These are ode’s of the form \(M dx + N dy=0\) where it is exact as is. Number of problems in this table is 3443
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) |
|
\[ {}y^{\prime } = 2 x^{2} y^{2} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.164 |
|
|
\[ {}y^{\prime } = x \ln \left (y\right ) \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.699 |
|
|
\[ {}y y^{\prime } = -1+x \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
4.47 |
|
|
\[ {}y y^{\prime } = -1+x \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
2.789 |
|
|
\[ {}2 x y+y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.871 |
|
|
\[ {}2 x y^{2}+y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.578 |
|
|
\[ {}y^{\prime } = y \sin \left (x \right ) \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.98 |
|
|
\[ {}\left (1+x \right ) y^{\prime } = 4 y \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.167 |
|
|
\[ {}2 \sqrt {x}\, y^{\prime } = \sqrt {1-y^{2}} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.404 |
|
|
\[ {}y^{\prime } = 2 x \sec \left (y\right ) \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.791 |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime } = 2 y \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.298 |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime } = \left (y+1\right )^{2} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.967 |
|
|
\[ {}y^{\prime } = x y^{3} \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
0.805 |
|
|
\[ {}y y^{\prime } = x \left (1+y^{2}\right ) \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
1.931 |
|
|
\[ {}y^{\prime } = \frac {1+\sqrt {x}}{1+\sqrt {y}} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
170.809 |
|
|
\[ {}y^{\prime } = \frac {\left (-1+x \right ) y^{5}}{x^{2} \left (-y+2 y^{3}\right )} \] |
1 |
1 |
3 |
[_separable] |
✓ |
✓ |
18.824 |
|
|
\[ {}\left (x^{2}+1\right ) \tan \left (y\right ) y^{\prime } = x \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.432 |
|
|
\[ {}y^{\prime } = 1+x +y+x y \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.866 |
|
|
\[ {}x^{2} y^{\prime } = 1-x^{2}+y^{2}-x^{2} y^{2} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.188 |
|
|
\[ {}y^{\prime } = {\mathrm e}^{x} y \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.815 |
|
|
\[ {}y^{\prime } = 3 x^{2} \left (1+y^{2}\right ) \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.2 |
|
|
\[ {}2 y y^{\prime } = \frac {x}{\sqrt {x^{2}-16}} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
5.32 |
|
|
\[ {}y^{\prime } = -y+4 x^{3} y \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.009 |
|
|
\[ {}\tan \left (x \right ) y^{\prime } = y \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.139 |
|
|
\[ {}-y+x y^{\prime } = 2 x^{2} y \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.973 |
|
|
\[ {}y^{\prime } = 2 x y^{2}+3 x^{2} y^{2} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.709 |
|
|
\[ {}y^{\prime } = 6 \,{\mathrm e}^{2 x -y} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.887 |
|
|
\[ {}2 \sqrt {x}\, y^{\prime } = \cos \left (y\right )^{2} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.51 |
|
|
\[ {}3 y+y^{\prime } = 2 x \,{\mathrm e}^{-3 x} \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.821 |
|
|
\[ {}x y^{\prime }+y = 3 x y \] |
1 |
0 |
1 |
[_separable] |
✓ |
✓ |
1.724 |
|
|
\[ {}2 x y+y^{\prime } = x \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.03 |
|
|
\[ {}y^{\prime } = \cos \left (x \right ) \left (1-y\right ) \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.056 |
|
|
\[ {}y+\left (1+x \right ) y^{\prime } = \cos \left (x \right ) \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.727 |
|
|
\[ {}y^{\prime } = 1+x +y+x y \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.757 |
|
|
\[ {}3 x y+\left (x^{2}+4\right ) y^{\prime } = x \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.406 |
|
|
\[ {}\left (x +y\right ) y^{\prime } = x -y \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.521 |
|
|
\[ {}2 x y^{3}+y^{2} y^{\prime } = 6 x \] |
1 |
1 |
3 |
[_separable] |
✓ |
✓ |
2.352 |
|
|
\[ {}\left ({\mathrm e}^{y}+x \right ) y^{\prime } = -1+x \,{\mathrm e}^{-y} \] |
1 |
1 |
2 |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
2.134 |
|
|
\[ {}2 x +3 y+\left (3 x +2 y\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.327 |
|
|
\[ {}4 x -y+\left (-x +6 y\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.744 |
|
|
\[ {}3 x^{2}+2 y^{2}+\left (4 x y+6 y^{2}\right ) y^{\prime } = 0 \] |
1 |
1 |
3 |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
2.955 |
|
|
\[ {}3 x^{2}+2 x y^{2}+\left (2 x^{2} y+4 y^{3}\right ) y^{\prime } = 0 \] |
1 |
1 |
4 |
[_exact, _rational] |
✓ |
✓ |
2.605 |
|
|
\[ {}x^{3}+\frac {y}{x}+\left (\ln \left (x \right )+y^{2}\right ) y^{\prime } = 0 \] |
1 |
1 |
3 |
[_exact] |
✓ |
✓ |
2.945 |
|
|
\[ {}1+{\mathrm e}^{x y} y+\left ({\mathrm e}^{x y} x +2 y\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_exact] |
✓ |
✓ |
3.511 |
|
|
\[ {}\cos \left (x \right )+\ln \left (y\right )+\left ({\mathrm e}^{y}+\frac {x}{y}\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_exact] |
✓ |
✓ |
5.824 |
|
|
\[ {}x +\arctan \left (y\right )+\frac {\left (x +y\right ) y^{\prime }}{1+y^{2}} = 0 \] |
1 |
1 |
1 |
[_exact] |
✓ |
✓ |
3.591 |
|
|
\[ {}3 x^{2} y^{3}+y^{4}+\left (3 x^{3} y^{2}+4 x y^{3}+y^{4}\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[_exact, _rational] |
✓ |
✓ |
2.685 |
|
|
\[ {}{\mathrm e}^{x} \sin \left (y\right )+\tan \left (y\right )+\left ({\mathrm e}^{x} \cos \left (y\right )+x \sec \left (y\right )^{2}\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_exact] |
✓ |
✓ |
24.46 |
|
|
\[ {}\frac {2 x}{y}-\frac {3 y^{2}}{x^{4}}+\left (-\frac {x^{2}}{y^{2}}+\frac {1}{\sqrt {y}}+\frac {2 y}{x^{3}}\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_exact, _rational] |
✓ |
✓ |
28.327 |
|
|
\[ {}\frac {2 x^{\frac {5}{2}}-3 y^{\frac {5}{3}}}{2 x^{\frac {5}{2}} y^{\frac {2}{3}}}+\frac {\left (-2 x^{\frac {5}{2}}+3 y^{\frac {5}{3}}\right ) y^{\prime }}{3 x^{\frac {3}{2}} y^{\frac {5}{3}}} = 0 \] |
1 |
1 |
6 |
[[_1st_order, _with_linear_symmetries], _exact, _rational] |
✓ |
✓ |
1.786 |
|
|
\[ {}3 y^{2}+x y^{2}-x^{2} y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.472 |
|
|
\[ {}{\mathrm e}^{x}+2 x y^{3}+\left (\sin \left (y\right )+3 x^{2} y^{2}\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_exact] |
✓ |
✓ |
4.056 |
|
|
\[ {}3 y+x^{4} y^{\prime } = 2 x y \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.549 |
|
|
\[ {}2 x y^{2}+x^{2} y^{\prime } = y^{2} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.87 |
|
|
\[ {}y^{\prime } = 1+x^{2}+y^{2}+x^{2} y^{2} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.974 |
|
|
\[ {}6 x y^{3}+2 y^{4}+\left (9 x^{2} y^{2}+8 x y^{3}\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
3.483 |
|
|
\[ {}3 y+y^{\prime } = 3 x^{2} {\mathrm e}^{-3 x} \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.836 |
|
|
\[ {}{\mathrm e}^{x}+{\mathrm e}^{x y} y+\left ({\mathrm e}^{y}+{\mathrm e}^{x y} x \right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_exact] |
✓ |
✓ |
3.445 |
|
|
\[ {}3 x^{5} y^{2}+x^{3} y^{\prime } = 2 y^{2} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.846 |
|
|
\[ {}{\mathrm e}^{y}+y \cos \left (x \right )+\left ({\mathrm e}^{y} x +\sin \left (x \right )\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_exact] |
✓ |
✓ |
39.608 |
|
|
\[ {}9 x^{2} y^{2}+x^{\frac {3}{2}} y^{\prime } = y^{2} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.177 |
|
|
\[ {}9 \sqrt {x}\, y^{\frac {4}{3}}-12 x^{\frac {1}{5}} y^{\frac {3}{2}}+\left (8 x^{\frac {3}{2}} y^{\frac {1}{3}}-15 x^{\frac {6}{5}} \sqrt {y}\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _exact, _rational] |
✓ |
✓ |
0.479 |
|
|
\[ {}x y^{\prime }+y = 2 \,{\mathrm e}^{2 x} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.766 |
|
|
\[ {}y^{\prime } = 3 x^{2} \left (7+y\right ) \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.994 |
|
|
\[ {}y^{\prime } = 3 x^{2} \left (7+y\right ) \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.671 |
|
|
\[ {}y^{\prime } = -x y+x y^{3} \] |
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 |
|
|
\[ {}y^{\prime } = \frac {x +3 y}{-3 x +y} \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.993 |
|
|
\[ {}y^{\prime } = \frac {2 x +2 x y}{x^{2}+1} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.07 |
|
|
\[ {}y^{\prime } = \cot \left (x \right ) \left (\sqrt {y}-y\right ) \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
7.763 |
|
|
\[ {}y+y^{\prime } = 1+t \,{\mathrm e}^{-t} \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.87 |
|
|
\[ {}\frac {y}{t}+y^{\prime } = 3 \cos \left (2 t \right ) \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.093 |
|
|
\[ {}2 t y+y^{\prime } = 2 t \,{\mathrm e}^{-t^{2}} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.909 |
|
|
\[ {}2 y+y^{\prime } = t \,{\mathrm e}^{-2 t} \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.334 |
|
|
\[ {}\frac {2 y}{t}+y^{\prime } = \frac {\cos \left (t \right )}{t^{2}} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.337 |
|
|
\[ {}\left (t +1\right ) y+t y^{\prime } = 2 t \,{\mathrm e}^{-t} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.252 |
|
|
\[ {}2 y+t y^{\prime } = \frac {\sin \left (t \right )}{t} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.239 |
|
|
\[ {}\cos \left (t \right ) y+\sin \left (t \right ) y^{\prime } = {\mathrm e}^{t} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
33.713 |
|
|
\[ {}y^{\prime } = \frac {x^{2}}{y} \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
1.209 |
|
|
\[ {}y^{\prime } = \frac {x^{2}}{\left (x^{3}+1\right ) y} \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
1.006 |
|
|
\[ {}\sin \left (x \right ) y^{2}+y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.796 |
|
|
\[ {}y^{\prime } = \frac {3 x^{2}-1}{3+2 y} \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
1.528 |
|
|
\[ {}y^{\prime } = \cos \left (x \right )^{2} \cos \left (2 y\right )^{2} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.35 |
|
|
\[ {}x y^{\prime } = \sqrt {1-y^{2}} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.28 |
|
|
\[ {}y^{\prime } = \frac {x^{2}}{1+y^{2}} \] |
1 |
1 |
3 |
[_separable] |
✓ |
✓ |
154.618 |
|
|
\[ {}y^{\prime } = \left (1-2 x \right ) y^{2} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.166 |
|
|
\[ {}y^{\prime } = \frac {1-2 x}{y} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
6.71 |
|
|
\[ {}x +y y^{\prime } {\mathrm e}^{-x} = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.847 |
|
|
\[ {}r^{\prime } = \frac {r^{2}}{x} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.269 |
|
|
\[ {}y^{\prime } = \frac {2 x}{y+x^{2} y} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.673 |
|
|
\[ {}y^{\prime } = \frac {x y^{2}}{\sqrt {x^{2}+1}} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.391 |
|
|
\[ {}y^{\prime } = \frac {2 x}{1+2 y} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
6.693 |
|
|
\[ {}y^{\prime } = \frac {x \left (x^{2}+1\right )}{4 y^{3}} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
3.85 |
|
|
\[ {}y^{\prime } = \frac {-{\mathrm e}^{x}+3 x^{2}}{-5+2 y} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.863 |
|
|
\[ {}y^{\prime } = \frac {{\mathrm e}^{-x}-{\mathrm e}^{x}}{3+4 y} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.872 |
|
|
\[ {}\sin \left (2 x \right )+\cos \left (3 y\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
10.198 |
|
|
\[ {}\sqrt {-x^{2}+1}\, y^{2} y^{\prime } = \arcsin \left (x \right ) \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
3.728 |
|
|
\[ {}y^{\prime } = \frac {3 x^{2}+1}{-6 y+3 y^{2}} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
3.06 |
|
|
\[ {}y^{\prime } = \frac {3 x^{2}}{-4+3 y^{2}} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
78.154 |
|
|
\[ {}y^{\prime } = 2 y^{2}+x y^{2} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.219 |
|
|
\[ {}y^{\prime } = \frac {2-{\mathrm e}^{x}}{3+2 y} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.759 |
|
|
\[ {}y^{\prime } = \frac {2 \cos \left (2 x \right )}{3+2 y} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.18 |
|
|
\[ {}y^{\prime } = 2 \left (1+x \right ) \left (1+y^{2}\right ) \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.824 |
|
|
\[ {}y^{\prime } = \frac {t \left (4-y\right ) y}{3} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.697 |
|
|
\[ {}y^{\prime } = \frac {t y \left (4-y\right )}{t +1} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.964 |
|
|
\[ {}y+\left (t -4\right ) t y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.551 |
|
|
\[ {}y^{\prime } = \frac {t^{2}+1}{3 y-y^{2}} \] |
1 |
1 |
3 |
[_separable] |
✓ |
✓ |
168.757 |
|
|
\[ {}y^{\prime } = \frac {\cot \left (t \right ) y}{y+1} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.37 |
|
|
\[ {}y^{\prime } = -\frac {4 t}{y} \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
1.775 |
|
|
\[ {}y^{\prime } = 2 t y^{2} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.711 |
|
|
\[ {}y^{\prime } = \frac {t^{2}}{\left (t^{3}+1\right ) y} \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
1.052 |
|
|
\[ {}y^{\prime } = t \left (3-y\right ) y \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.431 |
|
|
\[ {}3+2 x +\left (-2+2 y\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
2.759 |
|
|
\[ {}2+3 x^{2}-2 x y+\left (3-x^{2}+6 y^{2}\right ) y^{\prime } = 0 \] |
1 |
1 |
3 |
[_exact, _rational] |
✓ |
✓ |
18.126 |
|
|
\[ {}2 y+2 x y^{2}+\left (2 x +2 x^{2} y\right ) y^{\prime } = 0 \] |
1 |
1 |
3 |
[_separable] |
✓ |
✓ |
1.071 |
|
|
\[ {}y^{\prime } = \frac {-x a -b y}{b x +c y} \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.531 |
|
|
\[ {}{\mathrm e}^{x} \sin \left (y\right )-2 y \sin \left (x \right )+\left (2 \cos \left (x \right )+{\mathrm e}^{x} \cos \left (y\right )\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_exact] |
✓ |
✓ |
10.509 |
|
|
\[ {}2 x -2 \,{\mathrm e}^{x y} \sin \left (2 x \right )+{\mathrm e}^{x y} \cos \left (2 x \right ) y+\left (-3+{\mathrm e}^{x y} x \cos \left (2 x \right )\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_exact] |
✓ |
✓ |
9.246 |
|
|
\[ {}\frac {y}{x}+6 x +\left (\ln \left (x \right )-2\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.185 |
|
|
\[ {}\frac {x}{\left (x^{2}+y^{2}\right )^{\frac {3}{2}}}+\frac {y y^{\prime }}{\left (x^{2}+y^{2}\right )^{\frac {3}{2}}} = 0 \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
2.527 |
|
|
\[ {}2 x -y+\left (2 y-x \right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
4.914 |
|
|
\[ {}-1+9 x^{2}+y+\left (x -4 y\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
8.075 |
|
|
\[ {}x^{2} y^{3}+x \left (1+y^{2}\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.512 |
|
|
\[ {}\left (2+x \right ) \sin \left (y\right )+x \cos \left (y\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.997 |
|
|
\[ {}1+\left (-\sin \left (y\right )+\frac {x}{y}\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
2.234 |
|
|
\[ {}\frac {4 x^{3}}{y^{2}}+\frac {3}{y}+\left (\frac {3 x}{y^{2}}+4 y\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_rational] |
✓ |
✓ |
2.105 |
|
|
\[ {}3 x +\frac {6}{y}+\left (\frac {x^{2}}{y}+\frac {3 y}{x}\right ) y^{\prime } = 0 \] |
1 |
1 |
3 |
[_rational] |
✓ |
✓ |
14.87 |
|
|
\[ {}y^{\prime } = \frac {\cos \left (x \right )+1}{2-\sin \left (y\right )} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
3.089 |
|
|
\[ {}y^{\prime } = \frac {y+2 x}{3-x +3 y^{2}} \] |
1 |
1 |
1 |
[_rational] |
✓ |
✓ |
280.432 |
|
|
\[ {}y^{\prime } = 3-6 x +y-2 x y \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.21 |
|
|
\[ {}y^{\prime } = \frac {-1-2 x y-y^{2}}{x^{2}+2 x y} \] |
1 |
1 |
2 |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
1.851 |
|
|
\[ {}y^{\prime } = \frac {4 x^{3}+1}{y \left (2+3 y\right )} \] |
1 |
1 |
3 |
[_separable] |
✓ |
✓ |
89.541 |
|
|
\[ {}x y^{\prime }+2 y = \frac {\sin \left (x \right )}{x} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.504 |
|
|
\[ {}y^{\prime } = \frac {-1-2 x y}{x^{2}+2 y} \] |
1 |
1 |
2 |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.277 |
|
|
\[ {}\frac {-x^{2}+x +1}{x^{2}}+\frac {y y^{\prime }}{-2+y} = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.885 |
|
|
\[ {}x^{2}+y+\left ({\mathrm e}^{y}+x \right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_exact] |
✓ |
✓ |
3.525 |
|
|
\[ {}y^{\prime } = 1+2 x +y^{2}+2 x y^{2} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.109 |
|
|
\[ {}x +y+\left (2 y+x \right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
6.832 |
|
|
\[ {}\left (1+{\mathrm e}^{x}\right ) y^{\prime } = y-{\mathrm e}^{x} y \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.78 |
|
|
\[ {}y^{\prime } = \frac {3 x^{2}-2 y-y^{3}}{2 x +3 x y^{2}} \] |
1 |
1 |
3 |
[_rational] |
✓ |
✓ |
2.016 |
|
|
\[ {}y^{\prime } = {\mathrm e}^{x +y} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.915 |
|
|
\[ {}\frac {-4+6 x y+2 y^{2}}{3 x^{2}+4 x y+3 y^{2}}+y^{\prime } = 0 \] |
1 |
1 |
3 |
[_rational] |
✓ |
✓ |
2.35 |
|
|
\[ {}y^{\prime } = \frac {x^{2}-1}{1+y^{2}} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
67.306 |
|
|
\[ {}2 \cos \left (x \right ) \sin \left (x \right ) \sin \left (y\right )+\cos \left (y\right ) \sin \left (x \right )^{2} y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
3.416 |
|
|
\[ {}\frac {2 x}{y}-\frac {y}{x^{2}+y^{2}}+\left (-\frac {x^{2}}{y^{2}}+\frac {x}{x^{2}+y^{2}}\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_exact, _rational] |
✓ |
✓ |
2.711 |
|
|
\[ {}x y^{\prime }+y = x^{2} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.024 |
|
|
\[ {}2 x y+y^{\prime } = x \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.45 |
|
|
\[ {}2 y^{\prime }+x \left (y^{2}-1\right ) = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.173 |
|
|
\[ {}y^{\prime } = x^{2} \left (1+y^{2}\right ) \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.995 |
|
|
\[ {}y^{\prime } = x \left (1+y^{2}\right ) \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.637 |
|
|
\[ {}y^{\prime } = -\frac {y \left (y+1\right )}{x} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.308 |
|
|
\[ {}y^{\prime }+3 x^{2} y = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.029 |
|
|
\[ {}x y^{\prime }+y \ln \left (x \right ) = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.622 |
|
|
\[ {}x y^{\prime }+3 y = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.262 |
|
|
\[ {}x^{2} y^{\prime }+y = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.134 |
|
|
\[ {}y^{\prime }+\frac {\left (1+x \right ) y}{x} = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.648 |
|
|
\[ {}x y^{\prime }+\left (1+\frac {1}{\ln \left (x \right )}\right ) y = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.164 |
|
|
\[ {}x y^{\prime }+\left (1+x \cot \left (x \right )\right ) y = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.635 |
|
|
\[ {}y^{\prime }-\frac {2 x y}{x^{2}+1} = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.544 |
|
|
\[ {}y^{\prime }+\frac {k y}{x} = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.545 |
|
|
\[ {}y^{\prime }+\tan \left (k x \right ) y = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.376 |
|
|
\[ {}y^{\prime }+\frac {2 x y}{x^{2}+1} = \frac {{\mathrm e}^{-x^{2}}}{x^{2}+1} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.169 |
|
|
\[ {}\left (1+x \right ) y^{\prime }+2 y = \frac {\sin \left (x \right )}{1+x} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
3.65 |
|
|
\[ {}4 x y+\left (x^{2}+1\right ) y^{\prime } = \frac {2}{x^{2}+1} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.988 |
|
|
\[ {}2 x y+y^{\prime } = x \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.916 |
|
|
\[ {}x y^{\prime }-2 y = -1 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.029 |
|
|
\[ {}{\mathrm e}^{y^{2}} \left (2 y y^{\prime }+\frac {2}{x}\right ) = \frac {1}{x^{2}} \] |
1 |
1 |
2 |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
2.338 |
|
|
\[ {}y^{\prime } = \frac {3 x^{2}+2 x +1}{-2+y} \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
1.806 |
|
|
\[ {}\sin \left (x \right ) \sin \left (y\right )+\cos \left (y\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
3.586 |
|
|
\[ {}x y^{\prime }+y^{2}+y = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.447 |
|
|
\[ {}\left (3 y^{3}+3 \cos \left (y\right ) y+1\right ) y^{\prime }+\frac {\left (2 x +1\right ) y}{x^{2}+1} = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
8.067 |
|
|
\[ {}x^{2} y y^{\prime } = \left (y^{2}-1\right )^{\frac {3}{2}} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.878 |
|
|
\[ {}y^{\prime } = x^{2} \left (1+y^{2}\right ) \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.918 |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime }+x y = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.148 |
|
|
\[ {}y^{\prime } = \left (-1+x \right ) \left (y-1\right ) \left (-2+y\right ) \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.982 |
|
|
\[ {}\left (y-1\right )^{2} y^{\prime } = 2 x +3 \] |
1 |
1 |
3 |
[_separable] |
✓ |
✓ |
21.325 |
|
|
\[ {}y^{\prime } = \frac {x^{2}+3 x +2}{-2+y} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
3.9 |
|
|
\[ {}y^{\prime }+x \left (y^{2}+y\right ) = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.972 |
|
|
\[ {}\left (3 y^{2}+4 y\right ) y^{\prime }+2 x +\cos \left (x \right ) = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
5.135 |
|
|
\[ {}y^{\prime }+\frac {\left (y+1\right ) \left (y-1\right ) \left (-2+y\right )}{1+x} = 0 \] |
1 |
1 |
3 |
[_separable] |
✓ |
✓ |
37.897 |
|
|
\[ {}y^{\prime }+2 x \left (y+1\right ) = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.951 |
|
|
\[ {}y^{\prime } = 2 x y \left (1+y^{2}\right ) \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
10.752 |
|
|
\[ {}y^{\prime } \left (x^{2}+2\right ) = 4 x \left (y^{2}+2 y+1\right ) \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.424 |
|
|
\[ {}y^{\prime } = -2 x \left (y^{3}-3 y+2\right ) \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
3.414 |
|
|
\[ {}y^{\prime } = \frac {2 x}{1+2 y} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
4.329 |
|
|
\[ {}x +y y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
4.77 |
|
|
\[ {}y^{\prime }+x^{2} \left (y+1\right ) \left (-2+y\right )^{2} = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
3.463 |
|
|
\[ {}\left (1+x \right ) \left (-2+x \right ) y^{\prime }+y = 0 \] |
1 |
0 |
1 |
[_separable] |
✓ |
✓ |
2.488 |
|
|
\[ {}y^{\prime } = \frac {1+y^{2}}{x^{2}+1} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.064 |
|
|
\[ {}y^{\prime } \sqrt {-x^{2}+1}+\sqrt {1-y^{2}} = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.605 |
|
|
\[ {}y^{\prime } = \frac {\cos \left (x \right )}{\sin \left (y\right )} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.337 |
|
|
\[ {}y^{\prime } = 2 x y \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.059 |
|
|
\[ {}y^{\prime } = x \left (y^{2}-1\right )^{\frac {2}{3}} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.925 |
|
|
\[ {}y^{\prime } = \frac {\tan \left (y\right )}{-1+x} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.345 |
|
|
\[ {}y^{\prime } = 3 x \left (y-1\right )^{\frac {1}{3}} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.097 |
|
|
\[ {}y^{\prime } = 3 x \left (y-1\right )^{\frac {1}{3}} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.101 |
|
|
\[ {}y^{\prime } = 3 x \left (y-1\right )^{\frac {1}{3}} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
3.917 |
|
|
\[ {}y^{\prime }-x y = x y^{\frac {3}{2}} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
6.904 |
|
|
