y} \] |
1 |
1 |
2 |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
1.115 |
|
|
\[ {}\phi ^{\prime }-\frac {\phi ^{2}}{2}-\phi \cot \left (\theta \right ) = 0 \] |
1 |
1 |
1 |
[_Bernoulli] |
✓ |
✓ |
1.227 |
|
|
\[ {}x^{2}+y^{2}-2 x y y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.446 |
|
|
\[ {}x^{2}-y^{2}+2 x y y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
0.927 |
|
|
\[ {}2 x y y^{\prime } = x^{2}+y^{2} \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.457 |
|
|
\[ {}x y^{\prime }+y = x^{4} y^{3} \] |
1 |
1 |
2 |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
1.231 |
|
|
\[ {}x y^{2} y^{\prime }+y^{3} = x \cos \left (x \right ) \] |
1 |
1 |
3 |
[_Bernoulli] |
✓ |
✓ |
8.563 |
|
|
\[ {}x y^{\prime }+y = x y^{2} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
1.415 |
|
|
\[ {}y^{\prime }+x y = y^{4} x \] |
1 |
1 |
3 |
[_separable] |
✓ |
✓ |
7.695 |
|
|
\[ {}y^{\prime } = \frac {1-x y^{2}}{2 x^{2} y} \] |
1 |
1 |
2 |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
1.75 |
|
|
\[ {}y^{\prime } = \frac {2+3 x y^{2}}{4 x^{2} y} \] |
1 |
1 |
2 |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
2.215 |
|
|
\[ {}y^{\prime }+\frac {2 y}{x} = 6 x^{4} y^{2} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
1.166 |
|
|
\[ {}y^{\prime }+\frac {y}{3} = \frac {\left (1-2 x \right ) y^{4}}{3} \] |
1 |
3 |
3 |
[_Bernoulli] |
✓ |
✓ |
1.113 |
|
|
\[ {}y^{2}+\frac {2}{x}+2 x y y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class G‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
0.987 |
|
|
\[ {}y^{\prime } = 2 y \left (x \sqrt {y}-1\right ) \] |
1 |
1 |
1 |
[_Bernoulli] |
✓ |
✓ |
1.849 |
|
|
\[ {}v v^{\prime } = \frac {2 v^{2}}{r^{3}}+\frac {\lambda r}{3} \] |
1 |
1 |
2 |
[_rational, _Bernoulli] |
✓ |
✓ |
1.752 |
|
|
\[ {}c y^{\prime } = \frac {x a +b y^{2}}{y} \] |
1 |
1 |
2 |
[_rational, _Bernoulli] |
✓ |
✓ |
1.917 |
|
|
\[ {}y^{\prime }-x y^{2}-3 x y = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.435 |
|
|
\[ {}y^{\prime }+f \left (x \right ) y^{2}+g \left (x \right ) y = 0 \] |
1 |
1 |
1 |
[_Bernoulli] |
✓ |
✓ |
0.957 |
|
|
\[ {}y^{\prime }+2 a \,x^{3} y^{3}+2 x y = 0 \] |
1 |
2 |
2 |
[_Bernoulli] |
✓ |
✓ |
1.204 |
|
|
\[ {}x y^{\prime }+x y^{2}-y = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
1.065 |
|
|
\[ {}x y^{\prime }-y^{2} \ln \left (x \right )+y = 0 \] |
1 |
1 |
1 |
[_Bernoulli] |
✓ |
✓ |
1.306 |
|
|
\[ {}x y^{\prime }-y \left (2 y \ln \left (x \right )-1\right ) = 0 \] |
1 |
1 |
1 |
[_Bernoulli] |
✓ |
✓ |
1.316 |
|
|
\[ {}\left (1+x \right ) y^{\prime }+y \left (y-x \right ) = 0 \] |
1 |
1 |
1 |
[_rational, _Bernoulli] |
✓ |
✓ |
1.158 |
|
|
\[ {}3 x y^{\prime }-3 x y^{4} \ln \left (x \right )-y = 0 \] |
1 |
1 |
3 |
[_Bernoulli] |
✓ |
✓ |
2.128 |
|
|
\[ {}x^{2} y^{\prime }-y^{2}-x y = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.117 |
|
|
\[ {}\left (x^{2}-1\right ) y^{\prime }-y \left (y-x \right ) = 0 \] |
1 |
1 |
1 |
[_rational, _Bernoulli] |
✓ |
✓ |
1.102 |
|
|
\[ {}\left (x^{2}-1\right ) y^{\prime }+a x y^{2}+x y = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
3.3 |
|
|
\[ {}\left (x^{2}-4\right ) y^{\prime }+\left (2+x \right ) y^{2}-4 y = 0 \] |
1 |
1 |
1 |
[_rational, _Bernoulli] |
✓ |
✓ |
1.078 |
|
|
\[ {}x^{3} y^{\prime }-y^{2}-x^{2} y = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