\[ {}6 x^{2} y^{2}+4 x^{3} y y^{\prime } = 0 \] |
1 |
1 |
3 |
[_separable] |
✓ |
✓ |
1.474 |
|
|
\[ {}2 x -2 y^{2}+\left (12 y^{2}-4 x y\right ) y^{\prime } = 0 \] |
1 |
1 |
3 |
[_exact, _rational] |
✓ |
✓ |
2.083 |
|
|
\[ {}-2 \sin \left (x \right ) y^{2}+3 y^{3}-2 x +\left (4 y \cos \left (x \right )+9 x y^{2}\right ) y^{\prime } = 0 \] |
1 |
1 |
3 |
[_exact] |
✓ |
✓ |
35.72 |
|
|
\[ {}3 x^{2}+2 x y+4 y^{2}+\left (x^{2}+8 x y+18 y\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[_exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
2.122 |
|
|
\[ {}\frac {1}{x}+2 x +\left (\frac {1}{y}+2 y\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.542 |
|
|
\[ {}\frac {x}{\left (x^{2}+y^{2}\right )^{\frac {3}{2}}}+\frac {y y^{\prime }}{\left (x^{2}+y^{2}\right )^{\frac {3}{2}}} = 0 \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
3.012 |
|
|
\[ {}{\mathrm e}^{x} \left (x^{2} y^{2}+2 x y^{2}\right )+6 x +\left (2 x^{2} y \,{\mathrm e}^{x}+2\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[_exact, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
2.899 |
|
|
\[ {}x^{2} {\mathrm e}^{y+x^{2}} \left (2 x^{2}+3\right )+4 x +\left (x^{3} {\mathrm e}^{y+x^{2}}-12 y^{2}\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_exact] |
✓ |
✓ |
3.645 |
|
|
\[ {}{\mathrm e}^{x y} \left (x^{4} y+4 x^{3}\right )+3 y+\left (x^{5} {\mathrm e}^{x y}+3 x \right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_exact, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
16.681 |
|
|
\[ {}4 x^{3} y^{2}-6 x^{2} y-2 x -3+\left (2 x^{4} y-2 x^{3}\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
2.983 |
|
|
\[ {}-4 y \cos \left (x \right )+4 \sin \left (x \right ) \cos \left (x \right )+\sec \left (x \right )^{2}+\left (4 y-4 \sin \left (x \right )\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_exact, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
8.937 |
|
|
\[ {}\left (y^{3}-1\right ) {\mathrm e}^{x}+3 y^{2} \left (1+{\mathrm e}^{x}\right ) y^{\prime } = 0 \] |
1 |
1 |
3 |
[_separable] |
✓ |
✓ |
5.071 |
|
|
\[ {}\sin \left (x \right )-y \sin \left (x \right )-2 \cos \left (x \right )+\cos \left (x \right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
2.128 |
|
|
\[ {}\left (2 x -1\right ) \left (y-1\right )+\left (2+x \right ) \left (x -3\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.746 |
|
|
\[ {}7 x +4 y+\left (4 x +3 y\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
3.935 |
|
|
\[ {}{\mathrm e}^{x} \left (x^{4} y^{2}+4 x^{3} y^{2}+1\right )+\left (2 x^{4} y \,{\mathrm e}^{x}+2 y\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[_exact, _Bernoulli] |
✓ |
✓ |
2.301 |
|
|
\[ {}x^{3} y^{4}+x +\left (x^{4} y^{3}+y\right ) y^{\prime } = 0 \] |
1 |
1 |
4 |
[_exact, _rational] |
✓ |
✓ |
2.538 |
|
|
\[ {}3 x^{2}+2 y+\left (2 y+2 x \right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.579 |
|
|
\[ {}x^{3} y^{4}+2 x +\left (x^{4} y^{3}+3 y\right ) y^{\prime } = 0 \] |
1 |
1 |
4 |
[_exact, _rational] |
✓ |
✓ |
2.586 |
|
|
\[ {}x^{2}+y^{2}+2 x y y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
2.431 |
|
|
\[ {}y+\left (2 x +\frac {1}{y}\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
2.641 |
|
|
\[ {}-y^{2}+x^{2} y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.15 |
|
|
\[ {}y-x y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.003 |
|
|
\[ {}3 x^{2} y+2 x^{3} y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.039 |
|
|
\[ {}x^{2} y+4 x y+2 y+\left (x^{2}+x \right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.771 |
|
|
\[ {}-y+\left (x^{4}-x \right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.483 |
|
|
\[ {}y \sin \left (y\right )+x \left (\sin \left (y\right )-\cos \left (y\right ) y\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
4.327 |
|
|
\[ {}a y+b x y+\left (c x +d x y\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.798 |
|
|
\[ {}2 y+3 \left (x^{2}+x^{2} y^{3}\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.284 |
|
|
\[ {}x^{4} y^{4}+x^{5} y^{3} y^{\prime } = 0 \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
1.446 |
|
|
\[ {}y \left (x \cos \left (x \right )+2 \sin \left (x \right )\right )+x \left (y+1\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
3.591 |
|
|
\[ {}\cos \left (t \right ) y+y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.659 |
|
|
\[ {}\sqrt {t}\, \sin \left (t \right ) y+y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.694 |
|
|
\[ {}\frac {2 t y}{t^{2}+1}+y^{\prime } = \frac {1}{t^{2}+1} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.358 |
|
|
\[ {}t^{2} y+y^{\prime } = t^{2} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.554 |
|
|
\[ {}\sqrt {t^{2}+1}\, y+y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.88 |
|
|
\[ {}\sqrt {t^{2}+1}\, y \,{\mathrm e}^{-t}+y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.794 |
|
|
\[ {}y^{\prime }-2 t y = t \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.138 |
|
|
\[ {}4 t y+\left (t^{2}+1\right ) y^{\prime } = t \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.663 |
|
|
\[ {}\left (t^{2}+1\right ) y^{\prime } = 1+y^{2} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.366 |
|
|
\[ {}y^{\prime } = \left (t +1\right ) \left (y+1\right ) \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.266 |
|
|
\[ {}y^{\prime } = 1-t +y^{2}-t y^{2} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.581 |
|
|
\[ {}y^{\prime } = {\mathrm e}^{3+t +y} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.211 |
|
|
\[ {}\cos \left (y\right ) \sin \left (t \right ) y^{\prime } = \cos \left (t \right ) \sin \left (y\right ) \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
35.884 |
|
|
\[ {}t^{2} \left (1+y^{2}\right )+2 y y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
4.361 |
|
|
\[ {}y^{\prime } = \frac {2 t}{y+t^{2} y} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.757 |
|
|
\[ {}\sqrt {t^{2}+1}\, y^{\prime } = \frac {t y^{3}}{\sqrt {t^{2}+1}} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.577 |
|
|
\[ {}y^{\prime } = \frac {3 t^{2}+4 t +2}{-2+2 y} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
5.778 |
|
|
\[ {}\cos \left (y\right ) y^{\prime } = -\frac {t \sin \left (y\right )}{t^{2}+1} \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
5.118 |
|
|
\[ {}3 t y^{\prime } = \cos \left (t \right ) y \] |
1 |
0 |
1 |
[_separable] |
✓ |
✓ |
3.656 |
|
|
\[ {}t +2 y+3+\left (2 t +4 y-1\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.261 |
|
|
\[ {}2 t \sin \left (y\right )+{\mathrm e}^{t} y^{3}+\left (t^{2} \cos \left (y\right )+3 \,{\mathrm e}^{t} y^{2}\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_exact] |
✓ |
✓ |
5.098 |
|
|
\[ {}1+{\mathrm e}^{t y} \left (1+t y\right )+\left (1+{\mathrm e}^{t y} t^{2}\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_exact] |
✓ |
✓ |
2.973 |
|
|
\[ {}\sec \left (t \right ) \tan \left (t \right )+\sec \left (t \right )^{2} y+\left (\tan \left (t \right )+2 y\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[_exact, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
24.539 |
|
|
\[ {}2 t y^{3}+3 t^{2} y^{2} y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.492 |
|
|
\[ {}2 t \cos \left (y\right )+3 t^{2} y+\left (t^{3}-t^{2} \sin \left (y\right )-y\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_exact] |
✓ |
✓ |
3.773 |
|
|
\[ {}3 t^{2}+4 t y+\left (2 t^{2}+2 y\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
4.358 |
|
|
\[ {}2 t -2 \,{\mathrm e}^{t y} \sin \left (2 t \right )+{\mathrm e}^{t y} \cos \left (2 t \right ) y+\left (-3+{\mathrm e}^{t y} t \cos \left (2 t \right )\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_exact] |
✓ |
✓ |
9.996 |
|
|
\[ {}y^{\prime } = t \left (y+1\right ) \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.227 |
|
|
\[ {}y^{\prime } = t \sqrt {1-y^{2}} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.516 |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime }+x y = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.477 |
|
|
\[ {}x y^{2}+x +\left (y-x^{2} y\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
6.561 |
|
|
\[ {}1+y^{2}+\left (x^{2}+1\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.349 |
|
|
\[ {}x y^{\prime }+y = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.438 |
|
|
\[ {}y^{\prime } = 2 x y \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.27 |
|
|
\[ {}x y^{2}+x +\left (x^{2} y-y\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
4.193 |
|
|
\[ {}\sqrt {-x^{2}+1}+\sqrt {1-y^{2}}\, y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
3.84 |
|
|
\[ {}\left (1+x \right ) y^{\prime }-1+y = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.157 |
|
|
\[ {}\tan \left (x \right ) y^{\prime }-y = 1 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.954 |
|
|
\[ {}y+3+\cot \left (x \right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.181 |
|
|
\[ {}y^{\prime } = \frac {x}{y} \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
2.742 |
|
|
\[ {}x y^{\prime }+y = y^{2} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
3.193 |
|
|
\[ {}\sin \left (x \right ) \cos \left (y\right )^{2}+\cos \left (x \right )^{2} y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
3.836 |
|
|
\[ {}\sec \left (x \right ) \cos \left (y\right )^{2} = \cos \left (x \right ) \sin \left (y\right ) y^{\prime } \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
11.779 |
|
|
\[ {}x y^{\prime }+y = x y \left (y^{\prime }-1\right ) \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.763 |
|
|
\[ {}x y+\sqrt {x^{2}+1}\, y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.79 |
|
|
\[ {}y = x y+x^{2} y^{\prime } \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.965 |
|
|
\[ {}\tan \left (x \right ) \sin \left (x \right )^{2}+\cos \left (x \right )^{2} \cot \left (y\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
21.288 |
|
|
\[ {}y^{2}+y y^{\prime }+x^{2} y y^{\prime }-1 = 0 \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
3.517 |
|
|
\[ {}y^{\prime } = \frac {y}{x} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.68 |
|
|
\[ {}x y^{\prime }+2 y = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.239 |
|
|
\[ {}\sin \left (x \right ) \cos \left (y\right )+\cos \left (x \right ) \sin \left (y\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
5.179 |
|
|
\[ {}x^{2} y^{\prime }+y^{2} = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.876 |
|
|
\[ {}1+y^{2} = \frac {y^{\prime }}{x^{3} \left (-1+x \right )} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
3.212 |
|
|
\[ {}\left (x^{2}+x +1\right ) y^{\prime } = y^{2}+2 y+5 \] |
1 |
0 |
1 |
[_separable] |
✓ |
✓ |
22.352 |
|
|
\[ {}\left (x^{2}-2 x -8\right ) y^{\prime } = y^{2}+y-2 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
8.253 |
|
|
\[ {}y^{\prime } = \frac {2 x -y}{x +4 y} \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
4.781 |
|
|
\[ {}x +y+\left (x -y\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
3.725 |
|
|
\[ {}x -y+\left (-x +y+1\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.164 |
|
|
\[ {}x +y+\left (x -2 y\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
4.179 |
|
|
\[ {}3 x +y+\left (x +3 y\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
4.376 |
|
|
\[ {}a_{1} x +b_{1} y+c_{1} +\left (b_{1} x +b_{2} y+c_{2} \right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.795 |
|
|
\[ {}x \left (6 x y+5\right )+\left (2 x^{3}+3 y\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
3.313 |
|
|
\[ {}3 x^{2} y+x y^{2}+{\mathrm e}^{x}+\left (x^{3}+x^{2} y+\sin \left (y\right )\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_exact] |
✓ |
✓ |
3.523 |
|
|
\[ {}y \cos \left (x \right )-2 \sin \left (y\right ) = \left (2 x \cos \left (y\right )-\sin \left (x \right )\right ) y^{\prime } \] |
1 |
1 |
1 |
[_exact] |
✓ |
✓ |
16.003 |
|
|
\[ {}\frac {2 x y-1}{y}+\frac {\left (x +3 y\right ) y^{\prime }}{y^{2}} = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.958 |
|
|
\[ {}{\mathrm e}^{x} y-2 x +{\mathrm e}^{x} y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.329 |
|
|
\[ {}3 y \sin \left (x \right )-\cos \left (y\right )+\left (\sin \left (y\right ) x -3 \cos \left (x \right )\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_exact] |
✓ |
✓ |
27.461 |
|
|
\[ {}\frac {2}{y}-\frac {y}{x^{2}}+\left (\frac {1}{x}-\frac {2 x}{y^{2}}\right ) y^{\prime } = 0 \] |
1 |
1 |
4 |
[_separable] |
✓ |
✓ |
1.707 |
|
|
\[ {}\frac {x y+1}{y}+\frac {\left (2 y-x \right ) y^{\prime }}{y^{2}} = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.969 |
|
|
\[ {}\frac {y \left (2+x^{3} y\right )}{x^{3}} = \frac {\left (1-2 x^{3} y\right ) y^{\prime }}{x^{2}} \] |
1 |
1 |
2 |
[[_homogeneous, ‘class G‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
4.761 |
|
|
\[ {}y^{2} \csc \left (x \right )^{2}+6 x y-2 = \left (2 y \cot \left (x \right )-3 x^{2}\right ) y^{\prime } \] |
1 |
1 |
2 |
[_exact, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
58.102 |
|
|
\[ {}\frac {2 y}{x^{3}}+\frac {2 x}{y^{2}} = \left (\frac {1}{x^{2}}+\frac {2 x^{2}}{y^{3}}\right ) y^{\prime } \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _exact, _rational] |
✓ |
✓ |
5.387 |
|
|
\[ {}\cos \left (y\right )-\left (\sin \left (y\right ) x -y^{2}\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_exact, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
19.427 |
|
|
\[ {}2 y \sin \left (x y\right )+\left (2 x \sin \left (x y\right )+y^{3}\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_exact] |
✓ |
✓ |
88.614 |
|
|
\[ {}\frac {x \cos \left (\frac {x}{y}\right )}{y}+\sin \left (\frac {x}{y}\right )+\cos \left (x \right )-\frac {x^{2} \cos \left (\frac {x}{y}\right ) y^{\prime }}{y^{2}} = 0 \] |
1 |
1 |
1 |
[_exact] |
✓ |
✓ |
6.221 |
|
|
\[ {}{\mathrm e}^{x y} y+2 x y+\left ({\mathrm e}^{x y} x +x^{2}\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_exact] |
✓ |
✓ |
5.852 |
|
|
\[ {}\frac {x^{2}+3 y^{2}}{x \left (3 x^{2}+4 y^{2}\right )}+\frac {\left (2 x^{2}+y^{2}\right ) y^{\prime }}{y \left (3 x^{2}+4 y^{2}\right )} = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
18.233 |
|
|
\[ {}\frac {x^{2}-y^{2}}{x \left (2 x^{2}+y^{2}\right )}+\frac {\left (x^{2}+2 y^{2}\right ) y^{\prime }}{y \left (2 x^{2}+y^{2}\right )} = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
23.792 |
|
|
\[ {}\frac {2 x^{2}}{x^{2}+y^{2}}+\ln \left (x^{2}+y^{2}\right )+\frac {2 x y y^{\prime }}{x^{2}+y^{2}} = 0 \] |
1 |
1 |
2 |
[_exact] |
✓ |
✓ |
3.178 |
|
|
\[ {}\left (x -2 x y\right ) y^{\prime }+2 y = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.566 |
|
|
\[ {}y \left (x^{2}-1\right )+x \left (x^{2}+1\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.358 |
|
|
\[ {}\left (1+x \right ) y^{\prime }+2 y = \frac {{\mathrm e}^{x}}{1+x} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.405 |
|
|
\[ {}y^{2}+1+\left (2 x y-y^{2}\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
7.053 |
|
|
\[ {}y^{\prime }-x y = \frac {x}{y} \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
2.956 |
|
|
\[ {}r^{\prime }+\left (r-\frac {1}{r}\right ) \theta = 0 \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
4.374 |
|
|
\[ {}\cos \left (y\right ) y^{\prime }+\left (\sin \left (y\right )-1\right ) \cos \left (x \right ) = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
40.737 |
|
|
\[ {}\left (1-x \right ) y^{\prime }-y-1 = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.467 |
|
|
\[ {}2 x y-2 x y^{3}+x^{3}+\left (x^{2}+y^{2}-3 x^{2} y^{2}\right ) y^{\prime } = 0 \] |
1 |
1 |
3 |
[_exact, _rational] |
✓ |
✓ |
2.935 |
|
|
\[ {}6+2 y = x y y^{\prime } \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
4.969 |
|
|
\[ {}y \sin \left (x \right )-2 \cos \left (y\right )+\tan \left (x \right )-\left (\cos \left (x \right )-2 \sin \left (y\right ) x +\sin \left (y\right )\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_exact] |
✓ |
✓ |
39.367 |
|
|
\[ {}y-x y^{\prime } = 2 y^{2}+2 y^{\prime } \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
4.532 |
|
|
\[ {}\tan \left (y\right ) = \left (3 x +4\right ) y^{\prime } \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
3.477 |
|
|
\[ {}r^{\prime } = r \cot \left (\theta \right ) \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.394 |
|
|
\[ {}y^{\prime } = \cos \left (y\right ) \cos \left (x \right )^{2} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
5.968 |
|
|
\[ {}1+{\mathrm e}^{\frac {x}{y}}+{\mathrm e}^{\frac {x}{y}} \left (1-\frac {x}{y}\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _exact, _dAlembert] |
✓ |
✓ |
3.323 |
|
|
\[ {}-6+3 x = x y y^{\prime } \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
1.77 |
|
|
\[ {}x -2 x y+{\mathrm e}^{y}+\left (y-x^{2}+{\mathrm e}^{y} x \right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_exact] |
✓ |
✓ |
3.02 |
|
|
\[ {}x y^{\prime }+y \left (1+y^{2}\right ) = 0 \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
5.533 |
|
|
\[ {}3 \,{\mathrm e}^{x} \tan \left (y\right ) = \left (-{\mathrm e}^{x}+1\right ) \sec \left (y\right )^{2} y^{\prime } \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
7.693 |
|
|
\[ {}2 x \tan \left (y\right )+3 y^{2}+x^{2}+\left (x^{2} \sec \left (y\right )^{2}+6 x y-y^{2}\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_exact] |
✓ |
✓ |
72.064 |
|
|
\[ {}x \sqrt {1-y}-y^{\prime } \sqrt {-x^{2}+1} = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
6.065 |
|
|
\[ {}x \,{\mathrm e}^{-y^{2}}+y y^{\prime } = 0 \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
2.505 |
|
|
\[ {}\frac {2 y^{3}-2 x^{2} y^{3}-x +x y^{2} \ln \left (y\right )}{x y^{2}}+\frac {\left (2 y^{3} \ln \left (x \right )-x^{2} y^{3}+2 x +x y^{2}\right ) y^{\prime }}{y^{3}} = 0 \] |
1 |
1 |
1 |
[_exact] |
✓ |
✓ |
10.904 |
|
|
\[ {}4 x y^{2}+\left (x^{2}+1\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.096 |
|
|
\[ {}2 \left (x^{2}+1\right ) y^{\prime } = \left (2 y^{2}-1\right ) x y \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
12.092 |
|
|
\[ {}y^{\prime } = x y \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.436 |
|
|
\[ {}y^{\prime } = x^{2} y^{2} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.388 |
|
|
\[ {}y^{\prime } = -{\mathrm e}^{y} x \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.436 |
|
|
\[ {}y^{\prime } \sin \left (y\right ) = x^{2} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.825 |
|
|
\[ {}x y^{\prime } = \sqrt {1-y^{2}} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.892 |
|
|
\[ {}y^{\prime } = \frac {{\mathrm e}^{t}}{y} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.207 |
|
|
\[ {}y^{\prime } = \frac {y}{t} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.388 |
|
|
\[ {}y^{\prime } = -\frac {t}{y} \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
0.953 |
|
|
\[ {}y^{\prime } = \left (t^{2}+1\right ) y \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.48 |
|
|
\[ {}y^{\prime } = \frac {2 y}{t +1} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.977 |
|
|
\[ {}t y^{\prime } = -y+t^{3} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.793 |
|
|
\[ {}y^{\prime }-x y^{3} = 0 \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
0.509 |
|
|
\[ {}\frac {y^{\prime }}{\tan \left (x \right )}-\frac {y}{x^{2}+1} = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.223 |
|
|
\[ {}x^{2} y^{\prime }+x y^{2} = 4 y^{2} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.536 |
|
|
\[ {}y \left (2 x^{2} y^{2}+1\right ) y^{\prime }+x \left (y^{4}+1\right ) = 0 \] |
1 |
1 |
4 |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
1.227 |
|
|
\[ {}y^{\prime } = \tan \left (x \right ) \cos \left (y\right ) \left (\cos \left (y\right )+\sin \left (y\right )\right ) \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.569 |
|
|
\[ {}x \left (1-2 x^{2} y\right ) y^{\prime }+y = 3 x^{2} y^{2} \] |
1 |
1 |
2 |
[[_homogeneous, ‘class G‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
1.697 |
|
|
\[ {}y^{\prime } = \frac {4 y^{2}}{x^{2}}-y^{2} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.487 |
|
|
\[ {}y^{\prime } = 2 x y \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.505 |
|
|
\[ {}y^{\prime } = \frac {y^{2}}{x^{2}+1} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.513 |
|
|
\[ {}{\mathrm e}^{x +y} y^{\prime }-1 = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.407 |
|
|
\[ {}y^{\prime } = \frac {y}{x \ln \left (x \right )} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.674 |
|
|
\[ {}y-\left (-2+x \right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.615 |
|
|
\[ {}y^{\prime } = \frac {2 x \left (y-1\right )}{x^{2}+3} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.744 |
|
|
\[ {}y-x y^{\prime } = 3-2 x^{2} y^{\prime } \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.659 |
|
|
\[ {}y^{\prime } = \frac {\cos \left (x -y\right )}{\sin \left (x \right ) \sin \left (y\right )}-1 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
36.244 |
|
|
\[ {}y^{\prime } = \frac {x \left (y^{2}-1\right )}{2 \left (-2+x \right ) \left (-1+x \right )} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.073 |
|
|
\[ {}\left (x -a \right ) \left (x -b \right ) y^{\prime }-y+c = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.233 |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime }+y^{2} = -1 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.069 |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime }+x y = x a \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.399 |
|
|
\[ {}y^{\prime } = 1-\frac {\sin \left (x +y\right )}{\sin \left (y\right ) \cos \left (x \right )} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
36.764 |
|
|
\[ {}y^{\prime } = y^{3} \sin \left (x \right ) \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
0.524 |
|
|
\[ {}y^{\prime }+\frac {2 x y}{x^{2}+1} = 4 x \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.722 |
|
|
\[ {}y^{\prime } = \frac {y}{2 x} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.488 |
|
|
\[ {}y^{\prime } = \frac {{\mathrm e}^{x}-\sin \left (y\right )}{x \cos \left (y\right )} \] |
1 |
1 |
1 |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
1.505 |
|
|
\[ {}y^{\prime } = \frac {1-y^{2}}{2 x y+2} \] |
1 |
1 |
1 |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
1.023 |
|
|
\[ {}y^{\prime } = \frac {\left (1-{\mathrm e}^{x y} y\right ) {\mathrm e}^{-x y}}{x} \] |
1 |
1 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
1.167 |
|
|
\[ {}y^{\prime } = \frac {\cos \left (x \right )-2 x y^{2}}{2 x^{2} y} \] |
1 |
1 |
1 |
[_Bernoulli] |
✓ |
✓ |
33.947 |
|
|
\[ {}y^{\prime } = \frac {\cos \left (x -y\right )}{\sin \left (x \right ) \sin \left (y\right )}-1 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.547 |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime }+x y = x a \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.208 |
|
|
\[ {}y^{\prime } = 1-\frac {\sin \left (x +y\right )}{\sin \left (y\right ) \cos \left (x \right )} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.422 |
|
|
\[ {}y^{\prime }+\frac {y}{x} = \cos \left (x \right ) \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.568 |
|
|
\[ {}\left (1-\sqrt {3}\right ) y^{\prime }+y \sec \left (x \right ) = y^{\sqrt {3}} \sec \left (x \right ) \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
187.417 |
|
|
\[ {}\sec \left (y\right )^{2} y^{\prime }+\frac {\tan \left (y\right )}{2 \sqrt {1+x}} = \frac {1}{2 \sqrt {1+x}} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
32.49 |
|
|
\[ {}\cos \left (x y\right )-x y \sin \left (x y\right )-x^{2} \sin \left (x y\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _exact] |
✓ |
✓ |
0.332 |
|
|
\[ {}y+3 x^{2}+x y^{\prime } = 0 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.166 |
|
|
\[ {}2 \,{\mathrm e}^{y} x +\left (3 y^{2}+x^{2} {\mathrm e}^{y}\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_exact, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
0.252 |
|
|
\[ {}2 x y+\left (x^{2}+1\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.228 |
|
|
\[ {}y^{2}-2 x +2 x y y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class G‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
0.207 |
|
|
\[ {}4 \,{\mathrm e}^{2 x}+2 x y-y^{2}+\left (x -y\right )^{2} y^{\prime } = 0 \] |
1 |
1 |
3 |
[_exact, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
✓ |
0.302 |
|
|
\[ {}\frac {1}{x}-\frac {y}{x^{2}+y^{2}}+\frac {x y^{\prime }}{x^{2}+y^{2}} = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _exact, _rational, _Riccati] |
✓ |
✓ |
0.394 |
|
|
\[ {}y \cos \left (x y\right )-\sin \left (x \right )+x \cos \left (x y\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_exact, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
0.261 |
|
|
\[ {}2 \,{\mathrm e}^{2 x} y^{2}+3 x^{2}+2 y \,{\mathrm e}^{2 x} y^{\prime } = 0 \] |
1 |
1 |
2 |
[_exact, _Bernoulli] |
✓ |
✓ |
0.25 |
|
|
\[ {}y^{2}+\cos \left (x \right )+\left (2 x y+\sin \left (y\right )\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_exact] |
✓ |
✓ |
0.282 |
|
|
\[ {}\sin \left (y\right )+y \cos \left (x \right )+\left (x \cos \left (y\right )+\sin \left (x \right )\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_exact] |
✓ |
✓ |
0.319 |
|
|
\[ {}5 x +2 y+1+\left (2 x +y+1\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.762 |
|
|
\[ {}6 x +4 y+1+\left (4 x +2 y+2\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
5.622 |
|
|
\[ {}3 y-2 x +\left (-2+3 x \right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.383 |
|
|
\[ {}x^{2}+x -1+\left (2 x y+y\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
0.938 |
|
|
\[ {}{\mathrm e}^{2 y}+\left (1+x \right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.772 |
|
|
\[ {}\left (1+x \right ) y^{\prime }-x^{2} y^{2} = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.686 |
|
|
\[ {}y^{\prime } = {\mathrm e}^{x -2 y} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.099 |
|
|
\[ {}{\mathrm e}^{-y}+\left (x^{2}+1\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.299 |
|
|
\[ {}2 \sin \left (3 x \right ) \sin \left (2 y\right ) y^{\prime }-3 \cos \left (3 x \right ) \cos \left (2 y\right ) = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
4.279 |
|
|
\[ {}x y y^{\prime } = \left (1+x \right ) \left (y+1\right ) \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.736 |
|
|
|
||||||||
|
\[ {}\left (x +y^{2}\right ) y^{\prime }+y-x^{2} = 0 \] |
1 |
1 |
1 |
[_exact, _rational] |
✓ |
✓ |
68.71 |
|
|
\[ {}y y^{\prime } = x \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
1.506 |
|
|
\[ {}x y^{\prime }+y = x \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.986 |
|
|
\[ {}3 y^{2} y^{\prime } = 2 x -1 \] |
1 |
1 |
3 |
[_separable] |
✓ |
✓ |
9.704 |
|
|
\[ {}y^{\prime } = 6 x y^{2} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.573 |
|
|
\[ {}y^{\prime } = {\mathrm e}^{y} \sin \left (x \right ) \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.816 |
|
|
\[ {}y^{\prime } = {\mathrm e}^{x -y} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.619 |
|
|
\[ {}y^{\prime } = x \sec \left (y\right ) \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.799 |
|
|
\[ {}x y^{\prime } = y \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.723 |
|
|
\[ {}\left (1-x \right ) y^{\prime } = y \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.188 |
|
|
\[ {}y^{\prime } = \frac {4 x y}{x^{2}+1} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.889 |
|
|
\[ {}y^{\prime } = \frac {2 y}{x^{2}-1} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.866 |
|
|
\[ {}-y^{2}+x^{2} y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.083 |
|
|
\[ {}2 x y+y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.104 |
|
|
\[ {}\cot \left (x \right ) y^{\prime } = y \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.666 |
|
|
\[ {}y^{\prime } = x \,{\mathrm e}^{-2 y} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.018 |
|
|
\[ {}y^{\prime }-2 x y = 2 x \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.415 |
|
|
\[ {}x y^{\prime } = x y+y \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.151 |
|
|
\[ {}x \cos \left (y\right ) y^{\prime } = 1+\sin \left (y\right ) \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
3.685 |
|
|
\[ {}x y^{\prime } = 2 y \left (y-1\right ) \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
3.056 |
|
|
\[ {}2 x y^{\prime } = 1-y^{2} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.274 |
|
|
\[ {}\left (1-x \right ) y^{\prime } = x y \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.834 |
|
|
\[ {}\left (x^{2}-1\right ) y^{\prime } = \left (x^{2}+1\right ) y \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.848 |
|
|
\[ {}y^{\prime } = {\mathrm e}^{x} \left (1+y^{2}\right ) \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.822 |
|
|
\[ {}{\mathrm e}^{y} y^{\prime }+2 x = 2 \,{\mathrm e}^{y} x \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.122 |
|
|
\[ {}y \,{\mathrm e}^{2 x} y^{\prime }+2 x = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.919 |
|
|
\[ {}x y y^{\prime } = \sqrt {y^{2}-9} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.906 |
|
|
\[ {}\left (x +y-1\right ) y^{\prime } = x -y+1 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.594 |
|
|
\[ {}\left (x +\frac {2}{y}\right ) y^{\prime }+y = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
1.217 |
|
|
\[ {}y-x^{3}+\left (x +y^{3}\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_exact, _rational] |
✓ |
✓ |
1.237 |
|
|
\[ {}y+y \cos \left (x y\right )+\left (x +x \cos \left (x y\right )\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
1.069 |
|
|
\[ {}\cos \left (x \right ) \cos \left (y\right )^{2}+2 \sin \left (x \right ) \sin \left (y\right ) \cos \left (y\right ) y^{\prime } = 0 \] |
1 |
1 |
3 |
[_separable] |
✓ |
✓ |
38.22 |
|
|
\[ {}\left (\sin \left (x \right ) \sin \left (y\right )-{\mathrm e}^{y} x \right ) y^{\prime } = {\mathrm e}^{y}+\cos \left (x \right ) \cos \left (y\right ) \] |
1 |
1 |
1 |
[_exact] |
✓ |
✓ |
7.582 |
|
|
\[ {}-\frac {\sin \left (\frac {x}{y}\right )}{y}+\frac {x \sin \left (\frac {x}{y}\right ) y^{\prime }}{y^{2}} = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.973 |
|
|
\[ {}1+y+\left (1-x \right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.994 |
|
|
\[ {}2 x y^{3}+y \cos \left (x \right )+\left (3 x^{2} y^{2}+\sin \left (x \right )\right ) y^{\prime } = 0 \] |
1 |
1 |
3 |
[_exact, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
31.98 |
|
|
\[ {}1 = \frac {y}{1-x^{2} y^{2}}+\frac {x y^{\prime }}{1-x^{2} y^{2}} \] |
1 |
1 |
1 |
[_exact, _rational, _Riccati] |
✓ |
✓ |
1.38 |
|
|
\[ {}y-\left (x +x y^{3}\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.707 |
|
|
\[ {}2 x y+\left (x^{2}+1\right ) y^{\prime } = \cot \left (x \right ) \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.515 |
|
|
\[ {}x y^{\prime }+y = x \cos \left (x \right ) \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.263 |
|
|
\[ {}\left ({\mathrm e}^{x}-3 x^{2} y^{2}\right ) y^{\prime }+{\mathrm e}^{x} y = 2 x y^{3} \] |
1 |
1 |
3 |
[_exact, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
1.849 |
|
|
\[ {}x y^{\prime }+y = x^{2} \cos \left (x \right ) \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.962 |
|
|
\[ {}\cos \left (x +y\right )-x \sin \left (x +y\right ) = x \sin \left (x +y\right ) y^{\prime } \] |
1 |
1 |
1 |
[[_1st_order, _with_linear_symmetries], _exact] |
✓ |
✓ |
3.343 |
|
|
\[ {}y^{2} {\mathrm e}^{x y}+\cos \left (x \right )+\left ({\mathrm e}^{x y}+x y \,{\mathrm e}^{x y}\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_exact] |
✓ |
✓ |
32.26 |
|
|
\[ {}y^{\prime } \ln \left (x -y\right ) = 1+\ln \left (x -y\right ) \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _exact, _dAlembert] |
✓ |
✓ |
1.388 |
|
|
\[ {}2 x y+\left (x^{2}+1\right ) y^{\prime } = 4 x^{3} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.955 |
|
|
\[ {}{\mathrm e}^{x} \sin \left (y\right )-y \sin \left (x y\right )+\left ({\mathrm e}^{x} \cos \left (y\right )-x \sin \left (x y\right )\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_exact] |
✓ |
✓ |
33.056 |
|
|
\[ {}\left (y-x^{2}+{\mathrm e}^{y} x \right ) y^{\prime } = 2 x y-{\mathrm e}^{y}-x \] |
1 |
1 |
1 |
[_exact] |
✓ |
✓ |
1.879 |
|
|
\[ {}2 x y+x^{2} y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.918 |
|
|
\[ {}\ln \left (x \right ) y^{\prime }+\frac {x +y}{x} = 0 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.897 |
|
|
\[ {}\cos \left (y\right )-x \sin \left (y\right ) y^{\prime } = \sec \left (x \right )^{2} \] |
1 |
1 |
2 |
[_exact] |
✓ |
✓ |
32.435 |
|
|
\[ {}y \sin \left (\frac {x}{y}\right )+x \cos \left (\frac {x}{y}\right )-1+\left (x \sin \left (\frac {x}{y}\right )-\frac {x^{2} \cos \left (\frac {x}{y}\right )}{y}\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_exact] |
✓ |
✓ |
32.579 |
|
|
\[ {}\frac {x}{x^{2}+y^{2}}+\frac {y}{x^{2}}+\left (\frac {y}{x^{2}+y^{2}}-\frac {1}{x}\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
2.257 |
|
|
\[ {}3 x^{2}+6 x y^{2}+\left (6 x^{2} y+4 y^{3}\right ) y^{\prime } = 0 \] |
1 |
1 |
4 |
[_exact, _rational] |
✓ |
✓ |
1.747 |
|
|
\[ {}2 x^{2}-x y^{2}-2 y+3-\left (x^{2} y+2 x \right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[_exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
1.895 |
|
|
\[ {}x y^{2}+x -2 y+3+\left (x^{2} y-2 y-2 x \right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[_exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
1.693 |
|
|
\[ {}3 y \left (x^{2}-1\right )+\left (x^{3}+8 y-3 x \right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.217 |
|
|
\[ {}x^{2}+\ln \left (y\right )+\frac {x y^{\prime }}{y} = 0 \] |
1 |
1 |
1 |
[_exact, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
3.205 |
|
|
\[ {}2 x \left (3 x +y-y \,{\mathrm e}^{-x^{2}}\right )+\left (x^{2}+3 y^{2}+{\mathrm e}^{-x^{2}}\right ) y^{\prime } = 0 \] |
1 |
1 |
3 |
[_exact] |
✓ |
✓ |
32.388 |
|
|
\[ {}3+y+2 y^{2} \sin \left (x \right )^{2}+\left (x +2 x y-y \sin \left (2 x \right )\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[_exact, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
33.93 |
|
|
\[ {}1+y+\left (x -y \left (y+1\right )^{2}\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
4.974 |
|
|
\[ {}y^{\prime } = \frac {y+2}{1+x} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.021 |
|
|
\[ {}1+\sin \left (2 x \right ) y^{2}-2 y \cos \left (x \right )^{2} y^{\prime } = 0 \] |
1 |
1 |
2 |
[_exact, _Bernoulli] |
✓ |
✓ |
11.411 |
|
|
\[ {}y^{\prime } = a \,x^{n} y \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.195 |
|
|
\[ {}y^{\prime } = y \cot \left (x \right ) \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.142 |
|
|
\[ {}y^{\prime } = \left (2 \csc \left (2 x \right )+\cot \left (x \right )\right ) y \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
4.082 |
|
|
\[ {}y^{\prime } = y \sec \left (x \right ) \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.773 |
|
|
\[ {}y^{\prime } = y \tan \left (x \right ) \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.871 |
|
|
\[ {}y^{\prime } = \left (a +\cos \left (\ln \left (x \right )\right )+\sin \left (\ln \left (x \right )\right )\right ) y \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.095 |
|
|
\[ {}y^{\prime } = x y \left (3+y\right ) \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.513 |
|
|
\[ {}y^{\prime } = a x y^{2} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.592 |
|
|
\[ {}y^{\prime } = x^{n} \left (a +b y^{2}\right ) \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.323 |
|
|
\[ {}y^{\prime }+\tan \left (x \right ) \left (1-y^{2}\right ) = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.99 |
|
|
\[ {}y^{\prime } = \left (a +b y+c y^{2}\right ) f \left (x \right ) \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.484 |
|
|
\[ {}y^{\prime } = x y^{3} \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
0.73 |
|
|
\[ {}y^{\prime }+y^{3} \sec \left (x \right ) \tan \left (x \right ) = 0 \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
0.954 |
|
|
\[ {}y^{\prime } = \cos \left (y\right ) \cos \left (x \right )^{2} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.817 |
|
|
\[ {}y^{\prime } = \sec \left (x \right )^{2} \cot \left (y\right ) \cos \left (y\right ) \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.894 |
|
|
\[ {}y^{\prime }+\tan \left (x \right ) \sec \left (x \right ) \cos \left (y\right )^{2} = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.779 |
|
|
\[ {}y^{\prime } = \cot \left (x \right ) \cot \left (y\right ) \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.116 |
|
|
\[ {}y^{\prime }+\cot \left (x \right ) \cot \left (y\right ) = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.964 |
|
|
\[ {}y^{\prime } = \sin \left (x \right ) \left (\csc \left (y\right )-\cot \left (y\right )\right ) \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.105 |
|
|
\[ {}y^{\prime } = \tan \left (x \right ) \cot \left (y\right ) \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.789 |
|
|
\[ {}y^{\prime }+\tan \left (x \right ) \cot \left (y\right ) = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.756 |
|
|
\[ {}y^{\prime }+\sin \left (2 x \right ) \csc \left (2 y\right ) = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.735 |
|
|
\[ {}y^{\prime } = \cos \left (x \right ) \sec \left (y\right )^{2} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.069 |
|
|
\[ {}y^{\prime } = \sec \left (x \right )^{2} \sec \left (y\right )^{3} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.51 |
|
|
\[ {}y^{\prime }+\csc \left (2 x \right ) \sin \left (2 y\right ) = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.963 |
|
|
\[ {}y^{\prime } = {\mathrm e}^{x +y} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.585 |
|
|
\[ {}y^{\prime } = {\mathrm e}^{x} \left (a +b \,{\mathrm e}^{-y}\right ) \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.281 |
|
|
\[ {}y^{\prime }+y \ln \left (x \right ) \ln \left (y\right ) = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.967 |
|
|
\[ {}y^{\prime } = f \left (x \right ) g \left (y\right ) \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.615 |
|
|
\[ {}x y^{\prime }+x +y = 0 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.751 |
|
|
\[ {}x y^{\prime } = x^{3}-y \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.597 |
|
|
\[ {}x y^{\prime } = x \sin \left (x \right )-y \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.633 |
|
|
\[ {}x y^{\prime } = x^{n} \ln \left (x \right )-y \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.89 |
|
|
\[ {}x y^{\prime } = a y \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.015 |
|
|
\[ {}x y^{\prime }+\left (b x +a \right ) y = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.05 |
|
|
\[ {}x y^{\prime } = a +b y^{2} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.995 |
|
|
\[ {}x y^{\prime } = y \left (1+y^{2}\right ) \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
1.431 |
|
|
\[ {}x y^{\prime } = 4 y-4 \sqrt {y} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.38 |
|
|
\[ {}x y^{\prime }+2 y = \sqrt {1+y^{2}} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.276 |
|
|
\[ {}x y^{\prime } = \left (-2 x^{2}+1\right ) \cot \left (y\right )^{2} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.883 |
|
|
\[ {}x y^{\prime } = y-\cot \left (y\right )^{2} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.818 |
|
|
\[ {}x y^{\prime }+\tan \left (y\right ) = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.08 |
|
|
\[ {}x y^{\prime } = y \ln \left (y\right ) \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.782 |
|
|
\[ {}\left (x +a \right ) y^{\prime }+b \,x^{2}+y = 0 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.796 |
|
|
\[ {}\left (x +a \right ) y^{\prime } = b +c y \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.058 |
|
|
\[ {}\left (x +a \right ) y^{\prime } = y \left (1-a y\right ) \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.45 |
|
|
\[ {}2 x y^{\prime } = y \left (1+y^{2}\right ) \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
1.427 |
|
|
\[ {}2 x y^{\prime }+y \left (1+y^{2}\right ) = 0 \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
1.734 |
|
|
\[ {}2 x y^{\prime }+4 y+a +\sqrt {a^{2}-4 b -4 c y} = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
18.974 |
|
|
\[ {}\left (2 x +1\right ) y^{\prime } = 4 \,{\mathrm e}^{-y}-2 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.921 |
|
|
\[ {}x^{2} y^{\prime } = -y+a \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.778 |
|
|
\[ {}x^{2} y^{\prime } = \left (b x +a \right ) y \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.684 |
|
|
\[ {}x^{2} y^{\prime } = a +b y^{2} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.772 |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime }-x +x y = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.63 |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime }+2 x y = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.552 |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime } = 2 x \left (x -y\right ) \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.527 |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime }+\cos \left (x \right ) = 2 x y \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.158 |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime } = \tan \left (x \right )-2 x y \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.573 |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime } = \left (2 b x +a \right ) y \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.69 |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime } = 1+y^{2} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.555 |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime } = 1-y^{2} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.515 |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime }+x y \left (1-y\right ) = 0 \] |
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 |
|
|
\[ {}\left (a^{2}+x^{2}\right ) y^{\prime } = \left (b +y\right ) \left (x +\sqrt {a^{2}+x^{2}}\right ) \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.938 |
|
|
\[ {}\left (a^{2}+x^{2}\right ) y^{\prime }+x y+b x y^{2} = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.346 |
|
|
\[ {}x \left (1+x \right ) y^{\prime } = \left (1-2 x \right ) y \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.655 |
|
|
\[ {}x \left (x +a \right ) y^{\prime } = \left (b +c y\right ) y \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
3.375 |
|
|
\[ {}\left (x +a \right )^{2} y^{\prime } = 2 \left (x +a \right ) \left (b +y\right ) \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.874 |
|
|
\[ {}\left (x -a \right ) \left (x -b \right ) y^{\prime }+k y = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.49 |
|
|
\[ {}\left (x -a \right ) \left (x -b \right ) y^{\prime } = c y^{2} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.829 |
|
|
\[ {}\left (x -a \right ) \left (x -b \right ) y^{\prime }+k \left (y-a \right ) \left (y-b \right ) = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.154 |
|
|
\[ {}2 x^{2} y^{\prime } = y \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.647 |
|
|
\[ {}x \left (1-2 x \right ) y^{\prime }+1+\left (1-4 x \right ) y = 0 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.632 |
|
|
\[ {}\left (b \,x^{2}+a \right ) y^{\prime } = A +B y^{2} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.681 |
|
|
\[ {}\left (b \,x^{2}+a \right ) y^{\prime } = c x y \ln \left (y\right ) \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.227 |
|
|
\[ {}x \left (x a +1\right ) y^{\prime }+a -y = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.753 |
|
|
\[ {}x^{3} y^{\prime } = \left (1+x \right ) y^{2} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.538 |
|
|
\[ {}x \left (x^{2}+1\right ) y^{\prime } = \left (-x^{2}+1\right ) y \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.647 |
|
|
\[ {}x \left (-x^{2}+1\right ) y^{\prime } = \left (x^{2}-x +1\right ) y \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.71 |
|
|
\[ {}\left (-x^{4}+1\right ) y^{\prime } = 2 x \left (1-y^{2}\right ) \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.381 |
|
|
\[ {}x \left (-x^{3}+1\right ) y^{\prime } = 2 x -\left (-4 x^{3}+1\right ) y \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.726 |
|
|
\[ {}x \left (-2 x^{3}+1\right ) y^{\prime } = 2 \left (-x^{3}+1\right ) y \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.826 |
|
|
\[ {}y^{\prime } \sqrt {-x^{2}+1} = 1+y^{2} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.656 |
|
|
\[ {}\left (x -\sqrt {x^{2}+1}\right ) y^{\prime } = y+\sqrt {1+y^{2}} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.009 |
|
|
\[ {}y^{\prime } \sqrt {b^{2}+x^{2}} = \sqrt {y^{2}+a^{2}} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
11.581 |
|
|
\[ {}y^{\prime } \sqrt {b^{2}-x^{2}} = \sqrt {a^{2}-y^{2}} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.438 |
|
|
\[ {}x y^{\prime } \sqrt {a^{2}+x^{2}} = y \sqrt {b^{2}+y^{2}} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
9.665 |
|
|
\[ {}x y^{\prime } \sqrt {-a^{2}+x^{2}} = y \sqrt {y^{2}-b^{2}} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.847 |
|
|
\[ {}y^{\prime } \sqrt {x^{3}+1} = \sqrt {y^{3}+1} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
77.213 |
|
|
\[ {}y^{\prime } \sqrt {x \left (1-x \right ) \left (-x a +1\right )} = \sqrt {y \left (1-y\right ) \left (1-a y\right )} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
9.26 |
|
|
\[ {}y^{\prime } \sqrt {-x^{4}+1} = \sqrt {1-y^{4}} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.47 |
|
|
\[ {}y^{\prime } \sqrt {x^{4}+x^{2}+1} = \sqrt {1+y^{2}+y^{4}} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
3.326 |
|
|
\[ {}y^{\prime } \left (x^{3}+1\right )^{\frac {2}{3}}+\left (y^{3}+1\right )^{\frac {2}{3}} = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
6.859 |
|
|
\[ {}y^{\prime } \left (4 x^{3}+\operatorname {a1} x +\operatorname {a0} \right )^{\frac {2}{3}}+\left (\operatorname {a0} +\operatorname {a1} y+4 y^{3}\right )^{\frac {2}{3}} = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.793 |
|
|
\[ {}\left (1-4 \cos \left (x \right )^{2}\right ) y^{\prime } = \tan \left (x \right ) \left (1+4 \cos \left (x \right )^{2}\right ) y \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
4.974 |
|
|
\[ {}\left (1-\sin \left (x \right )\right ) y^{\prime }+y \cos \left (x \right ) = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.358 |
|
|
\[ {}\left (\cos \left (x \right )-\sin \left (x \right )\right ) y^{\prime }+y \left (\cos \left (x \right )+\sin \left (x \right )\right ) = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.652 |
|
|
\[ {}\left (\operatorname {a0} +\operatorname {a1} \sin \left (x \right )^{2}\right ) y^{\prime }+\operatorname {a2} x \left (\operatorname {a3} +\operatorname {a1} \sin \left (x \right )^{2}\right )+\operatorname {a1} y \sin \left (2 x \right ) = 0 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.44 |
|
|
\[ {}\left (x -{\mathrm e}^{x}\right ) y^{\prime }+x \,{\mathrm e}^{x}+\left (-{\mathrm e}^{x}+1\right ) y = 0 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.624 |
|
|
\[ {}x +y y^{\prime } = 0 \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
0.987 |
|
|
\[ {}y y^{\prime }+x \,{\mathrm e}^{x^{2}} = 0 \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
0.475 |
|
|
\[ {}y y^{\prime }+x \,{\mathrm e}^{-x} \left (y+1\right ) = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.954 |