1.181 |
|
|
\[ {}x^{2} \left (-1+x \right ) y^{\prime }-y^{2}-x \left (-2+x \right ) y = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
1.302 |
|
|
\[ {}\cos \left (x \right ) y^{\prime }-y^{4}-y \sin \left (x \right ) = 0 \] |
1 |
3 |
3 |
[_Bernoulli] |
✓ |
✓ |
47.638 |
|
|
\[ {}y y^{\prime }+4 \left (1+x \right ) x +y^{2} = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
2.217 |
|
|
\[ {}y y^{\prime }+a y^{2}-b \cos \left (x +c \right ) = 0 \] |
1 |
1 |
2 |
[_Bernoulli] |
✓ |
✓ |
3.21 |
|
|
\[ {}y y^{\prime }+x y^{2}-4 x = 0 \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
1.973 |
|
|
\[ {}2 y y^{\prime }-x y^{2}-x^{3} = 0 \] |
1 |
1 |
2 |
[_rational, _Bernoulli] |
✓ |
✓ |
1.375 |
|
|
\[ {}a y y^{\prime }+b y^{2}+f \left (x \right ) = 0 \] |
1 |
1 |
2 |
[_Bernoulli] |
✓ |
✓ |
1.867 |
|
|
\[ {}x y y^{\prime }+x^{2}+y^{2} = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.885 |
|
|
\[ {}x y y^{\prime }-y^{2}+a \,x^{3} \cos \left (x \right ) = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class D‘], _Bernoulli] |
✓ |
✓ |
1.794 |
|
|
\[ {}2 x y y^{\prime }-y^{2}+x a = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
1.388 |
|
|
\[ {}2 x y y^{\prime }-y^{2}+x^{2} a = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.811 |
|
|
\[ {}2 x y y^{\prime }+2 y^{2}+1 = 0 \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
2.362 |
|
|
\[ {}2 x^{2} y y^{\prime }+y^{2}-2 x^{3}-x^{2} = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
2.801 |
|
|
\[ {}2 x^{2} y y^{\prime }-y^{2}-x^{2} {\mathrm e}^{x -\frac {1}{x}} = 0 \] |
1 |
1 |
2 |
[_Bernoulli] |
✓ |
✓ |
1.458 |
|
|
\[ {}2 x^{3}+y y^{\prime }+3 x^{2} y^{2}+7 = 0 \] |
1 |
1 |
2 |
[_rational, _Bernoulli] |
✓ |
✓ |
3.064 |
|
|
\[ {}y y^{\prime } \sin \left (x \right )^{2}+y^{2} \cos \left (x \right ) \sin \left (x \right )-1 = 0 \] |
1 |
1 |
2 |
[_exact, _Bernoulli] |
✓ |
✓ |
12.353 |
|
|
\[ {}f \left (x \right ) y y^{\prime }+g \left (x \right ) y^{2}+h \left (x \right ) = 0 \] |
1 |
1 |
2 |
[_Bernoulli] |
✓ |
✓ |
1.951 |
|
|
\[ {}3 x y^{2} y^{\prime }+y^{3}-2 x = 0 \] |
1 |
1 |
3 |
[[_homogeneous, ‘class G‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
1.665 |
|
|
\[ {}6 x y^{2} y^{\prime }+x +2 y^{3} = 0 \] |
1 |
1 |
3 |
[[_homogeneous, ‘class G‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
1.436 |
|
|
\[ {}x y^{3} y^{\prime }+y^{4}-x \sin \left (x \right ) = 0 \] |
1 |
1 |
4 |
[_Bernoulli] |
✓ |
✓ |
7.618 |
|
|
\[ {}x \left (\sqrt {1+{y^{\prime }}^{2}}+y^{\prime }\right )-y = 0 \] |
1 |
2 |
2 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
3.247 |
|
|
\[ {}y^{\prime } = \frac {y \left (-1+\ln \left (\left (1+x \right ) x \right ) y x^{4}-\ln \left (\left (1+x \right ) x \right ) x^{3}\right )}{x} \] |
1 |
1 |
1 |
[_Bernoulli] |
✓ |
✓ |
3.632 |
|
|
\[ {}y^{\prime } = \frac {y \left (1-x +y x^{2} \ln \left (x \right )+x^{3} y-x \ln \left (x \right )-x^{2}\right )}{\left (-1+x \right ) x} \] |
1 |
1 |
1 |
[_Bernoulli] |
✓ |
✓ |
1.721 |
|
|
\[ {}y^{\prime } = -\frac {y \left (-\ln \left (\frac {1}{x}\right )+{\mathrm e}^{x}+y x^{2} \ln \left (x \right )+x^{3} y-x \ln \left (x \right )-x^{2}\right )}{\left (-\ln \left (\frac {1}{x}\right )+{\mathrm e}^{x}\right ) x} \] |
1 |
1 |
1 |
[_Bernoulli] |
✓ |
✓ |
1.694 |
|
|