|
|
\[ {}y y^{\prime } = x a +b x y^{2} \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
1.19 |
|
|
\[ {}\left (y+1\right ) y^{\prime } = x^{2} \left (1-y\right ) \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.658 |
|
|
\[ {}\left (x +y\right ) y^{\prime }+y = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.407 |
|
|
\[ {}\left (x +y\right ) y^{\prime } = x -y \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.351 |
|
|
\[ {}\left (2+x +y\right ) y^{\prime } = 1-x -y \] |
1 |
1 |
2 |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
0.888 |
|
|
\[ {}\left (5-2 x -y\right ) y^{\prime }+4-x -2 y = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.998 |
|
|
\[ {}\left (2-3 x +y\right ) y^{\prime }+5-2 x -3 y = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.981 |
|
|
\[ {}\left (x -2 y\right ) y^{\prime }+2 x +y = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.19 |
|
|
\[ {}\left (1+x -2 y\right ) y^{\prime } = 1+2 x -y \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.033 |
|
|
\[ {}2 \left (x +y\right ) y^{\prime }+x^{2}+2 y = 0 \] |
1 |
1 |
2 |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.186 |
|
|
\[ {}\left (3+2 x -2 y\right ) y^{\prime } = 1+6 x -2 y \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.346 |
|
|
\[ {}\left (x^{3}+2 y\right ) y^{\prime } = 3 x \left (2-x y\right ) \] |
1 |
1 |
2 |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.348 |
|
|
\[ {}3 y y^{\prime }+5 \cot \left (x \right ) \cot \left (y\right ) \cos \left (y\right )^{2} = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
5.5 |
|
|
\[ {}3 \left (2-y\right ) y^{\prime }+x y = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.803 |
|
|
\[ {}\left (5+2 x -4 y\right ) y^{\prime } = 3+x -2 y \] |
1 |
1 |
2 |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
0.953 |
|
|
\[ {}\left (5+3 x -4 y\right ) y^{\prime } = 2+7 x -3 y \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.467 |
|
|
\[ {}\left (8+5 x -12 y\right ) y^{\prime } = 3+2 x -5 y \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
3.115 |
|
|
\[ {}\left (x a +b y\right ) y^{\prime }+b x +a y = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.478 |
|
|
\[ {}x y y^{\prime }+1+y^{2} = 0 \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
1.368 |
|
|
\[ {}x y y^{\prime } = a +b y^{2} \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
1.295 |
|
|
\[ {}x y y^{\prime } = \left (x^{2}+1\right ) \left (1-y^{2}\right ) \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
12.514 |
|
|
\[ {}x \left (y+1\right ) y^{\prime }-\left (1-x \right ) y = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.731 |
|
|
\[ {}x \left (1-y\right ) y^{\prime }+\left (1+x \right ) y = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.76 |
|
|
\[ {}x \left (1-y\right ) y^{\prime }+\left (1-x \right ) y = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.755 |
|
|
\[ {}x \left (y+a \right ) y^{\prime } = y \left (B x +A \right ) \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.269 |
|
|
\[ {}y \left (1-x \right ) y^{\prime }+x \left (1-y\right ) = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.775 |
|
|
\[ {}\left (x +a \right ) \left (x +b \right ) y^{\prime } = x y \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.069 |
|
|
\[ {}2 x y y^{\prime }+a +y^{2} = 0 \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
1.216 |
|
|
\[ {}x^{2}+y^{2}+2 x y y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
1.293 |
|
|
\[ {}\left (3-x +2 x y\right ) y^{\prime }+3 x^{2}-y+y^{2} = 0 \] |
1 |
1 |
2 |
[_exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
1.229 |
|
|
\[ {}x \left (x -2 y\right ) y^{\prime }+\left (2 x -y\right ) y = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
2.526 |
|
|
\[ {}2 x \left (2 x^{2}+y\right ) y^{\prime }+\left (12 x^{2}+y\right ) y = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class G‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
2.415 |
|
|
\[ {}2 \left (1+x \right ) y y^{\prime }+2 x -3 x^{2}+y^{2} = 0 \] |
1 |
1 |
2 |
[_exact, _rational, _Bernoulli] |
✓ |
✓ |
0.92 |
|
|
\[ {}\left (3+6 x y+x^{2}\right ) y^{\prime }+2 x +2 x y+3 y^{2} = 0 \] |
1 |
1 |
2 |
[_exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
0.997 |
|
|
\[ {}3 x \left (2 y+x \right ) y^{\prime }+x^{3}+3 y \left (y+2 x \right ) = 0 \] |
1 |
1 |
2 |
[_exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
1.068 |
|
|
|
||||||||
|
\[ {}x \left (a +b y\right ) y^{\prime } = c y \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.72 |
|
|
\[ {}\left (1-x^{2} y\right ) y^{\prime }+1-x y^{2} = 0 \] |
1 |
1 |
2 |
[_exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
0.925 |
|
|
\[ {}x \left (2+x y\right ) y^{\prime } = 3+2 x^{3}-2 y-x y^{2} \] |
1 |
1 |
2 |
[_exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
1.267 |
|
|
\[ {}x^{2} \left (1-y\right ) y^{\prime }+\left (1-x \right ) y = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.03 |
|
|
\[ {}x^{2} \left (1-y\right ) y^{\prime }+\left (1+x \right ) y^{2} = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.244 |
|
|
\[ {}\left (x^{2}+1\right ) y y^{\prime }+x \left (1-y^{2}\right ) = 0 \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
3.071 |
|
|
\[ {}2 \left (1+x \right ) x y y^{\prime } = 1+y^{2} \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
1.658 |
|
|
\[ {}2 x^{3} y y^{\prime }+a +3 x^{2} y^{2} = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class G‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
0.829 |
|
|
\[ {}x \left (3-2 x^{2} y\right ) y^{\prime } = 4 x -3 y+3 x^{2} y^{2} \] |
1 |
1 |
2 |
[_exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
1.14 |
|
|
\[ {}x y \left (b \,x^{2}+a \right ) y^{\prime } = A +B y^{2} \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
3.143 |
|
|
\[ {}y y^{\prime } \sqrt {x^{2}+1}+x \sqrt {1+y^{2}} = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.895 |
|
|
\[ {}\left (y+1\right ) y^{\prime } \sqrt {x^{2}+1} = y^{3} \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
1.23 |
|
|
\[ {}y^{2} y^{\prime }+x \left (2-y\right ) = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.56 |
|
|
\[ {}y^{2} y^{\prime } = x \left (1+y^{2}\right ) \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.704 |
|
|
\[ {}\left (x +y^{2}\right ) y^{\prime }+y = b x +a \] |
1 |
1 |
3 |
[_exact, _rational] |
✓ |
✓ |
1.427 |
|
|
\[ {}\left (x -y^{2}\right ) y^{\prime } = x^{2}-y \] |
1 |
1 |
3 |
[_exact, _rational] |
✓ |
✓ |
9.654 |
|
|
\[ {}\left (x^{2}-y^{2}\right ) y^{\prime }+x \left (2 y+x \right ) = 0 \] |
1 |
1 |
3 |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
7.746 |
|
|
\[ {}\left (x^{2}+y^{2}\right ) y^{\prime }+2 x \left (y+2 x \right ) = 0 \] |
1 |
1 |
3 |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
9.385 |
|
|
\[ {}\left (a^{2}+x^{2}+y^{2}\right ) y^{\prime }+2 x y = 0 \] |
1 |
1 |
3 |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
8.592 |
|
|
\[ {}\left (a^{2}+x^{2}+y^{2}\right ) y^{\prime }+b^{2}+x^{2}+2 x y = 0 \] |
1 |
1 |
3 |
[_exact, _rational] |
✓ |
✓ |
1.213 |
|
|
\[ {}y \left (y+1\right ) y^{\prime } = \left (1+x \right ) x \] |
1 |
1 |
3 |
[_separable] |
✓ |
✓ |
165.359 |
|
|
\[ {}\left (x^{3}+2 y-y^{2}\right ) y^{\prime }+3 x^{2} y = 0 \] |
1 |
1 |
3 |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
10.477 |
|
|
\[ {}\left (2 x^{2}+4 x y-y^{2}\right ) y^{\prime } = x^{2}-4 x y-2 y^{2} \] |
1 |
1 |
3 |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
3.232 |
|
|
\[ {}\left (x^{2}-3 y^{2}\right ) y^{\prime }+1+2 x y = 0 \] |
1 |
1 |
3 |
[_exact, _rational] |
✓ |
✓ |
9.799 |
|
|
\[ {}\left (3 x^{2}+2 x y+4 y^{2}\right ) y^{\prime }+2 x^{2}+6 x y+y^{2} = 0 \] |
1 |
1 |
3 |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
1.765 |
|
|
\[ {}\left (1-3 x^{2} y+6 y^{2}\right ) y^{\prime }+x^{2}-3 x y^{2} = 0 \] |
1 |
1 |
3 |
[_exact, _rational] |
✓ |
✓ |
1.418 |
|
|
\[ {}\left (x -6 y\right )^{2} y^{\prime }+a +2 x y-6 y^{2} = 0 \] |
1 |
1 |
3 |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
✓ |
1.193 |
|
|
\[ {}\left (x^{2} a +2 b x y+c y^{2}\right ) y^{\prime }+k \,x^{2}+2 a x y+b y^{2} = 0 \] |
1 |
1 |
3 |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
3.106 |
|
|
\[ {}x \left (1-y^{2}\right ) y^{\prime } = \left (x^{2}+1\right ) y \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.766 |
|
|
\[ {}x \left (y+a \right )^{2} y^{\prime } = b y^{2} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.206 |
|
|
\[ {}3 x y^{2} y^{\prime } = 2 x -y^{3} \] |
1 |
1 |
3 |
[[_homogeneous, ‘class G‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
1.135 |
|
|
\[ {}x \left (x -3 y^{2}\right ) y^{\prime }+\left (2 x -y^{2}\right ) y = 0 \] |
1 |
1 |
3 |
[[_homogeneous, ‘class G‘], _exact, _rational] |
✓ |
✓ |
3.18 |
|
|
\[ {}6 x y^{2} y^{\prime }+x +2 y^{3} = 0 \] |
1 |
1 |
3 |
[[_homogeneous, ‘class G‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
0.997 |
|
|
\[ {}x^{2} y^{2} y^{\prime }+1-x +x^{3} = 0 \] |
1 |
1 |
3 |
[_separable] |
✓ |
✓ |
1.359 |
|
|
\[ {}x^{2} \left (y+a \right )^{2} y^{\prime } = \left (x^{2}+1\right ) \left (y^{2}+a^{2}\right ) \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.001 |
|
|
\[ {}\left (x^{2}+1\right ) \left (1+y^{2}\right ) y^{\prime }+2 x y \left (1-y^{2}\right ) = 0 \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
3.552 |
|
|
\[ {}\left (x^{2}+1\right ) \left (1+y^{2}\right ) y^{\prime }+2 x y \left (1-y\right )^{2} = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.2 |
|
|
\[ {}\left (1-x^{3}+6 x^{2} y^{2}\right ) y^{\prime } = \left (6+3 x y-4 y^{3}\right ) x \] |
1 |
1 |
3 |
[_exact, _rational] |
✓ |
✓ |
1.378 |
|
|
\[ {}x \left (3+5 x -12 x y^{2}+4 x^{2} y\right ) y^{\prime }+\left (3+10 x -8 x y^{2}+6 x^{2} y\right ) y = 0 \] |
1 |
1 |
3 |
[_exact, _rational] |
✓ |
✓ |
1.655 |
|
|
\[ {}x^{3} \left (1+y^{2}\right ) y^{\prime }+3 x^{2} y = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.556 |
|
|
\[ {}\left (3 x -y^{3}\right ) y^{\prime } = x^{2}-3 y \] |
1 |
1 |
1 |
[_exact, _rational] |
✓ |
✓ |
1.135 |
|
|
\[ {}\left (x^{3}+y^{3}\right ) y^{\prime }+x^{2} \left (x a +3 y\right ) = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
4.654 |
|
|
\[ {}\left (x -x^{2} y-y^{3}\right ) y^{\prime } = x^{3}-y+x y^{2} \] |
1 |
1 |
1 |
[_exact, _rational] |
✓ |
✓ |
1.349 |
|
|
\[ {}\left (a +x^{2}+y^{2}\right ) y y^{\prime } = x \left (a -x^{2}-y^{2}\right ) \] |
1 |
1 |
4 |
[_exact, _rational] |
✓ |
✓ |
1.224 |
|
|
\[ {}\left (y^{2}+3 x^{2}\right ) y y^{\prime }+x \left (x^{2}+3 y^{2}\right ) = 0 \] |
1 |
1 |
4 |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
1.694 |
|
|
\[ {}y \left (2 y^{2}+1\right ) y^{\prime } = x \left (2 x^{2}+1\right ) \] |
1 |
1 |
4 |
[_separable] |
✓ |
✓ |
2.901 |
|
|
\[ {}\left (5 x^{2}+2 y^{2}\right ) y y^{\prime }+x \left (x^{2}+5 y^{2}\right ) = 0 \] |
1 |
1 |
4 |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
1.744 |
|
|
\[ {}\left (3 x^{3}+6 x^{2} y-3 x y^{2}+20 y^{3}\right ) y^{\prime }+4 x^{3}+9 x^{2} y+6 x y^{2}-y^{3} = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
3.194 |
|
|
\[ {}x y^{3} y^{\prime } = \left (-x^{2}+1\right ) \left (1+y^{2}\right ) \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
3.384 |
|
|
\[ {}\left (2-10 x^{2} y^{3}+3 y^{2}\right ) y^{\prime } = x \left (1+5 y^{4}\right ) \] |
1 |
1 |
1 |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
1.213 |
|
|
\[ {}y^{\prime } \sqrt {b^{2}+y^{2}} = \sqrt {a^{2}+x^{2}} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
3.374 |
|
|
\[ {}y^{\prime } \sqrt {b^{2}-y^{2}} = \sqrt {a^{2}-x^{2}} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.537 |
|
|
\[ {}y^{\prime } \sqrt {y} = \sqrt {x} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
166.565 |
|
|
\[ {}\left (y+\sqrt {1+y^{2}}\right ) \left (x^{2}+1\right )^{\frac {3}{2}} y^{\prime } = 1+y^{2} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
8.955 |
|
|
\[ {}\left (y+\sqrt {1+y^{2}}\right ) \left (x^{2}+1\right )^{\frac {3}{2}} y^{\prime } = 1+y^{2} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
7.553 |
|
|
\[ {}y^{\prime } \cos \left (y\right ) \left (\cos \left (y\right )-\sin \left (A \right ) \sin \left (x \right )\right )+\cos \left (x \right ) \left (\cos \left (x \right )-\sin \left (A \right ) \sin \left (y\right )\right ) = 0 \] |
1 |
1 |
1 |
unknown |
✓ |
✓ |
4.592 |
|
|
\[ {}\left (a \cos \left (b x +a y\right )-b \sin \left (x a +b y\right )\right ) y^{\prime }+b \cos \left (b x +a y\right )-a \sin \left (x a +b y\right ) = 0 \] |
1 |
1 |
1 |
[_exact] |
✓ |
✓ |
2.376 |
|
|
\[ {}\left ({\mathrm e}^{x}+{\mathrm e}^{y} x \right ) y^{\prime }+{\mathrm e}^{x} y+{\mathrm e}^{y} = 0 \] |
1 |
1 |
1 |
[_exact] |
✓ |
✓ |
1.407 |
|
|
\[ {}\left (\sinh \left (x \right )+x \cosh \left (y\right )\right ) y^{\prime }+y \cosh \left (x \right )+\sinh \left (y\right ) = 0 \] |
1 |
1 |
1 |
[_exact] |
✓ |
✓ |
35.838 |
|
|
\[ {}y^{\prime } \left (1+\sinh \left (x \right )\right ) \sinh \left (y\right )+\cosh \left (x \right ) \left (\cosh \left (y\right )-1\right ) = 0 \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
3.651 |
|
|
\[ {}2 \left (y+1\right )^{\frac {3}{2}}+3 x y^{\prime }-3 y = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
8.423 |
|
|
\[ {}\frac {2 x}{y^{3}}+\frac {\left (y^{2}-3 x^{2}\right ) y^{\prime }}{y^{4}} = 0 \] |
1 |
1 |
3 |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
5.584 |
|
|
\[ {}x \left (1-y\right ) y^{\prime }+\left (1+x \right ) y = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.963 |
|
|
\[ {}y^{2}+x y^{2}+\left (x^{2}-x^{2} y\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.661 |
|
|
\[ {}x y \left (x^{2}+1\right ) y^{\prime }-1-y^{2} = 0 \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
6.803 |
|
|
\[ {}1+y^{2}-\left (y+\sqrt {1+y^{2}}\right ) \left (x^{2}+1\right )^{\frac {3}{2}} y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
23.264 |
|
|
\[ {}\sin \left (x \right ) \cos \left (y\right )-\cos \left (x \right ) \sin \left (y\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.344 |
|
|
\[ {}\sec \left (x \right )^{2} \tan \left (y\right )+\sec \left (y\right )^{2} \tan \left (x \right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
40.663 |
|
|
\[ {}\left (-x^{2}+1\right ) z^{\prime }-x z = a x z^{2} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
3.239 |
|
|
\[ {}x^{3}+3 x y^{2}+\left (y^{3}+3 x^{2} y\right ) y^{\prime } = 0 \] |
1 |
1 |
4 |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
0.334 |
|
|
\[ {}1+\frac {y^{2}}{x^{2}}-\frac {2 y y^{\prime }}{x} = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
0.256 |
|
|
\[ {}\frac {3 x}{y^{3}}+\left (\frac {1}{y^{2}}-\frac {3 x^{2}}{y^{4}}\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
0.381 |
|
|
\[ {}x +y y^{\prime }+\frac {x y^{\prime }}{x^{2}+y^{2}}-\frac {y}{x^{2}+y^{2}} = 0 \] |
1 |
1 |
1 |
[[_1st_order, _with_linear_symmetries], _exact, _rational] |
✓ |
✓ |
0.434 |
|
|
\[ {}1+{\mathrm e}^{\frac {x}{y}}+{\mathrm e}^{\frac {x}{y}} \left (1-\frac {x}{y}\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _exact, _dAlembert] |
✓ |
✓ |
0.387 |
|
|
\[ {}{\mathrm e}^{x} \left (x^{2}+y^{2}+2 x \right )+2 y \,{\mathrm e}^{x} y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class D‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
0.313 |
|
|
\[ {}n \cos \left (n x +m y\right )-m \sin \left (m x +n y\right )+\left (m \cos \left (n x +m y\right )-n \sin \left (m x +n y\right )\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_exact] |
✓ |
✓ |
0.605 |
|
|
\[ {}\frac {x}{\sqrt {1+x^{2}+y^{2}}}+\frac {y y^{\prime }}{\sqrt {1+x^{2}+y^{2}}}+\frac {y}{x^{2}+y^{2}}-\frac {x y^{\prime }}{x^{2}+y^{2}} = 0 \] |
1 |
1 |
1 |
[[_1st_order, _with_linear_symmetries], _exact] |
✓ |
✓ |
0.865 |
|
|
\[ {}2 x y+\left (y^{2}-2 x^{2}\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
0.365 |
|
|
\[ {}\frac {1}{x}+\frac {y^{\prime }}{y}+\frac {2}{y}-\frac {2 y^{\prime }}{x} = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
0.227 |
|
|
\[ {}\left (x \cos \left (\frac {y}{x}\right )+y \sin \left (\frac {y}{x}\right )\right ) y+\left (x \cos \left (\frac {y}{x}\right )-y \sin \left (\frac {y}{x}\right )\right ) x y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
0.647 |
|
|
\[ {}x^{2}+y^{2}+2 x +2 y y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
0.229 |
|
|
\[ {}x^{2}+y^{2}-2 x y y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
0.204 |
|
|
\[ {}2 x y+\left (y^{2}-3 x^{2}\right ) y^{\prime } = 0 \] |
1 |
1 |
3 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
0.243 |
|
|
\[ {}y+\left (2 y-x \right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
0.33 |
|
|
\[ {}\frac {\sqrt {f \,x^{4}+c \,x^{3}+c \,x^{2}+b x +a}\, y^{\prime }}{\sqrt {a +b y+c y^{2}+c y^{3}+f y^{4}}} = -1 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
96.521 |
|
|
\[ {}2 x y+\left (x^{2}+y^{2}\right ) y^{\prime } = 0 \] |
1 |
1 |
3 |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
9.542 |
|
|
\[ {}7 y-3+\left (2 x +1\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.137 |
|
|
\[ {}3 x -2 y+4-\left (2 x +7 y-1\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
5.572 |
|
|
\[ {}3 x^{2} y+8 x y^{2}+\left (x^{3}+8 x^{2} y+12 y^{2}\right ) y^{\prime } = 0 \] |
1 |
1 |
3 |
[_exact, _rational] |
✓ |
✓ |
0.43 |
|
|
\[ {}\frac {2 x y+1}{y}+\frac {\left (y-x \right ) y^{\prime }}{y^{2}} = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
0.494 |
|
|
\[ {}2 x y+\left (x^{2}+y^{2}\right ) y^{\prime } = 0 \] |
1 |
1 |
3 |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
0.262 |
|
|
\[ {}{\mathrm e}^{x} \sin \left (y\right )+{\mathrm e}^{-y}-\left (x \,{\mathrm e}^{-y}-{\mathrm e}^{x} \cos \left (y\right )\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_exact] |
✓ |
✓ |
0.45 |
|
|
\[ {}\cos \left (y\right )-\left (\sin \left (y\right ) x -y^{2}\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_exact, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
0.364 |
|
|
\[ {}x -2 x y+{\mathrm e}^{y}+\left (y-x^{2}+{\mathrm e}^{y} x \right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_exact] |
✓ |
✓ |
1.805 |
|
|
\[ {}x^{2}-x +y^{2}-\left ({\mathrm e}^{y}-2 x y\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_exact] |
✓ |
✓ |
1.616 |
|
|
\[ {}2 x +y \cos \left (x \right )+\left (2 y+\sin \left (x \right )-\sin \left (y\right )\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_exact] |
✓ |
✓ |
0.403 |
|
|
\[ {}x \sqrt {x^{2}+y^{2}}-\frac {x^{2} y y^{\prime }}{y-\sqrt {x^{2}+y^{2}}} = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _exact, _dAlembert] |
✓ |
✓ |
0.998 |
|
|
\[ {}4 x^{3}-\sin \left (x \right )+y^{3}-\left (y^{2}+1-3 x y^{2}\right ) y^{\prime } = 0 \] |
1 |
1 |
3 |
[_exact] |
✓ |
✓ |
0.685 |
|
|
\[ {}{\mathrm e}^{x} \left (y^{3}+x y^{3}+1\right )+3 y^{2} \left (x \,{\mathrm e}^{x}-6\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_exact, _Bernoulli] |
✓ |
✓ |
1.176 |
|
|
\[ {}\sin \left (x \right ) \cos \left (y\right )+\cos \left (x \right ) \sin \left (y\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
31.728 |
|
|
\[ {}y^{2} {\mathrm e}^{x y^{2}}+4 x^{3}+\left (2 x y \,{\mathrm e}^{x y^{2}}-3 y^{2}\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_exact] |
✓ |
✓ |
3.813 |
|
|
\[ {}y^{2}+y-x y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.007 |
|
|
\[ {}y \sec \left (x \right )+\sin \left (x \right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.883 |
|
|
\[ {}{\mathrm e}^{x}-\sin \left (y\right )+\cos \left (y\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
0.29 |
|
|
\[ {}x y+\left (x^{2}+1\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.407 |
|
|
\[ {}y^{3}+x y^{2}+y+\left (x^{3}+x^{2} y+x \right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[_rational, [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
0.377 |
|
|
\[ {}3 y-x y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.804 |
|
|
\[ {}y-3 x y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.34 |
|
|
\[ {}2 x y+x^{2}+\left (x^{2}+y^{2}\right ) y^{\prime } = 0 \] |
1 |
1 |
3 |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
0.328 |
|
|
\[ {}x^{2}+y \cos \left (x \right )+\left (y^{3}+\sin \left (x \right )\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_exact] |
✓ |
✓ |
0.353 |
|
|
\[ {}x^{2}+y^{2}+x +x y y^{\prime } = 0 \] |
1 |
1 |
2 |
[_rational, _Bernoulli] |
✓ |
✓ |
0.24 |
|
|
\[ {}x -2 x y+{\mathrm e}^{y}+\left (y-x^{2}+{\mathrm e}^{y} x \right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_exact] |
✓ |
✓ |
0.333 |
|
|
\[ {}{\mathrm e}^{x} \sin \left (y\right )+{\mathrm e}^{-y}-\left (x \,{\mathrm e}^{-y}-{\mathrm e}^{x} \cos \left (y\right )\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_exact] |
✓ |
✓ |
0.341 |
|
|
\[ {}x^{4} y^{2}-y+\left (x^{2} y^{4}-x \right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_rational] |
✓ |
✓ |
0.397 |
|
|
\[ {}y \left (2 x +y^{3}\right )-x \left (2 x -y^{3}\right ) y^{\prime } = 0 \] |
1 |
1 |
3 |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
0.32 |
|
|
\[ {}\arctan \left (x y\right )+\frac {x y-2 x y^{2}}{1+x^{2} y^{2}}+\frac {\left (x^{2}-2 x^{2} y\right ) y^{\prime }}{1+x^{2} y^{2}} = 0 \] |
1 |
1 |
1 |
[_exact] |
✓ |
✓ |
0.739 |
|
|
\[ {}{\mathrm e}^{x} \left (1+x \right )+\left (y \,{\mathrm e}^{y}-x \,{\mathrm e}^{x}\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
0.317 |
|
|
\[ {}\frac {x y+1}{y}+\frac {\left (2 y-x \right ) y^{\prime }}{y^{2}} = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
0.508 |
|
|
\[ {}y^{2}-3 x y-2 x^{2}+\left (x y-x^{2}\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
0.293 |
|
|
\[ {}y \left (2 x +y+1\right )-x \left (2 y+x -1\right ) y^{\prime } = 0 \] |
1 |
1 |
3 |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
0.45 |
|
|
\[ {}y \left (2 x -y-1\right )+x \left (2 y-x -1\right ) y^{\prime } = 0 \] |
1 |
1 |
3 |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
0.445 |
|
|
\[ {}y^{2}+12 x^{2} y+\left (2 x y+4 x^{3}\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class G‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
0.308 |
|
|
\[ {}3 \left (x +y\right )^{2}+x \left (3 y+2 x \right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
0.264 |
|
|
\[ {}2 x y+\left (a +x^{2}+y^{2}\right ) y^{\prime } = 0 \] |
1 |
1 |
3 |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
0.378 |
|
|
\[ {}2 x y+x^{2}+b +\left (a +x^{2}+y^{2}\right ) y^{\prime } = 0 \] |
1 |
1 |
3 |
[_exact, _rational] |
✓ |
✓ |
0.435 |
|
|
\[ {}x y^{\prime }+y = x^{3} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.864 |
|
|
\[ {}x y^{\prime }+y = x \sin \left (x \right ) \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.918 |
|
|
\[ {}y^{\prime }+\frac {y}{x} = \frac {y^{2}}{x} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.67 |
|
|
\[ {}y^{\prime } \sin \left (y\right )+\sin \left (x \right ) \cos \left (y\right ) = \sin \left (x \right ) \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
32.585 |
|
|
\[ {}\left (3 x +2 y+1\right ) y^{\prime }+4 x +3 y+2 = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
5.098 |
|
|
\[ {}y^{2} {\mathrm e}^{x y^{2}}+4 x^{3}+\left (2 x y \,{\mathrm e}^{x y^{2}}-3 y^{2}\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_exact] |
✓ |
✓ |
4.291 |
|
|
\[ {}2 y-x y \ln \left (x \right )-2 x \ln \left (x \right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.997 |
|
|
\[ {}x y^{\prime }-y^{2}+1 = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.028 |
|
|
\[ {}\left (3+6 x y+x^{2}\right ) y^{\prime }+2 x +2 x y+3 y^{2} = 0 \] |
1 |
1 |
2 |
[_exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
1.602 |
|
|
\[ {}\left (x^{2}-1\right ) y^{\prime }+2 x y-\cos \left (x \right ) = 0 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
2.146 |
|
|
\[ {}\left (x^{2} y-1\right ) y^{\prime }+x y^{2}-1 = 0 \] |
1 |
1 |
2 |
[_exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
1.329 |
|
|
\[ {}\left (x^{2}-1\right ) y^{\prime }+x y-3 x y^{2} = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
6.486 |
|
|
\[ {}\left (x^{2}-1\right ) y^{\prime }-2 x y \ln \left (y\right ) = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
4.984 |
|
|
\[ {}\left (1+x^{2}+y^{2}\right ) y^{\prime }+2 x y+x^{2}+3 = 0 \] |
1 |
1 |
3 |
[_exact, _rational] |
✓ |
✓ |
14.271 |
|
|
\[ {}y^{2}+12 x^{2} y+\left (2 x y+4 x^{3}\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class G‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
3.901 |
|
|
\[ {}\left (x^{2}+y^{2}\right ) y^{\prime }+2 x \left (y+2 x \right ) = 0 \] |
1 |
1 |
3 |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
12.457 |
|
|
\[ {}3 x y^{2} y^{\prime }+y^{3}-2 x = 0 \] |
1 |
1 |
3 |
[[_homogeneous, ‘class G‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
1.956 |
|
|
\[ {}\left (2 y^{3}+y\right ) y^{\prime }-2 x^{3}-x = 0 \] |
1 |
1 |
4 |
[_separable] |
✓ |
✓ |
4.438 |
|
|
\[ {}y^{\prime }-{\mathrm e}^{x -y}+{\mathrm e}^{x} = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
3.698 |
|
|
\[ {}y^{\prime }+y \tan \left (x \right ) = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.778 |
|
|
\[ {}x \left (1-y\right ) y^{\prime }+\left (1+x \right ) y = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.003 |
|
|
\[ {}y^{\prime } = a x y^{2} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.365 |
|
|
\[ {}y^{2}+x y^{2}+\left (x^{2}-x^{2} y\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.09 |
|
|
\[ {}x y \left (x^{2}+1\right ) y^{\prime } = 1+y^{2} \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
2.289 |
|
|
\[ {}\frac {x}{y+1} = \frac {y y^{\prime }}{1+x} \] |
1 |
1 |
3 |
[_separable] |
✓ |
✓ |
177.621 |
|
|
\[ {}y^{\prime } = \frac {1+y^{2}}{x^{2}+1} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.748 |
|
|
\[ {}\sin \left (x \right ) \cos \left (y\right ) = \cos \left (x \right ) \sin \left (y\right ) y^{\prime } \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
34.78 |
|
|
\[ {}a x y^{\prime }+2 y = x y y^{\prime } \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.761 |
|
|
\[ {}3 x y^{2} y^{\prime }+3 y^{3} = 1 \] |
1 |
1 |
3 |
[_separable] |
✓ |
✓ |
1.345 |
|
|
\[ {}2 x \,{\mathrm e}^{3 y}+{\mathrm e}^{x}+\left (3 x^{2} {\mathrm e}^{3 y}-y^{2}\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_exact] |
✓ |
✓ |
1.407 |
|
|
\[ {}\left (x -y\right ) y^{\prime }+1+x +y = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.817 |
|
|
\[ {}\cos \left (x \right ) \cos \left (y\right )+\sin \left (x \right )^{2}-\left (\sin \left (x \right ) \sin \left (y\right )+\cos \left (y\right )^{2}\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
unknown |
✓ |
✓ |
34.924 |
|
|
\[ {}\left (-1+x \right ) y^{\prime }+y-\frac {1}{x^{2}}+\frac {2}{x^{3}} = 0 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.739 |
|
|
\[ {}x \ln \left (y\right ) y^{\prime }-y \ln \left (x \right ) = 0 \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
1.005 |
|
|
\[ {}2 x -y \sin \left (2 x \right ) = \left (\sin \left (x \right )^{2}-2 y\right ) y^{\prime } \] |
1 |
1 |
2 |
[_exact, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
3.685 |
|
|
\[ {}u \left (-v +1\right )+v^{2} \left (1-u\right ) u^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.009 |
|
|
\[ {}\left (y+2 x \right ) y^{\prime }-x +2 y = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.436 |
|
|
\[ {}\sin \left (x \right )^{2} y^{\prime }+\sin \left (x \right )^{2}+\left (x +y\right ) \sin \left (2 x \right ) = 0 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
3.256 |
|
|
\[ {}y^{\prime }+x y = \frac {x}{y} \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
1.196 |
|
|
\[ {}3 x^{2} y+x^{3} y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.992 |
|
|
\[ {}x y^{\prime } = x y+y \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.536 |
|
|
\[ {}y^{\prime } = 3 x^{2} y \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.51 |
|
|
\[ {}x y^{\prime } = y \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.454 |
|
|
\[ {}y^{\prime } = \frac {y \,{\mathrm e}^{x +y}}{x^{2}+2} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.726 |
|
|
\[ {}\left (x y^{2}+3 y^{2}\right ) y^{\prime }-2 x = 0 \] |
1 |
1 |
3 |
[_separable] |
✓ |
✓ |
0.747 |
|
|
\[ {}x y^{\prime } = \frac {1}{y^{3}} \] |
1 |
1 |
4 |
[_separable] |
✓ |
✓ |
0.439 |
|
|
\[ {}x^{\prime } = 3 x t^{2} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.547 |
|
|
\[ {}x^{\prime } = \frac {t \,{\mathrm e}^{-t -2 x}}{x} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.743 |
|
|
\[ {}y^{\prime } = \frac {x}{y^{2} \sqrt {1+x}} \] |
1 |
1 |
3 |
[_separable] |
✓ |
✓ |
0.605 |
|
|
\[ {}x v^{\prime } = \frac {1-4 v^{2}}{3 v} \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
2.539 |
|
|
\[ {}y^{\prime } = \frac {\sec \left (y\right )^{2}}{x^{2}+1} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
82.737 |
|
|
\[ {}y^{\prime } = 3 x^{2} \left (1+y^{2}\right )^{\frac {3}{2}} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.89 |
|
|
\[ {}x +x y^{2}+{\mathrm e}^{x^{2}} y y^{\prime } = 0 \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
1.51 |
|
|
\[ {}\frac {y^{\prime }}{y}+y \,{\mathrm e}^{\cos \left (x \right )} \sin \left (x \right ) = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.726 |
|
|
\[ {}y^{\prime } = \left (1+y^{2}\right ) \tan \left (x \right ) \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.17 |
|
|
\[ {}y^{\prime } = x^{3} \left (1-y\right ) \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.085 |
|
|
\[ {}\frac {y^{\prime }}{2} = \sqrt {y+1}\, \cos \left (x \right ) \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.295 |
|
|
\[ {}x^{2} y^{\prime } = \frac {4 x^{2}-x -2}{\left (1+x \right ) \left (y+1\right )} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
10.971 |
|
|
\[ {}\frac {y^{\prime }}{\theta } = \frac {y \sin \left (\theta \right )}{y^{2}+1} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
3.456 |
|
|
\[ {}x^{2}+2 y y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.619 |
|
|
\[ {}y^{\prime } = 2 t \cos \left (y\right )^{2} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.257 |
|
|
\[ {}y^{\prime } = 8 x^{3} {\mathrm e}^{-2 y} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.196 |
|
|
\[ {}y^{\prime } = x^{2} \left (y+1\right ) \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.071 |
|
|
\[ {}\sqrt {y}+\left (1+x \right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.5 |
|
|
\[ {}y^{\prime } = \frac {{\mathrm e}^{x^{2}}}{y^{2}} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.085 |
|
|
\[ {}y^{\prime } = \sqrt {\sin \left (x \right )+1}\, \left (1+y^{2}\right ) \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
76.019 |
|
|
\[ {}y^{\prime } = 2 y-2 t y \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.283 |
|
|
\[ {}y^{\prime } = \left (x -3\right ) \left (y+1\right )^{\frac {2}{3}} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.638 |
|
|
\[ {}y^{\prime } = x y^{3} \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
0.57 |
|
|
\[ {}y^{\prime } = x y^{3} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.247 |
|
|
\[ {}y^{\prime } = x y^{3} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.102 |
|
|
\[ {}y^{\prime } = x y^{3} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.092 |
|
|
\[ {}\left (t^{2}+1\right ) y^{\prime } = t y-y \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.053 |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime }+x y-x = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.967 |
|
|
\[ {}\sin \left (x \right ) y^{\prime }+y \cos \left (x \right ) = x \sin \left (x \right ) \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.739 |
|
|
|
||||||||
|
\[ {}\sqrt {-2 y-y^{2}}+\left (-x^{2}+2 x +3\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.96 |
|
|
\[ {}{\mathrm e}^{x y} y+2 x +\left ({\mathrm e}^{x y} x -2 y\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_exact] |
✓ |
✓ |
0.312 |
|
|
\[ {}y^{\prime }+x y = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.279 |
|
|
\[ {}y^{2}+\left (2 x y+\cos \left (y\right )\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_exact, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
0.283 |
|
|
\[ {}2 x +y \cos \left (x y\right )+\left (x \cos \left (x y\right )-2 y\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_exact] |
✓ |
✓ |
0.399 |
|
|
\[ {}\theta r^{\prime }+3 r-\theta -1 = 0 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.266 |
|
|
\[ {}2 x y+3+\left (x^{2}-1\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.26 |
|
|
\[ {}\left (x -2 y\right ) y^{\prime }+2 x +y = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
0.24 |
|
|
\[ {}{\mathrm e}^{x} \sin \left (y\right )-3 x^{2}+\left ({\mathrm e}^{x} \cos \left (y\right )+\frac {1}{3 y^{\frac {2}{3}}}\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_exact] |
✓ |
✓ |
0.556 |
|
|
\[ {}\cos \left (x \right ) \cos \left (y\right )+2 x -\left (\sin \left (x \right ) \sin \left (y\right )+2 y\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_exact] |
✓ |
✓ |
7.503 |
|
|
\[ {}{\mathrm e}^{t} \left (-t +y\right )+\left (1+{\mathrm e}^{t}\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.265 |
|
|
\[ {}\frac {t y^{\prime }}{y}+1+\ln \left (y\right ) = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.477 |
|
|
\[ {}\cos \left (\theta \right ) r^{\prime }-r \sin \left (\theta \right )+{\mathrm e}^{\theta } = 0 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.293 |
|
|
\[ {}{\mathrm e}^{x y} y-\frac {1}{y}+\left ({\mathrm e}^{x y} x +\frac {x}{y^{2}}\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_exact] |
✓ |
✓ |
0.319 |
|
|
\[ {}\frac {1}{y}-\left (3 y-\frac {x}{y^{2}}\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
0.204 |
|
|
\[ {}y^{\prime } = \frac {{\mathrm e}^{x +y}}{y-1} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.007 |
|
|
\[ {}\left (x^{2}-\frac {2}{y^{3}}\right ) y^{\prime }+2 x y-3 x^{2} = 0 \] |
1 |
1 |
3 |
[_exact, _rational] |
✓ |
✓ |
1.542 |
|
|
\[ {}2 x y^{3}-\left (-x^{2}+1\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
1.431 |
|
|
\[ {}t^{3} y^{2}+\frac {t^{4} y^{\prime }}{y^{6}} = 0 \] |
1 |
1 |
7 |
[_separable] |
✓ |
✓ |
0.602 |
|
|
\[ {}x^{2} y^{\prime }+2 x y-x +1 = 0 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.41 |
|
|
\[ {}x^{2} y^{\prime }+2 x y = \sinh \left (x \right ) \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.306 |
|
|
\[ {}y^{\prime }+x y = x y^{2} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.536 |
|
|
\[ {}\left (1+x \right )^{2} y^{\prime } = 1+y^{2} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.693 |
|
|
\[ {}x \cos \left (y\right ) y^{\prime }-\sin \left (y\right ) = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.332 |
|
|
\[ {}\left (x^{2}-1\right ) y^{\prime }+2 x y = x \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.437 |
|
|
\[ {}x y y^{\prime }-\left (1+x \right ) \sqrt {y-1} = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.855 |
|
|
\[ {}y+\left (x^{2}-4 x \right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.238 |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime } = x \left (y+1\right ) \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.118 |
|
|
\[ {}y^{\prime } = {\mathrm e}^{3 x -2 y} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.455 |
|
|
\[ {}y^{\prime }+\frac {y}{x} = \sin \left (2 x \right ) \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.467 |
|
|
\[ {}2 x y y^{\prime } = x^{2}-y^{2} \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
1.6 |
|
|
\[ {}y^{\prime } = \frac {1+x -2 y}{2 x -4 y} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.503 |
|
|
\[ {}y^{\prime }+\frac {y}{x} = \sin \left (x \right ) \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.323 |
|
|
\[ {}y^{\prime }+x +x y^{2} = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.891 |
|
|
\[ {}y^{\prime }+\left (\frac {1}{x}-\frac {2 x}{-x^{2}+1}\right ) y = \frac {1}{-x^{2}+1} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.244 |
|
|
\[ {}x \left (1+y^{2}\right )-\left (x^{2}+1\right ) y y^{\prime } = 0 \] |
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 |
|
|
\[ {}x y^{\prime } = 2 y \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.257 |
|
|
\[ {}x +y y^{\prime } = 0 \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
1.714 |
|
|
\[ {}4 y+x y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.306 |
|
|
\[ {}1+2 y+\left (-x^{2}+4\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
3.143 |
|
|
\[ {}y^{2}-x^{2} y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.185 |
|
|
\[ {}1+y-\left (1+x \right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.408 |
|
|
\[ {}1+2 y-\left (4-x \right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.612 |
|
|
\[ {}x y+\left (x^{2}+1\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.198 |
|
|
\[ {}x y y^{\prime } = \left (y+1\right ) \left (1-x \right ) \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.465 |
|
|
\[ {}1+\left (-x^{2}+1\right ) \cot \left (y\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.492 |
|
|
\[ {}x^{3}+y^{3}+3 x y^{2} y^{\prime } = 0 \] |
1 |
1 |
3 |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
2.03 |
|
|
\[ {}x y^{\prime }+2 y = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.536 |
|
|
\[ {}\cos \left (y\right )+\left (1+{\mathrm e}^{-x}\right ) \sin \left (y\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.595 |
|
|
\[ {}x^{2}-y-x y^{\prime } = 0 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.237 |
|
|
\[ {}x^{2}+y^{2}+2 x y y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
0.259 |
|
|
\[ {}x +y \cos \left (x \right )+\sin \left (x \right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.286 |
|
|
\[ {}2 x +3 y+4+\left (3 x +4 y+5\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
0.289 |
|
|
\[ {}4 x^{3} y^{3}+\frac {1}{x}+\left (3 x^{4} y^{2}-\frac {1}{y}\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _exact, _rational] |
✓ |
✓ |
0.796 |
|
|
\[ {}2 u^{2}+2 u v+\left (u^{2}+v^{2}\right ) v^{\prime } = 0 \] |
1 |
1 |
3 |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
0.323 |
|
|
\[ {}x \sqrt {x^{2}+y^{2}}-y+\left (y \sqrt {x^{2}+y^{2}}-x \right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_exact] |
✓ |
✓ |
0.389 |
|
|
\[ {}x +y+1-\left (y-x +3\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
0.283 |
|
|
\[ {}y^{2}-\frac {y}{x \left (x +y\right )}+2+\left (\frac {1}{x +y}+2 \left (1+x \right ) y\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_exact, _rational] |
✓ |
✓ |
0.455 |
|
|
\[ {}2 x y \,{\mathrm e}^{x^{2} y}+y^{2} {\mathrm e}^{x y^{2}}+1+\left (x^{2} {\mathrm e}^{x^{2} y}+2 x y \,{\mathrm e}^{x y^{2}}-2 y\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_exact] |
✓ |
✓ |
0.46 |
|
|
\[ {}x^{2}+y^{2}+2 x y y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
1.734 |
|
|
\[ {}x -x^{2}-y^{2}+y y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
0.274 |
|
|
\[ {}2 y-3 x +x y^{\prime } = 0 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.249 |
|
|
\[ {}x -y^{2}+2 x y y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
0.256 |
|
|
\[ {}-y-3 x^{2} \left (x^{2}+y^{2}\right )+x y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘], _rational, _Riccati] |
✓ |
✓ |
0.334 |
|
|
\[ {}y-\ln \left (x \right )-x y^{\prime } = 0 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.296 |
|
|
\[ {}3 x^{2}+y^{2}-2 x y y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
0.231 |
|
|
\[ {}x y-2 y^{2}-\left (x^{2}-3 x y\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
0.441 |
|
|
\[ {}x +y-\left (x -y\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
0.286 |
|
|
\[ {}2 y-3 x y^{2}-x y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
10.922 |
|
|
\[ {}y+x \left (x^{2} y-1\right ) y^{\prime } = 0 \] |
1 |
1 |
9 |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
0.292 |
|
|
\[ {}y+x^{3} y+2 x^{2}+\left (x +4 y^{4} x +8 y^{3}\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_rational] |
✓ |
✓ |
0.365 |
|
|
\[ {}-y-x^{2} {\mathrm e}^{x}+x y^{\prime } = 0 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.295 |
|
|
\[ {}1+y^{2} = \left (x^{2}+x \right ) y^{\prime } \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.252 |
|
|
\[ {}2 y-x^{3}+x y^{\prime } = 0 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.26 |
|
|
\[ {}y+\left (-x +y^{2}\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
0.217 |
|
|
\[ {}3 y^{3}-x y-\left (x^{2}+6 x y^{2}\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
0.429 |
|
|
\[ {}3 x^{2} y^{2}+4 \left (x^{3} y-3\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
0.261 |
|
|
\[ {}y \left (x +y\right )-x^{2} y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
0.237 |
|
|
\[ {}2 y+3 x y^{2}+\left (x +2 x^{2} y\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
0.253 |
|
|
\[ {}y \left (y^{2}-2 x^{2}\right )+x \left (2 y^{2}-x^{2}\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
0.372 |
|
|
\[ {}-y+x y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.264 |
|
|
\[ {}y^{\prime }-y = x y \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.299 |
|
|
\[ {}\left (2 s-{\mathrm e}^{2 t}\right ) s^{\prime } = 2 s \,{\mathrm e}^{2 t}-2 \cos \left (2 t \right ) \] |
1 |
1 |
2 |
[_exact, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
5.523 |
|
|
\[ {}y y^{\prime }-x y^{2}+x = 0 \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
2.288 |
|
|
\[ {}y-2 x y+x^{2} y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.016 |
|
|
\[ {}\left (y^{\prime }+1\right ) \ln \left (\frac {x +y}{x +3}\right ) = \frac {x +y}{x +3} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _exact, _dAlembert] |
✓ |
✓ |
6.257 |
|
|
\[ {}x \left (2-9 x y^{2}\right )+y \left (4 y^{2}-6 x^{3}\right ) y^{\prime } = 0 \] |
1 |
1 |
4 |
[_exact, _rational] |
✓ |
✓ |
1.365 |
|
|
\[ {}\frac {y}{x}+\left (y^{3}+\ln \left (x \right )\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_exact, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
1.298 |
|
|
\[ {}3+2 x +\left (-2+2 y\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
2.096 |
|
|
\[ {}y^{\prime } = x^{2} \left (1+y^{2}\right ) \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.74 |
|
|
\[ {}y^{\prime } = \frac {x^{2}}{1-y^{2}} \] |
1 |
1 |
3 |
[_separable] |
✓ |
✓ |
164.3 |
|
|
\[ {}y^{\prime } = \frac {3 x^{2}+4 x +2}{-2+2 y} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
3.204 |
|
|
\[ {}{\mathrm e}^{x}+y+\left (x -2 \sin \left (y\right )\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_exact] |
✓ |
✓ |
1.74 |
|
|
\[ {}3 x +\frac {6}{y}+\left (\frac {x^{2}}{y}+\frac {3 y}{x}\right ) y^{\prime } = 0 \] |
1 |
1 |
3 |
[_rational] |
✓ |
✓ |
12.398 |
|
|
\[ {}y^{\prime } = -\frac {2}{t}+\frac {y}{t}+\frac {y^{2}}{t} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.951 |
|
|
\[ {}{\mathrm e}^{x y} y+x \,{\mathrm e}^{x y} y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.178 |
|
|
\[ {}x -2 x y+{\mathrm e}^{y}+\left (y-x^{2}+{\mathrm e}^{y} x \right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_exact] |
✓ |
✓ |
1.484 |
|
|
\[ {}y^{\prime }+y \cos \left (x \right ) = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.06 |
|
|
\[ {}y^{\prime }+2 x y = x \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.325 |
|
|
\[ {}x y^{\prime }+y = 3 x^{3}-1 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.842 |
|
|
\[ {}y^{\prime }+{\mathrm e}^{x} y = 3 \,{\mathrm e}^{x} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.077 |
|
|
\[ {}x^{2} y^{\prime }+2 x y = 1 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.868 |
|
|
\[ {}y^{\prime } = x^{2} y \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.765 |
|
|
\[ {}y y^{\prime } = x \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
1.651 |
|
|
\[ {}y^{\prime } = \frac {x^{2}+x}{y-y^{2}} \] |
1 |
1 |
3 |
[_separable] |
✓ |
✓ |
172.495 |
|
|
\[ {}y^{\prime } = \frac {{\mathrm e}^{x -y}}{1+{\mathrm e}^{x}} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.982 |
|
|
\[ {}y^{\prime } = x^{2} y^{2}-4 x^{2} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.866 |
|
|
\[ {}2 x y+\left (x^{2}+3 y^{2}\right ) y^{\prime } = 0 \] |
1 |
1 |
3 |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
0.279 |
|
|
\[ {}x^{2}+x y+\left (x +y\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[_quadrature] |
✓ |
✓ |
0.166 |
|
|
\[ {}{\mathrm e}^{x}+{\mathrm e}^{y} \left (y+1\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.303 |
|
|
\[ {}\cos \left (x \right ) \cos \left (y\right )^{2}-\sin \left (x \right ) \sin \left (2 y\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
1.139 |
|
|
\[ {}x^{2} y^{3}-x^{3} y^{2} y^{\prime } = 0 \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
0.329 |
|
|
\[ {}x +y+\left (x -y\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
0.236 |
|
|
\[ {}2 y \,{\mathrm e}^{2 x}+2 x \cos \left (y\right )+\left ({\mathrm e}^{2 x}-x^{2} \sin \left (y\right )\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_exact] |
✓ |
✓ |
0.428 |
|
|
\[ {}3 \ln \left (x \right ) x^{2}+x^{2}+y+x y^{\prime } = 0 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.294 |
|
|
\[ {}2 y^{3}+2+3 x y^{2} y^{\prime } = 0 \] |
1 |
1 |
3 |
[_separable] |
✓ |
✓ |
1.077 |
|
|
\[ {}\cos \left (x \right ) \cos \left (y\right )-2 \sin \left (x \right ) \sin \left (y\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
0.922 |
|
|
\[ {}5 x^{3} y^{2}+2 y+\left (3 x^{4} y+2 x \right ) y^{\prime } = 0 \] |
1 |
1 |
3 |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
0.348 |
|
|
\[ {}{\mathrm e}^{y}+{\mathrm e}^{y} x +x \,{\mathrm e}^{y} y^{\prime } = 0 \] |
1 |
1 |
1 |
[_quadrature] |
✓ |
✓ |
0.261 |
|
|
\[ {}x y^{\prime } = 2 y \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.975 |
|
|
\[ {}y y^{\prime } = {\mathrm e}^{2 x} \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
0.77 |
|
|
\[ {}y^{\prime }+x y = y^{4} x \] |
1 |
1 |
3 |
[_separable] |
✓ |
✓ |
7.695 |
|
|
\[ {}\left ({\mathrm e}^{y}-2 x y\right ) y^{\prime } = y^{2} \] |
1 |
1 |
1 |
[_exact, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
2.072 |
|
|
\[ {}x y^{\prime } = 2 x^{2} y+y \ln \left (x \right ) \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.501 |
|
|
\[ {}\left (x +\frac {2}{y}\right ) y^{\prime }+y = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
2.368 |
|
|
\[ {}y-x^{3}+\left (x +y^{3}\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_exact, _rational] |
✓ |
✓ |
2.069 |
|
|
\[ {}y+y \cos \left (x y\right )+\left (x +x \cos \left (x y\right )\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
2.158 |
|
|
\[ {}\cos \left (x \right ) \cos \left (y\right )^{2}+2 \sin \left (x \right ) \sin \left (y\right ) \cos \left (y\right ) y^{\prime } = 0 \] |
1 |
1 |
3 |
[_separable] |
✓ |
✓ |
8.104 |
|
|
\[ {}\left (\sin \left (x \right ) \sin \left (y\right )-{\mathrm e}^{y} x \right ) y^{\prime } = {\mathrm e}^{y}+\cos \left (x \right ) \cos \left (y\right ) \] |
1 |
1 |
1 |
[_exact] |
✓ |
✓ |
15.332 |
|
|
\[ {}-\frac {\sin \left (\frac {x}{y}\right )}{y}+\frac {x \sin \left (\frac {x}{y}\right ) y^{\prime }}{y^{2}} = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.669 |
|
|
\[ {}1+y+\left (1-x \right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.761 |
|
|
\[ {}2 x y^{3}+y \cos \left (x \right )+\left (3 x^{2} y^{2}+\sin \left (x \right )\right ) y^{\prime } = 0 \] |
1 |
1 |
3 |
[_exact, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
54.746 |
|
|
\[ {}\frac {y}{1-x^{2} y^{2}}+\frac {x y^{\prime }}{1-x^{2} y^{2}} = 1 \] |
1 |
1 |
1 |
[_exact, _rational, _Riccati] |
✓ |
✓ |
2.265 |
|
|