\[ {}y^{\prime } = \frac {y \left (-{\mathrm e}^{x}+\ln \left (2 x \right ) x^{2} y-\ln \left (2 x \right ) x \right ) {\mathrm e}^{-x}}{x} \] |
1 |
1 |
1 |
[_Bernoulli] |
✓ |
✓ |
1.566 |
|
|
\[ {}y^{\prime } = -\frac {y \left (\tan \left (x \right )+\ln \left (2 x \right ) x -\ln \left (2 x \right ) x^{2} y\right )}{x \tan \left (x \right )} \] |
1 |
1 |
1 |
[_Bernoulli] |
✓ |
✓ |
37.084 |
|
|
\[ {}y^{\prime } = \frac {y \left (-1-\ln \left (\frac {\left (-1+x \right ) \left (1+x \right )}{x}\right )+\ln \left (\frac {\left (-1+x \right ) \left (1+x \right )}{x}\right ) x y\right )}{x} \] |
1 |
1 |
1 |
[_Bernoulli] |
✓ |
✓ |
12.734 |
|
|
\[ {}y^{\prime } = \frac {y \left (-\ln \left (x \right )-x \ln \left (\frac {\left (-1+x \right ) \left (1+x \right )}{x}\right )+\ln \left (\frac {\left (-1+x \right ) \left (1+x \right )}{x}\right ) x^{2} y\right )}{x \ln \left (x \right )} \] |
1 |
1 |
1 |
[_Bernoulli] |
✓ |
✓ |
5.017 |
|
|
\[ {}y^{\prime } = \frac {y \left (-\ln \left (\frac {1}{x}\right )-\ln \left (\frac {x^{2}+1}{x}\right ) x +\ln \left (\frac {x^{2}+1}{x}\right ) x^{2} y\right )}{x \ln \left (\frac {1}{x}\right )} \] |
1 |
1 |
1 |
[_Bernoulli] |
✓ |
✓ |
5.582 |
|
|
\[ {}y^{\prime } = \frac {y \left (-\tanh \left (\frac {1}{x}\right )-\ln \left (\frac {x^{2}+1}{x}\right ) x +\ln \left (\frac {x^{2}+1}{x}\right ) x^{2} y\right )}{x \tanh \left (\frac {1}{x}\right )} \] |
1 |
1 |
1 |
[_Bernoulli] |
✓ |
✓ |
36.352 |
|
|
\[ {}y^{\prime } = -\frac {y \left (\tanh \left (x \right )+\ln \left (2 x \right ) x -\ln \left (2 x \right ) x^{2} y\right )}{x \tanh \left (x \right )} \] |
1 |
1 |
1 |
[_Bernoulli] |
✓ |
✓ |
14.089 |
|
|
\[ {}y^{\prime } = -\frac {y \left (\ln \left (-1+x \right )+\coth \left (1+x \right ) x -\coth \left (1+x \right ) x^{2} y\right )}{x \ln \left (-1+x \right )} \] |
1 |
1 |
1 |
[_Bernoulli] |
✓ |
✓ |
46.734 |
|
|
\[ {}y^{\prime } = \frac {y \left (-\cosh \left (\frac {1}{1+x}\right ) x +\cosh \left (\frac {1}{1+x}\right )-x +x^{2} y-x^{2}+x^{3} y\right )}{x \left (-1+x \right ) \cosh \left (\frac {1}{1+x}\right )} \] |
1 |
1 |
1 |
[_Bernoulli] |
✓ |
✓ |
18.688 |
|
|
\[ {}y^{\prime } = \frac {y \left (-1-\cosh \left (\frac {1+x}{-1+x}\right ) x +\cosh \left (\frac {1+x}{-1+x}\right ) x^{2} y-\cosh \left (\frac {1+x}{-1+x}\right ) x^{2}+\cosh \left (\frac {1+x}{-1+x}\right ) x^{3} y\right )}{x} \] |
1 |
1 |
1 |
[_Bernoulli] |
✓ |
✓ |
34.423 |
|
|
\[ {}y^{\prime } = \frac {y \left (-1-{\mathrm e}^{\frac {1+x}{-1+x}} x +x^{2} {\mathrm e}^{\frac {1+x}{-1+x}} y-x^{2} {\mathrm e}^{\frac {1+x}{-1+x}}+x^{3} {\mathrm e}^{\frac {1+x}{-1+x}} y\right )}{x} \] |
1 |
1 |
1 |
[_Bernoulli] |
✓ |
✓ |
5.467 |
|
|
\[ {}y^{\prime } = \frac {y \left (-1-x^{\frac {2}{1+\ln \left (x \right )}} {\mathrm e}^{\frac {2 \ln \left (x \right )^{2}}{1+\ln \left (x \right )}} x^{2}-x^{\frac {2}{1+\ln \left (x \right )}} {\mathrm e}^{\frac {2 \ln \left (x \right )^{2}}{1+\ln \left (x \right )}} x^{2} \ln \left (x \right )+x^{\frac {2}{1+\ln \left (x \right )}} {\mathrm e}^{\frac {2 \ln \left (x \right )^{2}}{1+\ln \left (x \right )}} x^{2} y+2 x^{\frac {2}{1+\ln \left (x \right )}} {\mathrm e}^{\frac {2 \ln \left (x \right )^{2}}{1+\ln \left (x \right )}} x^{2} y \ln \left (x \right )+x^{\frac {2}{1+\ln \left (x \right )}} {\mathrm e}^{\frac {2 \ln \left (x \right )^{2}}{1+\ln \left (x \right )}} x^{2} y \ln \left (x \right )^{2}\right )}{\left (1+\ln \left (x \right )\right ) x} \] |