\[ {}2 y^{4} x +\sin \left (y\right )+\left (4 x^{2} y^{3}+x \cos \left (y\right )\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_exact] |
✓ |
✓ |
4.274 |
|
|
\[ {}\frac {x y^{\prime }+y}{1-x^{2} y^{2}}+x = 0 \] |
1 |
1 |
1 |
[_exact, _rational, _Riccati] |
✓ |
✓ |
2.368 |
|
|
\[ {}2 x \left (1+\sqrt {x^{2}-y}\right ) = \sqrt {x^{2}-y}\, y^{\prime } \] |
1 |
1 |
1 |
[_exact, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
7.158 |
|
|
\[ {}x \ln \left (y\right )+x y+\left (y \ln \left (x \right )+x y\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.919 |
|
|
\[ {}{\mathrm e}^{y^{2}}-\csc \left (y\right ) \csc \left (x \right )^{2}+\left (2 x y \,{\mathrm e}^{y^{2}}-\csc \left (y\right ) \cot \left (y\right ) \cot \left (x \right )\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_exact] |
✓ |
✓ |
84.118 |
|
|
\[ {}1+y^{2} \sin \left (2 x \right )-2 y \cos \left (x \right )^{2} y^{\prime } = 0 \] |
1 |
1 |
2 |
[_exact, _Bernoulli] |
✓ |
✓ |
0.707 |
|
|
\[ {}\frac {x}{\left (x^{2}+y^{2}\right )^{\frac {3}{2}}}+\frac {y y^{\prime }}{\left (x^{2}+y^{2}\right )^{\frac {3}{2}}} = 0 \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
0.289 |
|
|
\[ {}3 x^{2} \left (1+\ln \left (y\right )\right )+\left (\frac {x^{3}}{y}-2 y\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_exact, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
3.157 |
|
|
\[ {}\frac {y-x y^{\prime }}{\left (x +y\right )^{2}}+y^{\prime } = 1 \] |
1 |
1 |
2 |
[[_1st_order, _with_linear_symmetries], _exact, _rational] |
✓ |
✓ |
8.179 |
|
|
\[ {}\frac {4 y^{2}-2 x^{2}}{4 x y^{2}-x^{3}}+\frac {\left (8 y^{2}-x^{2}\right ) y^{\prime }}{4 y^{3}-x^{2} y} = 0 \] |
1 |
1 |
4 |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
8.88 |
|
|
\[ {}\left (3 x^{2}-y^{2}\right ) y^{\prime }-2 x y = 0 \] |
1 |
1 |
3 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
0.444 |
|
|
\[ {}x y-1+\left (x^{2}-x y\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
0.382 |
|
|
\[ {}x y^{\prime }+y+3 x^{3} y^{4} y^{\prime } = 0 \] |
1 |
1 |
4 |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
0.537 |
|
|
\[ {}{\mathrm e}^{x}+\left ({\mathrm e}^{x} \cot \left (y\right )+2 y \csc \left (y\right )\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
0.559 |
|
|
\[ {}\left (2+x \right ) \sin \left (y\right )+x \cos \left (y\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.457 |
|
|
\[ {}y+\left (x -2 x^{2} y^{3}\right ) y^{\prime } = 0 \] |
1 |
1 |
3 |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
0.472 |
|
|
\[ {}x +3 y^{2}+2 x y y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
0.338 |
|
|
\[ {}y+\left (2 x -y \,{\mathrm e}^{y}\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
0.443 |
|
|
\[ {}y \ln \left (y\right )-2 x y+\left (x +y\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
0.879 |
|
|
\[ {}y^{2}+x y+1+\left (x^{2}+x y+1\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
0.46 |
|
|
\[ {}x^{3}+x y^{3}+3 y^{2} y^{\prime } = 0 \] |
1 |
1 |
3 |
[_rational, _Bernoulli] |
✓ |
✓ |
0.455 |
|
|
\[ {}x y^{\prime }+y = x \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
3.171 |
|
|
\[ {}x^{2} y^{\prime } = y \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.053 |
|
|
\[ {}\sec \left (x \right ) y^{\prime } = \sec \left (y\right ) \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
3.589 |
|
|
\[ {}x^{2} y^{\prime }+2 x y = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.572 |
|
|
\[ {}-\sin \left (x \right ) \sin \left (y\right )+\cos \left (x \right ) \cos \left (y\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
41.194 |
|
|
\[ {}y^{2} y^{\prime } = x \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
163.036 |
|
|
\[ {}\csc \left (x \right ) y^{\prime } = \csc \left (y\right ) \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
5.879 |
|
|
\[ {}2 x \cos \left (y\right )-x^{2} \sin \left (y\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
17.418 |
|
|
\[ {}\frac {1}{y}-\frac {x y^{\prime }}{y^{2}} = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.627 |
|
|
\[ {}y^{\prime } = 2 x y \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.815 |
|
|
\[ {}x y^{\prime } = y \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.5 |
|
|
\[ {}x^{2} y^{\prime } = y \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.664 |
|
|
\[ {}y^{\prime }+\frac {y}{x} = x \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
2.173 |
|
|
\[ {}y^{\prime } = \frac {y}{x \ln \left (x \right )} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.048 |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime }+y^{2} = -1 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.919 |
|
|
\[ {}y^{\prime } = \frac {2 x -y}{x +4 y} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
3.537 |
|
|
\[ {}y^{2}+\cos \left (x \right )+\left (2 x y+\sin \left (y\right )\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_exact] |
✓ |
✓ |
0.425 |
|
|
\[ {}x y-1+x^{2} y^{\prime } = 0 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.302 |
|
|
\[ {}y^{\prime } = \frac {\cos \left (y\right ) \sec \left (x \right )}{x} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.487 |
|
|
\[ {}y^{\prime } = x \left (\cos \left (y\right )+y\right ) \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.819 |
|
|
\[ {}y^{\prime } = \frac {\sec \left (x \right ) \left (\sin \left (y\right )+y\right )}{x} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.619 |
|
|
\[ {}y^{\prime } = \left (5+\frac {\sec \left (x \right )}{x}\right ) \left (\sin \left (y\right )+y\right ) \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
11.605 |
|
|
\[ {}y^{\prime } = \frac {2 y}{x} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.167 |
|
|
\[ {}y^{\prime } = \frac {2 y}{x} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.577 |
|
|
\[ {}y^{\prime } = \frac {\ln \left (1+y^{2}\right )}{\ln \left (x^{2}+1\right )} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.029 |
|
|
\[ {}y^{2}+\frac {2}{x}+2 x y y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class G‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
0.987 |
|
|
\[ {}y^{\prime } = \frac {y \left (1+\frac {a^{2} x}{\sqrt {a^{2} \left (x^{2}+1\right )}}\right )}{\sqrt {a^{2} \left (x^{2}+1\right )}} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
4.036 |
|
|
\[ {}y^{\prime } = \frac {y}{2 y \ln \left (y\right )+y-x} \] |
1 |
1 |
1 |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
2.548 |
|
|
\[ {}x^{2} y^{\prime }+{\mathrm e}^{-y} = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.014 |
|
|
\[ {}y^{\prime } = a x y \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.506 |
|
|
\[ {}y^{\prime } = {\mathrm e}^{x +y} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.191 |
|
|
\[ {}y^{\prime }-\left (a +\cos \left (\ln \left (x \right )\right )+\sin \left (\ln \left (x \right )\right )\right ) y = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.509 |
|
|
\[ {}y^{\prime }-x y^{2}-3 x y = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.435 |
|
|
\[ {}y^{\prime }-a \,x^{n} \left (1+y^{2}\right ) = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.48 |
|
|
\[ {}y^{\prime }+f \left (x \right ) \left (y^{2}+2 a y+b \right ) = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.998 |
|
|
\[ {}y^{\prime }-\frac {\sqrt {y^{2}-1}}{\sqrt {x^{2}-1}} = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
22.204 |
|
|
\[ {}y^{\prime }-\frac {\sqrt {x^{2}-1}}{\sqrt {y^{2}-1}} = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.974 |
|
|
\[ {}y^{\prime }-\frac {1+y^{2}}{{| y+\sqrt {y+1}|} \left (1+x \right )^{\frac {3}{2}}} = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
130.102 |
|
|
\[ {}y^{\prime }-\frac {\sqrt {{| y \left (y-1\right ) \left (-1+a y\right )|}}}{\sqrt {{| x \left (-1+x \right ) \left (x a -1\right )|}}} = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.278 |
|
|
\[ {}y^{\prime }-\frac {\sqrt {1-y^{4}}}{\sqrt {-x^{4}+1}} = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
4.066 |
|
|
\[ {}y^{\prime }-\operatorname {R1} \left (x , \sqrt {a_{4} x^{4}+a_{3} x^{3}+a_{2} x^{2}+a_{1} x +a_{0}}\right ) \operatorname {R2} \left (y, \sqrt {b_{4} y^{4}+b_{3} y^{3}+b_{2} y^{2}+b_{1} y+b_{0}}\right ) = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.336 |
|
|
\[ {}y^{\prime }-{\mathrm e}^{x -y}+{\mathrm e}^{x} = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.88 |
|
|
\[ {}x y^{\prime }+y-x \sin \left (x \right ) = 0 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.964 |
|
|
\[ {}x y^{\prime }-y^{2}+1 = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.039 |
|
|
\[ {}x y^{\prime }-y \ln \left (y\right ) = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.248 |
|
|
|
||||||||
|
\[ {}\left (2 x +1\right ) y^{\prime }-4 \,{\mathrm e}^{-y}+2 = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.796 |
|
|
\[ {}x^{2} y^{\prime }-\left (-1+x \right ) y = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.096 |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime }+2 x y-2 x^{2} = 0 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.036 |
|
|
\[ {}\left (x^{2}-1\right ) y^{\prime }+2 x y-\cos \left (x \right ) = 0 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
2.161 |
|
|
\[ {}\left (x^{2}-1\right ) y^{\prime }+a x y^{2}+x y = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
3.3 |
|
|
\[ {}\left (x^{2}-1\right ) y^{\prime }-2 x y \ln \left (y\right ) = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.702 |
|
|
\[ {}x \left (x^{2}+1\right ) y^{\prime }+x^{2} y = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.967 |
|
|
\[ {}\left (2 x^{4}-x \right ) y^{\prime }-2 \left (x^{3}-1\right ) y = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.318 |
|
|
\[ {}\sqrt {x^{2}-1}\, y^{\prime }-\sqrt {y^{2}-1} = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
15.137 |
|
|
\[ {}\sqrt {-x^{2}+1}\, y^{\prime }-y \sqrt {y^{2}-1} = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.783 |
|
|
\[ {}\sin \left (2 x \right ) y^{\prime }+\sin \left (2 y\right ) = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
27.957 |
|
|
\[ {}\left (a \sin \left (x \right )^{2}+b \right ) y^{\prime }+a y \sin \left (2 x \right )+A x \left (a \sin \left (x \right )^{2}+c \right ) = 0 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
2.359 |
|
|
\[ {}y y^{\prime }+x y^{2}-4 x = 0 \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
1.973 |
|
|
\[ {}\left (2 y-x \right ) y^{\prime }-y-2 x = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.146 |
|
|
\[ {}\left (4 y-3 x -5\right ) y^{\prime }-3 y+7 x +2 = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
4.281 |
|
|
\[ {}\left (12 y-5 x -8\right ) y^{\prime }-5 y+2 x +3 = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
3.935 |
|
|
\[ {}2 x y y^{\prime }+2 y^{2}+1 = 0 \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
2.362 |
|
|
\[ {}\left (3+6 x y+x^{2}\right ) y^{\prime }+2 x +2 x y+3 y^{2} = 0 \] |
1 |
1 |
2 |
[_exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
1.834 |
|
|
\[ {}\left (x^{2} y-1\right ) y^{\prime }+x y^{2}-1 = 0 \] |
1 |
1 |
2 |
[_exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
1.626 |
|
|
\[ {}x^{2} \left (y-1\right ) y^{\prime }+\left (-1+x \right ) y = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.733 |
|
|
\[ {}y y^{\prime } \sin \left (x \right )^{2}+y^{2} \cos \left (x \right ) \sin \left (x \right )-1 = 0 \] |
1 |
1 |
2 |
[_exact, _Bernoulli] |
✓ |
✓ |
12.353 |
|
|
\[ {}\left (-x +y^{2}\right ) y^{\prime }-y+x^{2} = 0 \] |
1 |
1 |
3 |
[_exact, _rational] |
✓ |
✓ |
12.393 |
|
|
\[ {}\left (x^{2}+y^{2}\right ) y^{\prime }+2 x \left (y+2 x \right ) = 0 \] |
1 |
1 |
3 |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
10.35 |
|
|
\[ {}\left (a +x^{2}+y^{2}\right ) y^{\prime }+2 x y = 0 \] |
1 |
1 |
3 |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
10.403 |
|
|
\[ {}2 x y+x^{2}+b +\left (a +x^{2}+y^{2}\right ) y^{\prime } = 0 \] |
1 |
1 |
3 |
[_exact, _rational] |
✓ |
✓ |
2.233 |
|
|
\[ {}\left (3 x^{2}+2 x y+4 y^{2}\right ) y^{\prime }+2 x^{2}+6 x y+y^{2} = 0 \] |
1 |
1 |
3 |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
2.693 |
|
|
\[ {}\left (1-3 x^{2} y+6 y^{2}\right ) y^{\prime }-3 x y^{2}+x = 0 \] |
1 |
1 |
3 |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
2.181 |
|
|
\[ {}\left (6 y-x \right )^{2} y^{\prime }-6 y^{2}+2 x y+a = 0 \] |
1 |
1 |
3 |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
✓ |
1.95 |
|
|
\[ {}\left (a y^{2}+2 b x y+c \,x^{2}\right ) y^{\prime }+b y^{2}+2 c x y+d \,x^{2} = 0 \] |
1 |
1 |
3 |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
4.631 |
|
|
\[ {}3 x y^{2} y^{\prime }+y^{3}-2 x = 0 \] |
1 |
1 |
3 |
[[_homogeneous, ‘class G‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
1.665 |
|
|
\[ {}\left (3 x y^{2}-x^{2}\right ) y^{\prime }+y^{3}-2 x y = 0 \] |
1 |
1 |
3 |
[[_homogeneous, ‘class G‘], _exact, _rational] |
✓ |
✓ |
2.623 |
|
|
\[ {}6 x y^{2} y^{\prime }+2 y^{3}+x = 0 \] |
1 |
1 |
3 |
[[_homogeneous, ‘class G‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
1.436 |
|
|
\[ {}\left (y^{3}-3 x \right ) y^{\prime }-3 y+x^{2} = 0 \] |
1 |
1 |
1 |
[_exact, _rational] |
✓ |
✓ |
1.838 |
|
|
\[ {}\left (a +x^{2}+y^{2}\right ) y y^{\prime }+\left (y^{2}+x^{2}-a \right ) x = 0 \] |
1 |
1 |
4 |
[_exact, _rational] |
✓ |
✓ |
2.072 |
|
|
\[ {}2 y^{3} y^{\prime }+x y^{2} = 0 \] |
1 |
1 |
3 |
[_separable] |
✓ |
✓ |
2.089 |
|
|
\[ {}\left (2 y^{3}+y\right ) y^{\prime }-2 x^{3}-x = 0 \] |
1 |
1 |
4 |
[_separable] |
✓ |
✓ |
4.007 |
|
|
\[ {}\left (2 y^{3}+5 x^{2} y\right ) y^{\prime }+5 x y^{2}+x^{3} = 0 \] |
1 |
1 |
4 |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
2.622 |
|
|
\[ {}\left (3 x^{3}+6 x^{2} y-3 x y^{2}+20 y^{3}\right ) y^{\prime }+4 x^{3}+9 x^{2} y+6 x y^{2}-y^{3} = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
4.909 |
|
|
\[ {}\left (10 x^{2} y^{3}-3 y^{2}-2\right ) y^{\prime }+5 y^{4} x +x = 0 \] |
1 |
1 |
1 |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
2.027 |
|
|
\[ {}\left (f \left (x +y\right )+1\right ) y^{\prime }+f \left (x +y\right ) = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _exact, _dAlembert] |
✓ |
✓ |
1.382 |
|
|
\[ {}\frac {y^{\prime } f_{\nu }\left (x \right ) \left (-y+y^{p +1}\right )}{y-1}-\frac {g_{\nu }\left (x \right ) \left (-y+y^{q +1}\right )}{y-1} = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.638 |
|
|
\[ {}\sqrt {y^{2}-1}\, y^{\prime }-\sqrt {x^{2}-1} = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.625 |
|
|
\[ {}\left (\sqrt {1+y^{2}}+x a \right ) y^{\prime }+\sqrt {x^{2}+1}+a y = 0 \] |
1 |
1 |
1 |
[_exact] |
✓ |
✓ |
2.711 |
|
|
\[ {}\left ({\mathrm e}^{x}+{\mathrm e}^{y} x \right ) y^{\prime }+{\mathrm e}^{x} y+{\mathrm e}^{y} = 0 \] |
1 |
1 |
1 |
[_exact] |
✓ |
✓ |
2.319 |
|
|
\[ {}y^{\prime } \left (\sin \left (x \right )+1\right ) \sin \left (y\right )+\cos \left (x \right ) \left (\cos \left (y\right )-1\right ) = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
6.272 |
|
|
\[ {}\left (x \cos \left (y\right )+\sin \left (x \right )\right ) y^{\prime }+y \cos \left (x \right )+\sin \left (y\right ) = 0 \] |
1 |
1 |
1 |
[_exact] |
✓ |
✓ |
13.434 |
|
|
\[ {}y^{\prime } \left (\cos \left (y\right )-\sin \left (\alpha \right ) \sin \left (x \right )\right ) \cos \left (y\right )+\left (\cos \left (x \right )-\sin \left (\alpha \right ) \sin \left (y\right )\right ) \cos \left (x \right ) = 0 \] |
1 |
1 |
1 |
unknown |
✓ |
✓ |
6.481 |
|
|
\[ {}x \cos \left (y\right ) y^{\prime }+\sin \left (y\right ) = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
3.712 |
|
|
\[ {}\left (x \cos \left (y\right )+\cos \left (x \right )\right ) y^{\prime }-y \sin \left (x \right )+\sin \left (y\right ) = 0 \] |
1 |
1 |
1 |
[_exact] |
✓ |
✓ |
8.404 |
|
|
\[ {}\left (x^{2} \cos \left (y\right )+2 y \sin \left (x \right )\right ) y^{\prime }+2 \sin \left (y\right ) x +y^{2} \cos \left (x \right ) = 0 \] |
1 |
1 |
1 |
[_exact] |
✓ |
✓ |
33.297 |
|
|
\[ {}\cos \left (x \right ) \sin \left (y\right ) y^{\prime }+\sin \left (x \right ) \cos \left (y\right ) = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
3.329 |
|
|
\[ {}3 \sin \left (x \right ) \sin \left (y\right ) y^{\prime }+5 \cos \left (x \right )^{4} y = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
32.413 |
|
|
\[ {}\left (x \sin \left (x y\right )+\cos \left (x +y\right )-\sin \left (y\right )\right ) y^{\prime }+y \sin \left (x y\right )+\cos \left (x +y\right )+\cos \left (x \right ) = 0 \] |
1 |
1 |
1 |
[_exact] |
✓ |
✓ |
37.063 |
|
|
\[ {}f \left (x^{2}+a y^{2}\right ) \left (a y y^{\prime }+x \right )-y-x y^{\prime } = 0 \] |
1 |
1 |
1 |
[_exact] |
✓ |
✓ |
2.684 |
|
|
\[ {}y^{\prime } = f \left (x \right ) g \left (y\right ) \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.701 |
|
|
\[ {}\left (y A +B x +a \right ) y^{\prime }+B y+k x +b = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.462 |
|
|
\[ {}\left (y+A \,x^{n}+a \right ) y^{\prime }+n A \,x^{n -1} y+k \,x^{m}+b = 0 \] |
1 |
1 |
2 |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.797 |
|
|
\[ {}\frac {2 x y+1}{y}+\frac {\left (y-x \right ) y^{\prime }}{y^{2}} = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.813 |
|
|
\[ {}\frac {y^{2}-2 x^{2}}{x y^{2}-x^{3}}+\frac {\left (2 y^{2}-x^{2}\right ) y^{\prime }}{y^{3}-x^{2} y} = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
6.898 |
|
|
\[ {}\frac {1}{\sqrt {x^{2}+y^{2}}}+\left (\frac {1}{y}-\frac {x}{y \sqrt {x^{2}+y^{2}}}\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
2.803 |
|
|
\[ {}y+x +x y^{\prime } = 0 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.278 |
|
|
\[ {}6 x -2 y+1+\left (2 y-2 x -3\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
4.003 |
|
|
\[ {}\sec \left (x \right ) \cos \left (y\right )^{2}-\cos \left (x \right ) \sin \left (y\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
7.841 |
|
|
\[ {}\left (1+x \right ) y^{2}-x^{3} y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.849 |
|
|
\[ {}2 \left (1-y^{2}\right ) x y+\left (x^{2}+1\right ) \left (1+y^{2}\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
3.162 |
|
|
\[ {}\sin \left (x \right ) \cos \left (y\right )^{2}+\cos \left (x \right )^{2} y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.36 |
|
|
\[ {}y^{3}+x^{3} y^{\prime } = 0 \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
1.187 |
|
|
\[ {}y y^{\prime }+x y^{2} = x \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
2.46 |
|
|
\[ {}y^{\prime } \sin \left (y\right )+\sin \left (x \right ) \cos \left (y\right ) = \sin \left (x \right ) \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
32.255 |
|
|
\[ {}y^{2} \left (3 y-6 x y^{\prime }\right )-x \left (y-2 x y^{\prime }\right ) = 0 \] |
1 |
1 |
3 |
[_separable] |
✓ |
✓ |
1.021 |
|
|
\[ {}x^{3} y-y^{4}+\left (x y^{3}-x^{4}\right ) y^{\prime } = 0 \] |
1 |
1 |
4 |
[_separable] |
✓ |
✓ |
0.923 |
|
|
\[ {}x \sqrt {1-y^{2}}+y \sqrt {-x^{2}+1}\, y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.969 |
|
|
\[ {}\sqrt {1-y^{2}}+\sqrt {-x^{2}+1}\, y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.859 |
|
|
\[ {}\left (1-x \right ) y+x \left (1-y\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.22 |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime }-x y = a x y^{2} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
3.538 |
|
|
\[ {}\left (1-x \right ) y-x \left (y+1\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.126 |
|
|
\[ {}3 x^{2} y+\left (x^{3}+x^{3} y^{2}\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.99 |
|
|
\[ {}x^{\prime } = \frac {2 x}{t} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.427 |
|
|
\[ {}x^{\prime } = -\frac {t}{x} \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
2.038 |
|
|
\[ {}2 t x^{\prime } = x \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.954 |
|
|
\[ {}x^{\prime } = \frac {2 x}{t +1} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.369 |
|
|
\[ {}\theta ^{\prime } = t \sqrt {t^{2}+1}\, \sec \left (\theta \right ) \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.33 |
|
|
\[ {}\left (2 u+1\right ) u^{\prime }-t -1 = 0 \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
2.651 |
|
|
\[ {}R^{\prime } = \left (t +1\right ) \left (1+R^{2}\right ) \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.952 |
|
|
\[ {}\left (t +1\right ) x^{\prime }+x^{2} = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.79 |
|
|
\[ {}x^{\prime } = 2 t x^{2} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.859 |
|
|
\[ {}x^{\prime } = t^{2} {\mathrm e}^{-x} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.192 |
|
|
\[ {}x^{\prime } = {\mathrm e}^{t +x} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.159 |
|
|
\[ {}T^{\prime } = 2 a t \left (T^{2}-a^{2}\right ) \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
3.982 |
|
|
\[ {}y^{\prime } = t^{2} \tan \left (y\right ) \] |
1 |
0 |
1 |
[_separable] |
✓ |
✓ |
1.928 |
|
|
\[ {}x^{\prime } = \frac {\left (4+2 t \right ) x}{\ln \left (x\right )} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.101 |
|
|
\[ {}y^{\prime } = \frac {2 t y^{2}}{t^{2}+1} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.32 |
|
|
\[ {}x^{\prime } = \frac {t^{2}}{1-x^{2}} \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
34.553 |
|
|
\[ {}x^{\prime } = 6 t \left (x-1\right )^{\frac {2}{3}} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.516 |
|
|
\[ {}x^{\prime } {\mathrm e}^{2 t}+2 x \,{\mathrm e}^{2 t} = {\mathrm e}^{-t} \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.14 |
|
|
\[ {}y^{\prime } = -y^{2} {\mathrm e}^{-t^{2}} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.162 |
|
|
\[ {}\cos \left (t \right ) x^{\prime }-2 x \sin \left (x\right ) = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.375 |
|
|
\[ {}t x^{\prime } = -x+t^{2} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.892 |
|
|
\[ {}\left (t^{2}+1\right ) x^{\prime } = -3 x t +6 t \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.603 |
|
|
\[ {}x^{\prime } = \left (a +\frac {b}{t}\right ) x \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.794 |
|
|
\[ {}\cos \left (\theta \right ) v^{\prime }+v = 3 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.734 |
|
|
\[ {}x^{\prime } = 2 x t \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.963 |
|
|
\[ {}x^{\prime }+p \left (t \right ) x = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.148 |
|
|
\[ {}x^{\prime } = -\frac {x}{t}+\frac {1}{t x^{2}} \] |
1 |
1 |
3 |
[_separable] |
✓ |
✓ |
3.64 |
|
|
\[ {}x^{3}+3 t x^{2} x^{\prime } = 0 \] |
1 |
1 |
4 |
[_separable] |
✓ |
✓ |
1.018 |
|
|
\[ {}t^{3}+\frac {x}{t}+\left (x^{2}+\ln \left (t \right )\right ) x^{\prime } = 0 \] |
1 |
1 |
3 |
[_exact] |
✓ |
✓ |
1.697 |
|
|
\[ {}x^{\prime } = -\frac {\sin \left (x\right )-x \sin \left (t \right )}{t \cos \left (x\right )+\cos \left (t \right )} \] |
1 |
1 |
1 |
[NONE] |
✓ |
✓ |
6.304 |
|
|
\[ {}x+3 t x^{2} x^{\prime } = 0 \] |
1 |
1 |
3 |
[_separable] |
✓ |
✓ |
1.022 |
|
|
\[ {}x^{2}-t^{2} x^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.919 |
|
|
\[ {}t \cot \left (x\right ) x^{\prime } = -2 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
3.178 |
|
|
\[ {}x^{2}+y^{2}+2 x y y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
2.398 |
|
|
\[ {}y^{\prime }+4 x y = 8 x \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.668 |
|
|
\[ {}y^{\prime } = x^{2} \sin \left (y\right ) \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
8.564 |
|
|
\[ {}y^{\prime } = \frac {y^{2}}{-2+x} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.306 |
|
|
\[ {}3 x +2 y+\left (y+2 x \right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
4.587 |
|
|
\[ {}y^{2}+3+\left (2 x y-4\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
1.392 |
|
|