1 |
1 |
1 |
[_Bernoulli] |
✓ |
✓ |
11.429 |
|
|
\[ {}y^{\prime } = \frac {y \left (-1-x^{3} x^{\frac {2}{1+\ln \left (x \right )}} {\mathrm e}^{\frac {2 \ln \left (x \right )^{2}}{1+\ln \left (x \right )}}-x^{3} x^{\frac {2}{1+\ln \left (x \right )}} {\mathrm e}^{\frac {2 \ln \left (x \right )^{2}}{1+\ln \left (x \right )}} \ln \left (x \right )+x^{3} x^{\frac {2}{1+\ln \left (x \right )}} {\mathrm e}^{\frac {2 \ln \left (x \right )^{2}}{1+\ln \left (x \right )}} y+2 x^{3} x^{\frac {2}{1+\ln \left (x \right )}} {\mathrm e}^{\frac {2 \ln \left (x \right )^{2}}{1+\ln \left (x \right )}} y \ln \left (x \right )+x^{3} x^{\frac {2}{1+\ln \left (x \right )}} {\mathrm e}^{\frac {2 \ln \left (x \right )^{2}}{1+\ln \left (x \right )}} y \ln \left (x \right )^{2}\right )}{\left (1+\ln \left (x \right )\right ) x} \] |
1 |
1 |
1 |
[_Bernoulli] |
✓ |
✓ |
10.642 |
|
|
\[ {}g \left (x \right ) y^{\prime } = f_{1} \left (x \right ) y+f_{n} \left (x \right ) y^{n} \] |
1 |
1 |
1 |
[_Bernoulli] |
✓ |
✓ |
0.948 |
|
|
\[ {}x^{2} y^{\prime }+y^{2}-x y = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
0.946 |
|
|
\[ {}2 x^{2} y+y^{3}-x^{3} y^{\prime } = 0 \] |
1 |
2 |
2 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.338 |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime }-2 \left (1+x \right ) y = y^{\frac {5}{2}} \] |
1 |
3 |
1 |
[_rational, _Bernoulli] |
✓ |
✓ |
16.983 |
|
|
\[ {}y y^{\prime }+x y^{2} = x \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
2.46 |
|
|
\[ {}4 x y^{\prime }+3 y+{\mathrm e}^{x} x^{4} y^{5} = 0 \] |
1 |
4 |
4 |
[_Bernoulli] |
✓ |
✓ |
1.53 |
|
|
\[ {}x^{2} y^{\prime }+y^{2}-x y = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
0.939 |
|
|
\[ {}x^{2}+y^{2}-2 x y y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.666 |
|
|
\[ {}x -y^{2}+2 x y y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
0.887 |
|
|
\[ {}x y^{\prime }+y+x^{4} y^{4} {\mathrm e}^{x} = 0 \] |
1 |
1 |
3 |
[_Bernoulli] |
✓ |
✓ |
1.786 |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime }-x y = a x y^{2} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
3.538 |
|
|
\[ {}y+x y^{2}-x y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
0.929 |
|
|
\[ {}x y^{\prime }-y^{2} \ln \left (x \right )+y = 0 \] |
1 |
1 |
1 |
[_Bernoulli] |
✓ |
✓ |
1.163 |
|
|
\[ {}x^{\prime } = \frac {4 t^{2}+3 x^{2}}{2 t x} \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.906 |
|
|
\[ {}y^{\prime } = \frac {y^{2}+2 t y}{t^{2}} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.068 |
|
|
\[ {}x^{\prime } = \frac {2 x}{3 t}+\frac {2 t}{x} \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.877 |
|
|
\[ {}x^{\prime } = x \left (1+x \,{\mathrm e}^{t}\right ) \] |
1 |
1 |
1 |
[[_1st_order, _with_linear_symmetries], _Bernoulli] |
✓ |
✓ |
0.825 |
|
|
\[ {}x^{\prime } = -\frac {x}{t}+\frac {1}{t x^{2}} \] |
1 |
1 |
3 |
[_separable] |
✓ |
✓ |
3.64 |
|
|
\[ {}t^{2} y^{\prime }+2 t y-y^{2} = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.054 |
|
|
\[ {}w^{\prime } = t w+t^{3} w^{3} \] |
1 |
2 |
2 |
[_Bernoulli] |
✓ |
✓ |
1.114 |
|
|
\[ {}x^{2}+y^{2}+2 x y y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
2.398 |
|
|
\[ {}x y^{\prime }+y = x^{3} y^{3} \] |
1 |
1 |
2 |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
1.318 |
|
|
\[ {}4 x +3 y^{2}+2 x y y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
1.25 |
|
|
\[ {}y^{2}+2 x y-x^{2} y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.13 |
|
|
\[ {}\left (x +4\right ) \left (1+y^{2}\right )+y \left (x^{2}+3 x +2\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
6.879 |
|
|
\[ {}\left (3 x +8\right ) \left (y^{2}+4\right )-4 y \left (x^{2}+5 x +6\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
4.756 |
|
|
\[ {}x^{2}+3 y^{2}-2 x y y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
2.539 |
|
|
\[ {}y^{\prime }-\frac {y}{x} = -\frac {y^{2}}{x} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.38 |
|
|
\[ {}x y^{\prime }+y = -2 x^{6} y^{4} \] |
1 |
1 |
3 |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
2.023 |
|
|
\[ {}y^{\prime }+\left (4 y-\frac {8}{y^{3}}\right ) x = 0 \] |
1 |
1 |
4 |
[_separable] |
✓ |
✓ |
3.195 |
|
|
\[ {}x^{\prime }+\frac {\left (t +1\right ) x}{2 t} = \frac {t +1}{x t} \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
2.929 |
|
|
\[ {}y^{\prime }+\frac {y}{2 x} = \frac {x}{y^{3}} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
1.193 |
|
|
\[ {}x^{2} y^{\prime }+x y = x y^{3} \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
6.259 |
|
|
\[ {}x^{2}+y^{2}-2 x y y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
2.645 |
|
|
\[ {}2 y^{2}+8+\left (-x^{2}+1\right ) y y^{\prime } = 0 \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
2.822 |
|
|
\[ {}{\mathrm e}^{2 x} y^{2}-2 x +{\mathrm e}^{2 x} y y^{\prime } = 0 \] |
1 |
1 |
1 |
[_exact, _Bernoulli] |
✓ |
✓ |
1.389 |
|
|
\[ {}4 x y y^{\prime } = 1+y^{2} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
9.377 |
|
|
\[ {}x^{2} y^{\prime }+x y = \frac {y^{3}}{x} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
2.162 |
|
|
\[ {}y = x y^{\prime }+\frac {1}{y} \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
6.814 |
|
|
|
||||||||
|
\[ {}y^{\prime }-\frac {y}{1+x}+y^{2} = 0 \] |
1 |
1 |
1 |
[[_1st_order, _with_linear_symmetries], _rational, _Bernoulli] |
✓ |
✓ |
1.172 |
|
|
\[ {}y \left (x -y\right )-x^{2} y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.256 |
|
|
\[ {}x^{\prime } = \frac {x}{t}+\frac {x^{2}}{t^{3}} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
1.663 |
|
|
\[ {}y^{\prime }-\frac {3 y}{x}+x^{3} y^{2} = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
1.12 |
|
|
\[ {}y \left (x -y\right )-x^{2} y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.2 |
|
|
\[ {}x y^{\prime }-y^{2} \ln \left (x \right )+y = 0 \] |
1 |
1 |
1 |
[_Bernoulli] |
✓ |
✓ |
1.475 |
|
|
\[ {}3 x y^{2} y^{\prime }+y^{3}-2 x = 0 \] |
1 |
1 |
3 |
[[_homogeneous, ‘class G‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
2.188 |
|
|
\[ {}x y^{\prime }+y = x y^{2} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
0.898 |
|
|
\[ {}x -x y^{2}+\left (y-x^{2} y\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
2.376 |
|
|
\[ {}x y^{2} y^{\prime } = x^{3}+y^{3} \] |
1 |
1 |
3 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.569 |
|
|
\[ {}y^{\prime }+x y = x^{3} y^{3} \] |
1 |
2 |
2 |
[_Bernoulli] |
✓ |
✓ |
0.788 |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime }-x y+a x y^{2} = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
3.735 |
|
|
\[ {}3 y^{2} y^{\prime }-a y^{3}-x -1 = 0 \] |
1 |
1 |
3 |