\[ {}2 x y+1+\left (x^{2}+4 y\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.852 |
|
|
\[ {}6 x y+2 y^{2}-5+\left (3 x^{2}+4 x y-6\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[_exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
1.518 |
|
|
\[ {}y \sec \left (x \right )^{2}+\sec \left (x \right ) \tan \left (x \right )+\left (\tan \left (x \right )+2 y\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[_exact, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
12.638 |
|
|
\[ {}\frac {\left (2 s-1\right ) s^{\prime }}{t}+\frac {s-s^{2}}{t^{2}} = 0 \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
1.515 |
|
|
\[ {}2 x y-3+\left (x^{2}+4 y\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
3.571 |
|
|
\[ {}3 x^{2} y^{2}-y^{3}+2 x +\left (2 x^{3} y-3 x y^{2}+1\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_exact, _rational] |
✓ |
✓ |
66.192 |
|
|
\[ {}2 y \sin \left (x \right ) \cos \left (x \right )+y^{2} \sin \left (x \right )+\left (\sin \left (x \right )^{2}-2 y \cos \left (x \right )\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_exact, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
43.238 |
|
|
\[ {}{\mathrm e}^{x} y+2 \,{\mathrm e}^{x}+y^{2}+\left ({\mathrm e}^{x}+2 x y\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_exact, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
1.919 |
|
|
\[ {}\frac {3-y}{x^{2}}+\frac {\left (y^{2}-2 x \right ) y^{\prime }}{x y^{2}} = 0 \] |
1 |
1 |
1 |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
5.309 |
|
|
\[ {}\frac {1+8 x y^{\frac {2}{3}}}{x^{\frac {2}{3}} y^{\frac {1}{3}}}+\frac {\left (2 x^{\frac {4}{3}} y^{\frac {2}{3}}-x^{\frac {1}{3}}\right ) y^{\prime }}{y^{\frac {4}{3}}} = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _exact, _rational] |
✓ |
✓ |
4.96 |
|
|
\[ {}4 x y+\left (x^{2}+1\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.021 |
|
|
\[ {}x y+2 x +y+2+\left (x^{2}+2 x \right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.643 |
|
|
\[ {}2 r \left (s^{2}+1\right )+\left (r^{4}+1\right ) s^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.425 |
|
|
\[ {}\csc \left (y\right )+\sec \left (x \right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.87 |
|
|
\[ {}\tan \left (\theta \right )+2 r \theta ^{\prime } = 0 \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
3.254 |
|
|
\[ {}\left ({\mathrm e}^{v}+1\right ) \cos \left (u \right )+{\mathrm e}^{v} \left (1+\sin \left (u \right )\right ) v^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
3.265 |
|
|
\[ {}\left (x +4\right ) \left (1+y^{2}\right )+y \left (x^{2}+3 x +2\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
6.879 |
|
|
\[ {}\left (2 s^{2}+2 s t +t^{2}\right ) s^{\prime }+s^{2}+2 s t -t^{2} = 0 \] |
1 |
1 |
3 |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
2.428 |
|
|
\[ {}y+2+y \left (x +4\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
20.057 |
|
|
\[ {}8 \cos \left (y\right )^{2}+\csc \left (x \right )^{2} y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
4.664 |
|
|
\[ {}\left (3 x +8\right ) \left (y^{2}+4\right )-4 y \left (x^{2}+5 x +6\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
4.756 |
|
|
\[ {}x +2 y+\left (2 x -y\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.956 |
|
|
\[ {}3 x -y-\left (x +y\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
4.328 |
|
|
\[ {}x^{2}+2 y^{2}+\left (4 x y-y^{2}\right ) y^{\prime } = 0 \] |
1 |
1 |
3 |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
2.16 |
|
|
\[ {}2 x^{2}+2 x y+y^{2}+\left (2 x y+x^{2}\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
3.18 |
|
|
\[ {}y^{\prime }+4 x y = 8 x \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.616 |
|
|
\[ {}x^{\prime }+\frac {x}{t^{2}} = \frac {1}{t^{2}} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.453 |
|
|
\[ {}\left (u^{2}+1\right ) v^{\prime }+4 u v = 3 u \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.74 |
|
|
\[ {}x y^{\prime }+\frac {\left (2 x +1\right ) y}{1+x} = -1+x \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.237 |
|
|
\[ {}\cos \left (x \right )^{2}-y \cos \left (x \right )-\left (\sin \left (x \right )+1\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.928 |
|
|
\[ {}y \sin \left (2 x \right )-\cos \left (x \right )+\left (1+\sin \left (x \right )^{2}\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
4.107 |
|
|
\[ {}y^{\prime }-\frac {y}{x} = -\frac {y^{2}}{x} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.38 |
|
|
\[ {}y^{\prime }+\left (4 y-\frac {8}{y^{3}}\right ) x = 0 \] |
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 |
|
|
\[ {}y^{\prime }+3 x^{2} y = x^{2} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.121 |
|
|
\[ {}{\mathrm e}^{x} \left (y-3 \left (1+{\mathrm e}^{x}\right )^{2}\right )+\left (1+{\mathrm e}^{x}\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.398 |
|
|
\[ {}2 x \left (y+1\right )-\left (x^{2}+1\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.696 |
|
|
\[ {}\cos \left (y\right ) y^{\prime }+\frac {\sin \left (y\right )}{x} = 1 \] |
1 |
1 |
1 |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
1.662 |
|
|
\[ {}\left (y+1\right ) y^{\prime }+x \left (y^{2}+2 y\right ) = x \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
2.131 |
|
|
\[ {}6 x^{2} y-\left (x^{3}+1\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.217 |
|
|
\[ {}\left (3 x^{2} y^{2}-x \right ) y^{\prime }+2 x y^{3}-y = 0 \] |
1 |
1 |
6 |
[[_homogeneous, ‘class G‘], _exact, _rational] |
✓ |
✓ |
3.475 |
|
|
\[ {}y-1+x \left (1+x \right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.235 |
|
|
\[ {}{\mathrm e}^{2 x} y^{2}+\left ({\mathrm e}^{2 x} y-2 y\right ) y^{\prime } = 0 \] |
1 |
1 |
3 |
[_separable] |
✓ |
✓ |
2.839 |
|
|
\[ {}8 x^{3} y-12 x^{3}+\left (x^{4}+1\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.727 |
|
|
\[ {}x^{2} y^{\prime }+x y = x y^{3} \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
6.259 |
|
|
\[ {}\left (x^{3}+1\right ) y^{\prime }+6 x^{2} y = 6 x^{2} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.814 |
|
|
\[ {}2 y^{2}+8+\left (-x^{2}+1\right ) y y^{\prime } = 0 \] |
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 |
|
|
\[ {}3 x^{2}+2 x y^{2}+\left (2 x^{2} y+6 y^{2}\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_exact, _rational] |
✓ |
✓ |
66.261 |
|
|
\[ {}4 x y y^{\prime } = 1+y^{2} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
9.377 |
|
|
\[ {}y^{\prime } = \frac {x y}{x^{2}+1} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.28 |
|
|
\[ {}5 x +2 y+1+\left (2 x +y+1\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
4.466 |
|
|
\[ {}6 x +4 y+1+\left (4 x +2 y+2\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
9.043 |
|
|
\[ {}x^{\prime } {\mathrm e}^{3 t}+3 x \,{\mathrm e}^{3 t} = {\mathrm e}^{-t} \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.396 |
|
|
\[ {}x^{\prime } = t^{3} \left (-x+1\right ) \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.519 |
|
|
\[ {}y^{\prime } = \left (1+y^{2}\right ) \tan \left (x \right ) \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
4.773 |
|
|
\[ {}x^{\prime } = t^{2} x \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.078 |
|
|
\[ {}y^{\prime } = y^{2} {\mathrm e}^{-t^{2}} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.004 |
|
|
\[ {}x y^{\prime } = k y \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.334 |
|
|
\[ {}i^{\prime } = p \left (t \right ) i \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.553 |
|
|
\[ {}y^{\prime }+\frac {y}{x} = x^{2} \] |
1 |
0 |
0 |
[_linear] |
✗ |
N/A |
1.396 |
|
|
\[ {}x^{\prime }+x t = 4 t \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.01 |
|
|
\[ {}2 x y-\sec \left (x \right )^{2}+\left (x^{2}+2 y\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[_exact, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
6.938 |
|
|
\[ {}1+{\mathrm e}^{x} y+x \,{\mathrm e}^{x} y+\left (x \,{\mathrm e}^{x}+2\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.229 |
|
|
\[ {}\left (x \cos \left (y\right )+\cos \left (x \right )\right ) y^{\prime }-y \sin \left (x \right )+\sin \left (y\right ) = 0 \] |
1 |
1 |
1 |
[_exact] |
✓ |
✓ |
7.517 |
|
|
\[ {}{\mathrm e}^{x} \sin \left (y\right )+y+\left ({\mathrm e}^{x} \cos \left (y\right )+x +{\mathrm e}^{y}\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_exact] |
✓ |
✓ |
2.416 |
|
|
\[ {}V^{\prime }\left (x \right )+2 y y^{\prime } = 0 \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
1.548 |
|
|
\[ {}\left (\frac {1}{y}-a \right ) y^{\prime }+\frac {2}{x}-b = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
3.09 |
|
|
\[ {}\tan \left (y\right )-\cot \left (x \right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
3.395 |
|
|
\[ {}x y^{\prime }+y = x^{3} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.125 |
|
|
\[ {}y^{\prime } = {\mathrm e}^{x -y} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.956 |
|
|
\[ {}y = x y^{\prime }+\frac {1}{y} \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
6.814 |
|
|
\[ {}y^{\prime } = \frac {x +y-3}{-x +y+1} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
4.433 |
|
|
\[ {}\left (x^{2}-1\right ) y^{\prime }+2 x y-\cos \left (x \right ) = 0 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
2.432 |
|
|
\[ {}\left (-x +y^{2}\right ) y^{\prime }-y+x^{2} = 0 \] |
1 |
1 |
3 |
[_exact, _rational] |
✓ |
✓ |
13.914 |
|
|
\[ {}3 x y^{2} y^{\prime }+y^{3}-2 x = 0 \] |
1 |
1 |
3 |
[[_homogeneous, ‘class G‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
2.188 |
|
|
\[ {}y^{\prime } = y \,{\mathrm e}^{x +y} \left (x^{2}+1\right ) \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.653 |
|
|
\[ {}x^{2} y^{\prime } = 1+y^{2} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.689 |
|
|
\[ {}x \left ({\mathrm e}^{y}+4\right ) = {\mathrm e}^{x +y} y^{\prime } \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.537 |
|
|
\[ {}y^{\prime } = x \,{\mathrm e}^{-x +y^{2}} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.623 |
|
|
\[ {}x \left (y+1\right )^{2} = \left (x^{2}+1\right ) y \,{\mathrm e}^{y} y^{\prime } \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.859 |
|
|
\[ {}5 y^{\prime }-x y = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.864 |
|
|
\[ {}y-x y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.044 |
|
|
\[ {}\left (1+u \right ) v+\left (1-v\right ) u v^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.807 |
|
|
|
||||||||
|
\[ {}1+y-\left (1-x \right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.373 |
|
|
\[ {}\left (t^{2}+t^{2} x\right ) x^{\prime }+x^{2}+t x^{2} = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.522 |
|
|
\[ {}y-a +x^{2} y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.454 |
|
|
\[ {}z-\left (-a^{2}+t^{2}\right ) z^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.063 |
|
|
\[ {}y^{\prime } = \frac {1+y^{2}}{x^{2}+1} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.121 |
|
|
\[ {}1+s^{2}-\sqrt {t}\, s^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.293 |
|
|
\[ {}r^{\prime }+r \tan \left (t \right ) = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.293 |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime }-\sqrt {1-y^{2}} = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.972 |
|
|
\[ {}\sqrt {-x^{2}+1}\, y^{\prime }-\sqrt {1-y^{2}} = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.769 |
|
|
\[ {}3 \,{\mathrm e}^{x} \tan \left (y\right )+\left (-{\mathrm e}^{x}+1\right ) \sec \left (y\right )^{2} y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
3.153 |
|
|
\[ {}x -x y^{2}+\left (y-x^{2} y\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
2.376 |
|
|
\[ {}y-x +\left (x +y\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.889 |
|
|
\[ {}y+x +x y^{\prime } = 0 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.254 |
|
|
\[ {}\frac {x +y y^{\prime }}{\sqrt {x^{2}+y^{2}}} = m \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _exact, _dAlembert] |
✓ |
✓ |
3.546 |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime }-x y+a x y^{2} = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
3.735 |
|
|
\[ {}x^{2}+y+\left (x -2 y\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.257 |
|
|
\[ {}y-3 x^{2}-\left (4 y-x \right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.303 |
|
|
\[ {}\left (y^{3}-x \right ) y^{\prime } = y \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _exact, _rational] |
✓ |
✓ |
2.472 |
|
|
\[ {}\frac {y^{2}}{\left (x -y\right )^{2}}-\frac {1}{x}+\left (\frac {1}{y}-\frac {x^{2}}{\left (x -y\right )^{2}}\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_exact, _rational] |
✓ |
✓ |
2.048 |
|
|
\[ {}6 x y^{2}+4 x^{3}+3 \left (2 x^{2} y+y^{2}\right ) y^{\prime } = 0 \] |
1 |
1 |
3 |
[_exact, _rational] |
✓ |
✓ |
1.201 |
|
|
\[ {}\frac {x}{\left (x +y\right )^{2}}+\frac {\left (y+2 x \right ) y^{\prime }}{\left (x +y\right )^{2}} = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
✓ |
1.196 |
|
|
\[ {}\frac {1}{x^{2}}+\frac {3 y^{2}}{x^{4}} = \frac {2 y y^{\prime }}{x^{3}} \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
1.155 |
|
|
\[ {}\frac {x^{2} y^{\prime }}{\left (x -y\right )^{2}}-\frac {y^{2}}{\left (x -y\right )^{2}} = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.786 |
|
|
\[ {}x +y y^{\prime } = \frac {y}{x^{2}+y^{2}}-\frac {x y^{\prime }}{x^{2}+y^{2}} \] |
1 |
1 |
1 |
[[_1st_order, _with_linear_symmetries], _exact, _rational] |
✓ |
✓ |
1.104 |
|
|
\[ {}y = x y^{\prime }+y^{\prime } \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.766 |
|
|
\[ {}\frac {x^{2} y^{\prime }}{\left (x -y\right )^{2}}-\frac {y^{2}}{\left (x -y\right )^{2}} = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.8 |
|
|
\[ {}3 \,{\mathrm e}^{x} \tan \left (y\right )+\left (-{\mathrm e}^{x}+1\right ) \sec \left (y\right )^{2} y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.802 |
|
|
\[ {}y^{\prime }+\frac {y}{x} = {\mathrm e}^{x} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.924 |
|
|
\[ {}-y+x y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.635 |
|
|
\[ {}x^{2} y^{\prime }+2 x y = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.812 |
|
|
\[ {}2 x y^{\prime }-y = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.7 |
|
|
\[ {}y^{\prime }-2 x y = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.699 |
|
|
\[ {}y^{\prime } = x \sqrt {y} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.069 |
|
|
\[ {}x \ln \left (x \right ) y^{\prime }-\left (1+\ln \left (x \right )\right ) y = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.98 |
|
|
\[ {}y^{\prime } = x y \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.642 |
|
|
\[ {}y^{\prime } = -x y \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.712 |
|
|
\[ {}y^{\prime } = x y \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.557 |
|
|
\[ {}y^{\prime } = \frac {x}{y} \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
1.197 |
|
|
\[ {}y^{\prime } = \frac {y}{x} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.602 |
|
|
\[ {}y^{\prime } = {\mathrm e}^{x -y} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.626 |
|
|
\[ {}y^{\prime } = \frac {2 x -y}{x +3 y} \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.579 |
|
|
\[ {}y^{\prime } = \frac {1}{x y} \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
0.677 |
|
|
\[ {}y^{\prime } = \frac {y}{y-x} \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.806 |
|
|
\[ {}y^{\prime } = \frac {x}{y^{2}} \] |
1 |
1 |
3 |
[_separable] |
✓ |
✓ |
5.332 |
|
|
\[ {}y^{\prime } = \frac {\sqrt {y}}{x} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.188 |
|
|
\[ {}y^{\prime } = \frac {x y}{1-y} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.788 |
|
|
\[ {}y^{\prime } = -x \sqrt {1-y^{2}} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.98 |
|
|
\[ {}y^{\prime } = x \,{\mathrm e}^{y-x^{2}} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.371 |
|
|
\[ {}y^{\prime } = \frac {y}{x} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.887 |
|
|
\[ {}y^{\prime } = \frac {2 x}{y} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.724 |
|
|
\[ {}y^{\prime } = x y+x \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.167 |
|
|
\[ {}{\mathrm e}^{y} x +y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.982 |
|
|
\[ {}y-x^{2} y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.328 |
|
|
\[ {}2 x y y^{\prime }+y^{2} = -1 \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
1.467 |
|
|
\[ {}y^{\prime } = -\frac {y \left (y+2 x \right )}{x \left (2 y+x \right )} \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
1.775 |
|
|
\[ {}y^{\prime } = \frac {y}{x} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.926 |
|
|
\[ {}x -y y^{\prime } = 0 \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
1.227 |
|
|
\[ {}y-x y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.654 |
|
|
\[ {}x y \left (1-y\right )-2 y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.379 |
|
|
\[ {}x \left (1-y^{3}\right )-3 y^{2} y^{\prime } = 0 \] |
1 |
1 |
3 |
[_separable] |
✓ |
✓ |
1.635 |
|
|
\[ {}y \left (2 x -1\right )+x \left (1+x \right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.972 |
|
|
\[ {}y^{\prime } = \frac {y}{x} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.887 |
|
|
\[ {}y^{\prime } = \frac {y}{x} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.849 |
|
|
\[ {}y^{\prime } = -\frac {3 x^{2}}{2 y} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.566 |
|
|
\[ {}y^{\prime } = -\frac {3 x^{2}}{2 y} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
3.958 |
|
|
\[ {}y^{\prime } = -\frac {3 x^{2}}{2 y} \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
3.991 |
|
|
\[ {}y^{\prime } = -\frac {3 x^{2}}{2 y} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.318 |
|
|
\[ {}y^{\prime } = \frac {\sqrt {y}}{x} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
4.206 |
|
|
\[ {}y^{\prime } = \frac {\sqrt {y}}{x} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
3.059 |
|
|
\[ {}y^{\prime } = \frac {\sqrt {y}}{x} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
3.874 |
|
|
\[ {}y^{\prime } = \frac {\sqrt {y}}{x} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.662 |
|
|
\[ {}y^{\prime } = 3 x y^{\frac {1}{3}} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.885 |
|
|
\[ {}y^{\prime } = 3 x y^{\frac {1}{3}} \] |
1 |
0 |
1 |
[_separable] |
✓ |
✓ |
1.247 |
|
|
\[ {}y^{\prime } = 3 x y^{\frac {1}{3}} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.645 |
|
|
\[ {}y^{\prime } = 3 x y^{\frac {1}{3}} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.622 |
|
|
\[ {}y^{\prime } = 3 x y^{\frac {1}{3}} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.546 |
|
|
\[ {}y^{\prime } = \frac {y}{y-x} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.643 |
|
|
\[ {}y^{\prime } = \frac {y}{y-x} \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
3.719 |
|
|
\[ {}y^{\prime } = \frac {y}{y-x} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.141 |
|
|
\[ {}y^{\prime } = \frac {y}{y-x} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
3.289 |
|
|
\[ {}y^{\prime } = x \sqrt {1-y^{2}} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.947 |
|
|
\[ {}y^{\prime } = x \sqrt {1-y^{2}} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
9.96 |
|
|
\[ {}y^{\prime } = x \sqrt {1-y^{2}} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
12.649 |
|
|
\[ {}y^{\prime } = x \sqrt {1-y^{2}} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.989 |
|
|
\[ {}y^{\prime } = \frac {y+1}{t +1} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.167 |
|
|
\[ {}y^{\prime } = t^{2} y^{2} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.587 |
|
|
\[ {}y^{\prime } = t^{4} y \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.699 |
|
|
\[ {}y^{\prime } = 2 t y^{2}+3 y^{2} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.711 |
|
|
\[ {}y^{\prime } = \frac {t}{y} \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
1.332 |
|
|
\[ {}y^{\prime } = \frac {t}{t^{2} y+y} \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
0.818 |
|
|
\[ {}y^{\prime } = t y^{\frac {1}{3}} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.068 |
|
|
\[ {}y^{\prime } = \frac {2 y+1}{t} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.311 |
|
|
\[ {}y^{\prime } = \frac {4 t}{1+3 y^{2}} \] |
1 |
1 |
3 |
[_separable] |
✓ |
✓ |
154.546 |
|
|
\[ {}v^{\prime } = t^{2} v-2-2 v+t^{2} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.914 |
|
|
\[ {}y^{\prime } = \frac {1}{t y+t +y+1} \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
0.904 |
|
|
\[ {}y^{\prime } = \frac {{\mathrm e}^{t} y}{1+y^{2}} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.037 |
|
|
\[ {}w^{\prime } = \frac {w}{t} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.747 |
|
|
\[ {}x^{\prime } = -x t \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.188 |
|
|
\[ {}y^{\prime } = t y \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.984 |
|
|
\[ {}y^{\prime } = t^{2} y^{3} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.401 |
|
|
\[ {}y^{\prime } = \frac {t}{y-t^{2} y} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
3.08 |
|
|
\[ {}y^{\prime } = t y^{2}+2 y^{2} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.93 |
|
|
\[ {}x^{\prime } = \frac {t^{2}}{x+t^{3} x} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.807 |
|
|
\[ {}y^{\prime } = \left (1+y^{2}\right ) t \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.343 |
|
|
\[ {}y^{\prime } = 2 t y^{2}+3 t^{2} y^{2} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.02 |
|
|
\[ {}y^{\prime } = \left (t +1\right ) y \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.127 |
|
|
\[ {}y^{\prime } = t y+t y^{2} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.455 |
|
|
\[ {}y^{\prime } = t^{2}+t^{2} y \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.767 |
|
|
\[ {}y^{\prime } = t +t y \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.754 |
|
|
\[ {}y^{\prime } = \frac {1}{\left (y+1\right ) \left (t -2\right )} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.741 |
|
|
\[ {}y^{\prime } = \frac {t}{y-2} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
6.28 |
|
|
\[ {}y^{\prime } = -\frac {y}{t}+2 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.137 |
|
|
\[ {}y^{\prime } = -\frac {y}{t +1}+t^{2} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.833 |
|
|
\[ {}y^{\prime } = -\frac {y}{t +1}+2 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.886 |
|
|
\[ {}y^{\prime } = -\frac {y}{t}+2 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.484 |
|
|
\[ {}y^{\prime } = \frac {\left (t^{2}-4\right ) \left (y+1\right ) {\mathrm e}^{y}}{\left (-1+t \right ) \left (3-y\right )} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.492 |
|
|
\[ {}y^{\prime } = t y \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.671 |
|
|
\[ {}y^{\prime } = \frac {t y}{t^{2}+1} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.777 |
|
|
\[ {}x^{\prime } = -x t \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.101 |
|
|
\[ {}y^{\prime } = t^{2} y^{3}+y^{3} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.82 |
|
|
\[ {}y^{\prime } = \frac {\left (t +1\right )^{2}}{\left (y+1\right )^{2}} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
142.759 |
|
|
\[ {}y^{\prime } = 2 t y^{2}+3 t^{2} y^{2} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.585 |
|
|
\[ {}y^{\prime } = \frac {t^{2}}{y+t^{3} y} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.47 |
|
|
\[ {}y^{\prime } = t^{2} y+1+y+t^{2} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.416 |
|
|
\[ {}y^{\prime } = \frac {2 y+1}{t} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.338 |
|
|
\[ {}y y^{\prime } = 2 x \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