[_rational, _Bernoulli] |
✓ |
✓ |
1.909 |
|
|
\[ {}x y^{\prime } = \left (y \ln \left (x \right )-2\right ) y \] |
1 |
1 |
1 |
[_Bernoulli] |
✓ |
✓ |
1.277 |
|
|
\[ {}y-\cos \left (x \right ) y^{\prime } = y^{2} \cos \left (x \right ) \left (1-\sin \left (x \right )\right ) \] |
1 |
1 |
1 |
[_Bernoulli] |
✓ |
✓ |
4.242 |
|
|
\[ {}\frac {1}{x^{2}}+\frac {3 y^{2}}{x^{4}} = \frac {2 y y^{\prime }}{x^{3}} \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
1.155 |
|
|
\[ {}x y^{\prime }-y^{2} \ln \left (x \right )+y = 0 \] |
1 |
1 |
1 |
[_Bernoulli] |
✓ |
✓ |
0.868 |
|
|
\[ {}y^{\prime } = -\frac {y}{x}+y^{\frac {1}{4}} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
2.401 |
|
|
\[ {}2 x y y^{\prime }+y^{2} = -1 \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
1.467 |
|
|
\[ {}x y \left (1-y\right )-2 y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.379 |
|
|
\[ {}x \left (1-y^{3}\right )-3 y^{2} y^{\prime } = 0 \] |
1 |
1 |
3 |
[_separable] |
✓ |
✓ |
1.635 |
|
|
\[ {}y^{\prime } = t y+t y^{2} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.455 |
|
|
\[ {}x y y^{\prime } = y^{2}+9 \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
2.068 |
|
|
\[ {}y y^{\prime } = x y^{2}+x \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.479 |
|
|
\[ {}y y^{\prime } = x y^{2}-9 x \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
1.435 |
|
|
\[ {}x y^{\prime } = y^{2}-y \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.388 |
|
|
\[ {}x y^{\prime } = y^{2}-y \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.352 |
|
|
\[ {}y^{\prime } = \frac {y^{2}-1}{x y} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
7.687 |
|
|
\[ {}x^{2} y^{\prime }-x y = y^{2} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
0.936 |
|
|
\[ {}y^{\prime } = \frac {y}{x}+\frac {x}{y} \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.075 |
|
|
\[ {}y^{\prime }-\frac {3 y}{x} = \frac {y^{2}}{x^{2}} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.058 |
|
|
\[ {}y^{\prime }+3 \cot \left (x \right ) y = 6 \cos \left (x \right ) y^{\frac {2}{3}} \] |
1 |
1 |
1 |
[_Bernoulli] |
✓ |
✓ |
3.814 |
|
|
\[ {}y^{\prime }-\frac {y}{x} = \frac {1}{y} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
1.112 |
|
|
\[ {}y^{\prime } = \frac {y}{x}+\frac {x^{2}}{y^{2}} \] |
1 |
1 |
3 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.426 |
|
|
\[ {}3 y^{\prime }+\frac {2 y}{x} = 4 \sqrt {y} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
1.432 |
|
|
\[ {}y^{\prime }+\frac {y}{x} = y^{3} x^{2} \] |
1 |
1 |
2 |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
1.13 |
|
|
\[ {}y^{\prime }+3 y = \frac {28 \,{\mathrm e}^{2 x}}{y^{3}} \] |
1 |
1 |
4 |
[[_1st_order, _with_linear_symmetries], _Bernoulli] |
✓ |
✓ |
1.609 |
|
|
\[ {}y^{\prime } = \frac {1}{y}-\frac {y}{2 x} \] |
1 |
1 |
2 |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
0.885 |
|
|
\[ {}{\mathrm e}^{x y^{2}-x^{2}} \left (y^{2}-2 x \right )+2 \,{\mathrm e}^{x y^{2}-x^{2}} x y y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class G‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
0.941 |
|
|
\[ {}2 x y^{3}+4 x^{3}+3 x^{2} y^{2} y^{\prime } = 0 \] |
1 |
1 |
3 |
[[_homogeneous, ‘class G‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
1.638 |
|
|
\[ {}1+3 x^{2} y^{2}+\left (2 x^{3} y+6 y\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[_exact, _rational, _Bernoulli] |
✓ |
✓ |
1.307 |
|
|
\[ {}1+y^{4}+x y^{3} y^{\prime } = 0 \] |
1 |
1 |
4 |
[_separable] |
✓ |
✓ |
2.348 |
|
|
\[ {}x y^{\prime } = 2 y^{2}-6 y \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.752 |
|
|
\[ {}x y^{2}-6+x^{2} y y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class G‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
1.003 |
|
|
\[ {}x^{3}+y^{3}+x y^{2} y^{\prime } = 0 \] |
1 |
1 |
3 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
2.127 |
|
|
\[ {}1+2 x y^{2}+\left (2 x^{2} y+2 y\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[_exact, _rational, _Bernoulli] |
✓ |
✓ |
1.183 |
|
|
\[ {}3 x y^{3}-y+x y^{\prime } = 0 \] |
1 |
2 |
2 |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
1.03 |
|
|
\[ {}y^{\prime } = \frac {3 y}{1+x}-y^{2} \] |
1 |
1 |
1 |
[[_1st_order, _with_linear_symmetries], _rational, _Bernoulli] |
✓ |
✓ |
0.89 |
|
|
\[ {}x y y^{\prime } = 2 x^{2}+2 y^{2} \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.588 |
|
|
\[ {}x y^{3} y^{\prime } = y^{4}-x^{2} \] |
1 |
1 |
4 |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
1.307 |
|
|
\[ {}y^{\prime } = 4 y-\frac {16 \,{\mathrm e}^{4 x}}{y^{2}} \] |
1 |
1 |
3 |
[[_1st_order, _with_linear_symmetries], _Bernoulli] |
✓ |
✓ |
1.252 |
|
|
\[ {}y y^{\prime }-x y^{2} = 6 x \,{\mathrm e}^{4 x^{2}} \] |
1 |
1 |
2 |
[_Bernoulli] |
✓ |
✓ |
2.217 |
|
|
\[ {}y^{\prime } = \frac {y^{2}+2 x y}{x^{2}} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.803 |
|
|
\[ {}3 t^{2}+3 y^{2}+6 t y y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
2.386 |
|
|
\[ {}\frac {1}{t^{2}+1}-y^{2}-2 t y y^{\prime } = 0 \] |
1 |
1 |
0 |
[_exact, _rational, _Bernoulli] |
✓ |
✓ |
1.777 |
|
|
\[ {}2 t y+y^{2}-t^{2} y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.324 |
|
|
\[ {}5 t y^{2}+y+\left (2 t^{3}-t \right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
1.608 |
|
|
\[ {}y^{\prime }-\frac {y}{2} = \frac {t}{y} \] |
1 |
1 |
2 |
[_rational, _Bernoulli] |
✓ |
✓ |
1.296 |
|
|
\[ {}y^{\prime }+y = t y^{2} \] |
1 |
1 |
1 |
[_Bernoulli] |
✓ |
✓ |
0.944 |
|
|
\[ {}2 t y^{\prime }-y = 2 t y^{3} \cos \left (t \right ) \] |
1 |
1 |
2 |
[_Bernoulli] |
✓ |
✓ |
35.666 |
|
|
\[ {}t y^{\prime }-y = t y^{3} \sin \left (t \right ) \] |
1 |
2 |
2 |
[[_homogeneous, ‘class D‘], _Bernoulli] |
✓ |
✓ |
32.289 |
|
|
\[ {}y^{\prime }-2 y = \frac {\cos \left (t \right )}{\sqrt {y}} \] |
1 |
1 |
1 |
[_Bernoulli] |
✓ |
✓ |
10.556 |
|
|
\[ {}y^{\prime }+3 y = \sqrt {y}\, \sin \left (t \right ) \] |
1 |
1 |
1 |
[_Bernoulli] |
✓ |
✓ |
41.946 |
|
|
\[ {}y^{\prime }-\frac {y}{t} = t y^{2} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
1.211 |
|
|
\[ {}y^{\prime }-\frac {y}{t} = \frac {y^{2}}{t^{2}} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.177 |
|
|
\[ {}y^{\prime }-\frac {y}{t} = \frac {y^{2}}{t} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.685 |
|
|
\[ {}y^{\prime }-\frac {y}{t} = t^{2} y^{\frac {3}{2}} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
2.291 |
|
|
\[ {}\frac {2}{t}+\frac {1}{y}+\frac {t y^{\prime }}{y^{2}} = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.791 |
|
|
\[ {}t^{3}+y^{3}-t y^{2} y^{\prime } = 0 \] |
1 |
1 |
3 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
2.089 |
|
|
\[ {}y^{\prime }+2 y = t^{2} \sqrt {y} \] |
1 |
1 |
1 |
[_Bernoulli] |
✓ |
✓ |
2.97 |
|
|
\[ {}y^{\prime }-2 y = t^{2} \sqrt {y} \] |
1 |
1 |
1 |
[_Bernoulli] |
✓ |
✓ |
3.215 |
|
|
\[ {}y^{\prime } = \frac {4 y^{2}-t^{2}}{2 t y} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
2.464 |
|
|
\[ {}y^{3}-t^{3}-t y^{2} y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.701 |
|
|
\[ {}y^{\prime }+\cot \left (x \right ) y = y^{4} \] |
1 |
1 |
1 |
[_Bernoulli] |
✓ |
✗ |
37.984 |
|
|
\[ {}y^{\prime } = \frac {y^{2}-t^{2}}{t y} \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.677 |
|
|
\[ {}y^{\prime }-\frac {y}{t} = \frac {y^{2}}{t} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.98 |
|
|
\[ {}r^{\prime } = \frac {r^{2}+t^{2}}{r t} \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.603 |
|
|
\[ {}y^{\prime }-y = t y^{3} \] |
1 |
2 |
2 |
[_Bernoulli] |
✓ |
✓ |
1.333 |
|
|
\[ {}y^{\prime }+y = \frac {{\mathrm e}^{t}}{y^{2}} \] |
1 |
1 |
3 |
[[_1st_order, _with_linear_symmetries], _Bernoulli] |
✓ |
✓ |
1.687 |
|
|
\[ {}y-t y^{\prime } = 2 y^{2} \ln \left (t \right ) \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘], _Bernoulli] |
✓ |
✓ |
1.624 |
|
|
\[ {}x y y^{\prime }+1+y^{2} = 0 \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
3.681 |
|
|
\[ {}4 y^{6}+x^{3} = 6 x y^{5} y^{\prime } \] |
1 |
1 |
6 |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
2.838 |
|
|
\[ {}y^{\prime }+2 x y = 2 x y^{2} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
3.732 |
|
|
\[ {}3 x y^{2} y^{\prime }-2 y^{3} = x^{3} \] |
1 |
1 |
3 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
2.863 |
|
|
\[ {}2 y^{\prime } \ln \left (x \right )+\frac {y}{x} = \frac {\cos \left (x \right )}{y} \] |
1 |
1 |
2 |
[_Bernoulli] |
✓ |
✓ |
10.419 |
|
|
\[ {}2 y^{\prime } \sin \left (x \right )+y \cos \left (x \right ) = y^{3} \sin \left (x \right )^{2} \] |
1 |
2 |
2 |
[_Bernoulli] |
✓ |
✓ |
10.866 |
|
|
\[ {}y^{\prime }-y \cos \left (x \right ) = y^{2} \cos \left (x \right ) \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
4.376 |
|
|
\[ {}x +y^{2}-2 x y y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
1.652 |
|
|
\[ {}x^{4} \ln \left (x \right )-2 x y^{3}+3 x^{2} y^{2} y^{\prime } = 0 \] |
1 |
1 |
3 |
[_Bernoulli] |
✓ |
✓ |
1.855 |
|
|
\[ {}x^{2}+y^{2}+1-2 x y y^{\prime } = 0 \] |
1 |
1 |
2 |
[_rational, _Bernoulli] |
✓ |
✓ |
1.676 |
|
|
\[ {}y^{\prime }+y \cos \left (x \right ) = y^{n} \sin \left (2 x \right ) \] |
1 |
1 |
1 |
[_Bernoulli] |
✓ |
✓ |
9.935 |
|
|
\[ {}y-x y^{2} \ln \left (x \right )+x y^{\prime } = 0 \] |
1 |
1 |
1 |
[_Bernoulli] |
✓ |
✓ |
0.984 |
|
|
\[ {}x y y^{\prime }-y^{2} = x^{4} \] |
1 |
1 |
2 |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
0.998 |
|
|
\[ {}x y^{2} y^{\prime }-y^{3} = \frac {x^{4}}{3} \] |
1 |
1 |
3 |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
1.174 |
|
|
\[ {}x^{2}+y^{2}-x y y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.013 |
|
|
\[ {}y+x y^{2}-x y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
0.939 |
|
|
\[ {}x^{2}+y^{2}+2 x +2 y y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
1.345 |
|
|
\[ {}x -y^{2}+2 x y y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
0.971 |
|
|
\[ {}x y^{\prime }+y = y^{2} \ln \left (x \right ) \] |
1 |
1 |
1 |
[_Bernoulli] |
✓ |
✓ |
1.35 |
|
|
|
||||||||
|
|
||||||||
|
|