1.46 |
|
|
\[ {}y^{\prime }+3 x y = 6 x \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.275 |
|
|
\[ {}x^{2} y^{\prime }+x y^{2} = x \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.619 |
|
|
\[ {}\left (-2+x \right ) y^{\prime } = 3+y \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.36 |
|
|
\[ {}\left (-2+y\right ) y^{\prime } = x -3 \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
2.321 |
|
|
\[ {}y^{\prime } = 3 y^{2}-y^{2} \sin \left (x \right ) \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.945 |
|
|
\[ {}y^{\prime }+x y = 4 x \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.996 |
|
|
\[ {}y^{\prime } = x y-3 x -2 y+6 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.914 |
|
|
\[ {}y y^{\prime } = {\mathrm e}^{x -3 y^{2}} \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
1.176 |
|
|
\[ {}y^{\prime } = \frac {x}{y} \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
1.408 |
|
|
\[ {}x y y^{\prime } = y^{2}+9 \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
2.068 |
|
|
\[ {}y^{\prime } = \frac {1+y^{2}}{x^{2}+1} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.79 |
|
|
\[ {}\cos \left (y\right ) y^{\prime } = \sin \left (x \right ) \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.252 |
|
|
\[ {}y^{\prime } = {\mathrm e}^{2 x -3 y} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.785 |
|
|
\[ {}y^{\prime } = \frac {x}{y} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
3.223 |
|
|
\[ {}y^{\prime } = 2 x -1+2 x y-y \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.231 |
|
|
\[ {}y y^{\prime } = x y^{2}+x \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.479 |
|
|
\[ {}y^{\prime } = x y-4 x \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.863 |
|
|
\[ {}y y^{\prime } = x y^{2}-9 x \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
1.435 |
|
|
\[ {}y^{\prime } = {\mathrm e}^{x +y^{2}} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.653 |
|
|
\[ {}y^{\prime } = x y-4 x \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.678 |
|
|
\[ {}y^{\prime } = x y-3 x -2 y+6 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.895 |
|
|
\[ {}y^{\prime } = 3 y^{2}-y^{2} \sin \left (x \right ) \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.82 |
|
|
\[ {}y^{\prime } = \frac {y}{x} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.754 |
|
|
\[ {}y^{\prime } = \frac {6 x^{2}+4}{3 y^{2}-4 y} \] |
1 |
1 |
3 |
[_separable] |
✓ |
✓ |
163.516 |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime } = 1+y^{2} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.79 |
|
|
\[ {}\left (y^{2}-1\right ) y^{\prime } = 4 x y^{2} \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
1.783 |
|
|
\[ {}y^{\prime } = 3 x y^{3} \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
0.864 |
|
|
\[ {}y^{\prime } = \frac {2+\sqrt {x}}{2+\sqrt {y}} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
99.218 |
|
|
\[ {}y^{\prime }-3 x^{2} y^{2} = -3 x^{2} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.275 |
|
|
\[ {}y^{\prime }-3 x^{2} y^{2} = 3 x^{2} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.945 |
|
|
\[ {}y y^{\prime } = \sin \left (x \right ) \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.444 |
|
|
\[ {}y^{\prime } = 2 x -1+2 x y-y \] |
1 |
0 |
1 |
[_separable] |
✓ |
✓ |
1.051 |
|
|
\[ {}x y^{\prime } = y^{2}-y \] |
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 |
|
|
\[ {}\left (y^{2}-1\right ) y^{\prime } = 4 x y \] |
1 |
0 |
1 |
[_separable] |
✓ |
✓ |
4.379 |
|
|
\[ {}y^{\prime } = y \sin \left (x \right ) \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.004 |
|
|
\[ {}y^{\prime }-2 x y = x \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.043 |
|
|
\[ {}x^{2} y^{\prime }+2 x y = \sin \left (x \right ) \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.803 |
|
|
\[ {}\cos \left (-4 y+8 x -3\right ) y^{\prime } = 2+2 \cos \left (-4 y+8 x -3\right ) \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _exact, _dAlembert] |
✓ |
✓ |
42.072 |
|
|
\[ {}y^{\prime } = \frac {x -y}{x +y} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
3.326 |
|
|
\[ {}y^{\prime } = 4+\frac {1}{\sin \left (4 x -y\right )} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
3.558 |
|
|
\[ {}y^{\prime } = \frac {1}{y}-\frac {y}{2 x} \] |
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 |
|
|
\[ {}2 x y+y^{2}+\left (2 x y+x^{2}\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
2.411 |
|
|
\[ {}2 x y^{3}+4 x^{3}+3 x^{2} y^{2} y^{\prime } = 0 \] |
1 |
1 |
3 |
[[_homogeneous, ‘class G‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
1.638 |
|
|
\[ {}2-2 x +3 y^{2} y^{\prime } = 0 \] |
1 |
1 |
3 |
[_separable] |
✓ |
✓ |
12.222 |
|
|
\[ {}1+3 x^{2} y^{2}+\left (2 x^{3} y+6 y\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[_exact, _rational, _Bernoulli] |
✓ |
✓ |
1.307 |
|
|
\[ {}4 x^{3} y+\left (x^{4}-y^{4}\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
2.842 |
|
|
\[ {}1+\ln \left (x y\right )+\frac {x y^{\prime }}{y} = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _exact] |
✓ |
✓ |
2.614 |
|
|
\[ {}1+{\mathrm e}^{y}+x \,{\mathrm e}^{y} y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.158 |
|
|
\[ {}{\mathrm e}^{y}+\left ({\mathrm e}^{y} x +1\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_1st_order, _with_exponential_symmetries], _exact] |
✓ |
✓ |
0.989 |
|
|
\[ {}1+y^{4}+x y^{3} y^{\prime } = 0 \] |
1 |
1 |
4 |
[_separable] |
✓ |
✓ |
2.348 |
|
|
\[ {}3 y+3 y^{2}+\left (2 x +4 x y\right ) y^{\prime } = 0 \] |
1 |
1 |
4 |
[_separable] |
✓ |
✓ |
2.772 |
|
|
\[ {}2 x \left (y+1\right )-y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.078 |
|
|
\[ {}x y^{\prime } = 2 y^{2}-6 y \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.752 |
|
|
\[ {}4 y^{2}-x^{2} y^{2}+y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.845 |
|
|
\[ {}x y^{2}-6+x^{2} y y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class G‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
1.003 |
|
|
\[ {}1+2 x y^{2}+\left (2 x^{2} y+2 y\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[_exact, _rational, _Bernoulli] |
✓ |
✓ |
1.183 |
|
|
\[ {}y^{\prime } = \frac {1}{x y-3 x} \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
0.931 |
|
|
\[ {}\sin \left (y\right )+\left (x +y\right ) \cos \left (y\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_exact, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
10.493 |
|
|
\[ {}\sin \left (y\right )+\left (1+x \right ) \cos \left (y\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
10.951 |
|
|
\[ {}y^{\prime } = x y^{2}+3 y^{2}+x +3 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.981 |
|
|
\[ {}\ln \left (y\right )+\left (\frac {x}{y}+3\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_exact, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
1.429 |
|
|
\[ {}x y^{2}+\left (x^{2} y+10 y^{4}\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class G‘], _exact, _rational] |
✓ |
✓ |
2.127 |
|
|
\[ {}\left (y-x +3\right )^{2} \left (y^{\prime }-1\right ) = 1 \] |
1 |
1 |
3 |
[[_homogeneous, ‘class C‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
1.268 |
|
|
\[ {}x +{\mathrm e}^{x y} y+x \,{\mathrm e}^{x y} y^{\prime } = 0 \] |
1 |
1 |
1 |
[_exact, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
1.372 |
|
|
\[ {}y^{2}-y^{2} \cos \left (x \right )+y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.0 |
|
|
\[ {}y^{\prime } = y^{3}-y^{3} \cos \left (x \right ) \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
1.077 |
|
|
\[ {}y^{2} {\mathrm e}^{x y^{2}}-2 x +2 x y \,{\mathrm e}^{x y^{2}} y^{\prime } = 0 \] |
1 |
1 |
2 |
[_exact, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
1.64 |
|
|
\[ {}y^{\prime } = {\mathrm e}^{4 x +3 y} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.825 |
|
|
\[ {}y^{\prime } = {\mathrm e}^{4 x +3 y} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.732 |
|
|
\[ {}x \left (1-2 y\right )+\left (y-x^{2}\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.736 |
|
|
\[ {}y^{\prime }+x y = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.553 |
|
|
|
||||||||
|
\[ {}y^{\prime } = -\frac {x}{y} \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
2.871 |
|
|
\[ {}3 y \left (t^{2}+y\right )+t \left (t^{2}+6 y\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class G‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
4.441 |
|
|
\[ {}y \cos \left (t \right )+\left (2 y+\sin \left (t \right )\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[_exact, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
3.627 |
|
|
\[ {}\frac {y}{x}+\cos \left (y\right )+\left (\ln \left (x \right )-\sin \left (y\right ) x \right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_exact] |
✓ |
✓ |
5.138 |
|
|
\[ {}y^{\prime } = \frac {\left (x -4\right ) y^{3}}{x^{3} \left (-2+y\right )} \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
2.083 |
|
|
\[ {}x y^{\prime }+y = \cos \left (x \right ) \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.547 |
|
|
\[ {}y^{\prime }+y \cos \left (x \right ) = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.975 |
|
|
\[ {}2 x -3 y+\left (2 y-3 x \right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
3.77 |
|
|
\[ {}y \cos \left (x y\right )+\sin \left (x \right )+x \cos \left (x y\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_exact, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
9.581 |
|
|
\[ {}\frac {y^{\prime }}{t} = \sqrt {y} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.411 |
|
|
\[ {}y^{\prime } = y \sqrt {t} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.45 |
|
|
\[ {}t y^{\prime } = y \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.45 |
|
|
\[ {}y^{\prime } = y \tan \left (t \right ) \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
3.138 |
|
|
\[ {}t y^{\prime }+y = t^{3} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
2.257 |
|
|
\[ {}t y^{\prime }+y = t \sin \left (t \right ) \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
2.056 |
|
|
\[ {}y^{\prime } = t y^{2} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.537 |
|
|
\[ {}y^{\prime } = -\frac {t}{y} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
20.007 |
|
|
\[ {}y^{\prime } = \frac {x}{y^{2}} \] |
1 |
1 |
3 |
[_separable] |
✓ |
✓ |
6.905 |
|
|
\[ {}\frac {1}{2 \sqrt {t}}+y^{2} y^{\prime } = 0 \] |
1 |
1 |
3 |
[_separable] |
✓ |
✓ |
2.367 |
|
|
\[ {}y^{\prime } = \frac {\sqrt {y}}{x^{2}} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.974 |
|
|
\[ {}6+4 t^{3}+\left (5+\frac {9}{y^{8}}\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.216 |
|
|
\[ {}\frac {6}{t^{9}}-\frac {6}{t^{3}}+t^{7}+\left (9+\frac {1}{s^{2}}-4 s^{8}\right ) s^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.842 |
|
|
\[ {}4 \sinh \left (4 y\right ) y^{\prime } = 6 \cosh \left (3 x \right ) \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
7.496 |
|
|
\[ {}y^{\prime } = \frac {y+1}{t +1} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.514 |
|
|
\[ {}y^{\prime } = \frac {y+2}{1+2 t} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.882 |
|
|
\[ {}\frac {3}{t^{2}} = \left (\frac {1}{\sqrt {y}}+\sqrt {y}\right ) y^{\prime } \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.525 |
|
|
\[ {}3 \sin \left (x \right )-4 \cos \left (y\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.569 |
|
|
\[ {}\cos \left (y\right ) y^{\prime } = 8 \sin \left (8 t \right ) \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.514 |
|
|
\[ {}\left (5 x^{5}-4 \cos \left (x\right )\right ) x^{\prime }+2 \cos \left (9 t \right )+2 \sin \left (7 t \right ) = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
38.446 |
|
|
\[ {}\cosh \left (6 t \right )+5 \sinh \left (4 t \right )+20 \sinh \left (y\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
10.86 |
|
|
\[ {}y^{\prime } = {\mathrm e}^{2 y+10 t} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.952 |
|
|
\[ {}y^{\prime } = {\mathrm e}^{3 y+2 t} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.931 |
|
|
\[ {}\sin \left (t \right )^{2} = \cos \left (y\right )^{2} y^{\prime } \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.695 |
|
|
\[ {}3 \sin \left (t \right )-\sin \left (3 t \right ) = \left (\cos \left (4 y\right )-4 \cos \left (y\right )\right ) y^{\prime } \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
36.885 |
|
|
\[ {}x^{\prime } = \frac {\sec \left (t \right )^{2}}{\sec \left (x\right ) \tan \left (x\right )} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
35.875 |
|
|
\[ {}\left (2-\frac {5}{y^{2}}\right ) y^{\prime }+4 \cos \left (x \right )^{2} = 0 \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
3.216 |
|
|
\[ {}\tan \left (y\right ) \sec \left (y\right )^{2} y^{\prime }+\cos \left (2 x \right )^{3} \sin \left (2 x \right ) = 0 \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
37.102 |
|
|
\[ {}y^{\prime } = \frac {\left (1+2 \,{\mathrm e}^{y}\right ) {\mathrm e}^{-y}}{t \ln \left (t \right )} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
3.635 |
|
|
\[ {}x \sin \left (x^{2}\right ) = \frac {\cos \left (\sqrt {y}\right ) y^{\prime }}{\sqrt {y}} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
37.088 |
|
|
\[ {}\frac {-2+x}{x^{2}-4 x +3} = \frac {\left (1-\frac {1}{y}\right )^{2} y^{\prime }}{y^{2}} \] |
1 |
1 |
3 |
[_separable] |
✓ |
✓ |
10.648 |
|
|
\[ {}\frac {\cos \left (y\right ) y^{\prime }}{\left (1-\sin \left (y\right )\right )^{2}} = \sin \left (x \right )^{3} \cos \left (x \right ) \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
37.259 |
|
|
\[ {}y^{\prime } = \frac {\left (5-2 \cos \left (x \right )\right )^{3} \sin \left (x \right ) \cos \left (y\right )^{4}}{\sin \left (y\right )} \] |
1 |
1 |
3 |
[_separable] |
✓ |
✓ |
36.439 |
|
|
\[ {}\frac {\sqrt {\ln \left (x \right )}}{x} = \frac {{\mathrm e}^{\frac {3}{y}} y^{\prime }}{y} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.431 |
|
|
\[ {}y^{\prime } = \frac {5^{-t}}{y^{2}} \] |
1 |
1 |
3 |
[_separable] |
✓ |
✓ |
50.23 |
|
|
\[ {}y^{\prime } = t^{2} y^{2}+y^{2}-t^{2}-1 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.637 |
|
|
\[ {}4 \left (-1+x \right )^{2} y^{\prime }-3 \left (3+y\right )^{2} = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.885 |
|
|
\[ {}y^{\prime } = \sin \left (t -y\right )+\sin \left (t +y\right ) \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
3.093 |
|
|
\[ {}y^{\prime } = \frac {\sqrt {t}}{y} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
5.73 |
|
|
\[ {}y^{\prime } = \frac {{\mathrm e}^{t}}{y+1} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.654 |
|
|
\[ {}y^{\prime } = {\mathrm e}^{t -y} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.177 |
|
|
\[ {}y^{\prime } = \frac {\sin \left (x \right )}{\cos \left (y\right )+1} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.88 |
|
|
\[ {}y^{\prime } = \frac {3+y}{1+3 x} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.444 |
|
|
\[ {}y^{\prime } = {\mathrm e}^{x -y} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.232 |
|
|
\[ {}y^{\prime } = {\mathrm e}^{2 x -y} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.476 |
|
|
\[ {}y^{\prime } = \frac {3 y+1}{x +3} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.701 |
|
|
\[ {}y^{\prime } = y \cos \left (t \right ) \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.632 |
|
|
\[ {}y^{\prime } = y^{2} \cos \left (t \right ) \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.333 |
|
|
\[ {}y^{\prime } = \sqrt {y}\, \cos \left (t \right ) \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
3.479 |
|
|
\[ {}y^{\prime }+f \left (t \right ) y = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.801 |
|
|
\[ {}y^{\prime } = -\frac {-2+y}{-2+x} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.186 |
|
|
\[ {}y^{\prime } = f \left (t \right ) y \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.638 |
|
|
\[ {}t y^{\prime }+y = t^{2} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.039 |
|
|
\[ {}t y^{\prime }+y = t \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.537 |
|
|
\[ {}x y^{\prime }+y = x \,{\mathrm e}^{x} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.965 |
|
|
\[ {}x y^{\prime }+y = {\mathrm e}^{-x} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.992 |
|
|
\[ {}y^{\prime }-x y = x \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.14 |
|
|
\[ {}x^{\prime } = \frac {3 x t^{2}}{-t^{3}+1} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.479 |
|
|
\[ {}y^{\prime }+2 t y = 2 t \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.138 |
|
|
\[ {}t y^{\prime }+y = \cos \left (t \right ) \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.395 |
|
|
\[ {}t y^{\prime }+y = 2 \,{\mathrm e}^{t} t \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.293 |
|
|
\[ {}\left (1+{\mathrm e}^{t}\right ) y^{\prime }+{\mathrm e}^{t} y = t \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.49 |
|
|
\[ {}\left (t^{2}+4\right ) y^{\prime }+2 t y = 2 t \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.252 |
|
|
\[ {}t y^{\prime }+y = t \cos \left (t \right ) \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.155 |
|
|
\[ {}y^{2}-\frac {y}{2 \sqrt {t}}+\left (2 t y-\sqrt {t}+1\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[_exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
13.151 |
|
|
\[ {}\frac {t}{\sqrt {t^{2}+y^{2}}}+\frac {y y^{\prime }}{\sqrt {t^{2}+y^{2}}} = 0 \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
2.712 |
|
|
\[ {}y \cos \left (t y\right )+t \cos \left (t y\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
1.697 |
|
|
\[ {}y \sec \left (t \right )^{2}+2 t +\tan \left (t \right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
11.383 |
|
|
\[ {}3 t y^{2}+y^{3} y^{\prime } = 0 \] |
1 |
1 |
3 |
[_separable] |
✓ |
✓ |
1.883 |
|
|
\[ {}t -y \sin \left (t \right )+\left (y^{6}+\cos \left (t \right )\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_exact] |
✓ |
✓ |
3.112 |
|
|
\[ {}\ln \left (t y\right )+\frac {t y^{\prime }}{y} = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _exact] |
✓ |
✓ |
3.692 |
|
|
\[ {}{\mathrm e}^{t y}+\frac {t \,{\mathrm e}^{t y} y^{\prime }}{y} = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.963 |
|
|
\[ {}y^{2}+2 t y y^{\prime } = 0 \] |
1 |
1 |
3 |
[_separable] |
✓ |
✓ |
1.162 |
|
|
\[ {}\frac {3 t^{2}}{y}-\frac {t^{3} y^{\prime }}{y^{2}} = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.835 |
|
|
\[ {}2 t +y^{3}+\left (3 t y^{2}+4\right ) y^{\prime } = 0 \] |
1 |
1 |
3 |
[_exact, _rational] |
✓ |
✓ |
1.446 |
|
|
\[ {}-\frac {1}{y}+\left (\frac {t}{y^{2}}+3 y^{2}\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _exact, _rational] |
✓ |
✓ |
1.446 |
|
|
\[ {}2 t y+\left (t^{2}+y^{2}\right ) y^{\prime } = 0 \] |
1 |
1 |
3 |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
10.187 |
|
|
\[ {}2 t y^{3}+\left (1+3 t^{2} y^{2}\right ) y^{\prime } = 0 \] |
1 |
1 |
3 |
[[_homogeneous, ‘class G‘], _exact, _rational] |
✓ |
✓ |
3.243 |
|
|
\[ {}\sin \left (y\right )^{2}+t \sin \left (2 y\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
6.826 |
|
|
\[ {}3 t^{2}+3 y^{2}+6 t y y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
2.386 |
|
|
\[ {}{\mathrm e}^{t} \sin \left (y\right )+\left (1+{\mathrm e}^{t} \cos \left (y\right )\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_exact, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
2.067 |
|
|
\[ {}3 t^{2} y+3 y^{2}-1+\left (t^{3}+6 t y\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[_exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
1.608 |
|
|
\[ {}-2 t y^{2} \sin \left (t^{2}\right )+2 y \cos \left (t^{2}\right ) y^{\prime } = 0 \] |
1 |
1 |
3 |
[_separable] |
✓ |
✓ |
3.513 |
|
|
\[ {}2 t -y^{2} \sin \left (t y\right )+\left (\cos \left (t y\right )-t y \sin \left (t y\right )\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_exact] |
✓ |
✓ |
11.457 |
|
|
\[ {}2 t \sin \left (y\right )-2 t y \sin \left (t^{2}\right )+\left (t^{2} \cos \left (y\right )+\cos \left (t^{2}\right )\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_exact] |
✓ |
✓ |
35.254 |
|
|
\[ {}\left (3+t \right ) \cos \left (t +y\right )+\sin \left (t +y\right )+\left (3+t \right ) \cos \left (t +y\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_1st_order, _with_linear_symmetries], _exact] |
✓ |
✓ |
10.316 |
|
|
\[ {}\frac {2 t^{2} y \cos \left (t^{2}\right )-y \sin \left (t^{2}\right )}{t^{2}}+\frac {\left (2 t y+\sin \left (t^{2}\right )\right ) y^{\prime }}{t} = 0 \] |
1 |
1 |
2 |
[_exact, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
9.75 |
|
|
\[ {}-\frac {y^{2} {\mathrm e}^{\frac {y}{t}}}{t^{2}}+1+{\mathrm e}^{\frac {y}{t}} \left (1+\frac {y}{t}\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _exact, _dAlembert] |
✓ |
✓ |
3.293 |
|
|
\[ {}2 t \sin \left (\frac {y}{t}\right )-y \cos \left (\frac {y}{t}\right )+t \cos \left (\frac {y}{t}\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _exact, _dAlembert] |
✓ |
✓ |
3.123 |
|
|
\[ {}2 t y^{2}+2 t^{2} y y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.845 |
|
|
\[ {}1+\frac {y}{t^{2}}-\frac {y^{\prime }}{t} = 0 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.148 |
|
|
\[ {}2 t y+3 t^{2}+\left (t^{2}-1\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.512 |
|
|
\[ {}1+5 t -y-\left (t +2 y\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
5.456 |
|
|
\[ {}{\mathrm e}^{y}-2 t y+\left (t \,{\mathrm e}^{y}-t^{2}\right ) y^{\prime } = 0 \] |
1 |
0 |
0 |
[_exact] |
✗ |
N/A |
4.658 |
|
|
\[ {}2 t y \,{\mathrm e}^{t^{2}}+2 t \,{\mathrm e}^{-y}+\left ({\mathrm e}^{t^{2}}-t^{2} {\mathrm e}^{-y}+1\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_exact] |
✓ |
✓ |
36.807 |
|
|
\[ {}y^{2}-2 \sin \left (2 t \right )+\left (1+2 t y\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_exact, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
8.174 |
|
|
\[ {}\cos \left (t \right )^{2}-\sin \left (t \right )^{2}+y+\left (\sec \left (y\right ) \tan \left (y\right )+t \right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_exact] |
✓ |
✓ |
39.358 |
|
|
\[ {}\frac {1}{t^{2}+1}-y^{2}-2 t y y^{\prime } = 0 \] |
1 |
1 |
0 |
[_exact, _rational, _Bernoulli] |
✓ |
✓ |
1.777 |
|
|
\[ {}\frac {2 t}{t^{2}+1}+y+\left ({\mathrm e}^{y}+t \right ) y^{\prime } = 0 \] |
1 |
0 |
0 |
[_exact] |
✗ |
N/A |
9.528 |
|
|
\[ {}-2 x -y \cos \left (x y\right )+\left (2 y-x \cos \left (x y\right )\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_exact] |
✓ |
✓ |
35.291 |
|
|
\[ {}-4 x^{3}+6 y \sin \left (6 x y\right )+\left (4 y^{3}+6 x \sin \left (6 x y\right )\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_exact] |
✓ |
✓ |
44.442 |
|
|
\[ {}t^{2} y+t^{3} y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.45 |
|
|
\[ {}y \left (2 \,{\mathrm e}^{t}+4 t \right )+3 \left ({\mathrm e}^{t}+t^{2}\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.579 |
|
|
\[ {}2 t -y^{2} \sin \left (t y\right )+\left (\cos \left (t y\right )-t y \sin \left (t y\right )\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_exact] |
✓ |
✓ |
11.434 |
|
|
\[ {}-1+{\mathrm e}^{t y} y+y \cos \left (t y\right )+\left (1+{\mathrm e}^{t y} t +t \cos \left (t y\right )\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_exact] |
✓ |
✓ |
41.909 |
|
|
\[ {}\frac {9 t}{5}+2 y+\left (2 t +2 y\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
3.082 |
|
|
\[ {}2 t +\frac {19 y}{10}+\left (\frac {19 t}{10}+2 y\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
3.076 |
|
|
\[ {}y^{\prime }-\frac {y}{t} = \frac {y^{2}}{t} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.685 |
|
|
\[ {}2 \ln \left (t \right )-\ln \left (4 y^{2}\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
5.747 |
|
|
\[ {}\frac {\sin \left (2 t \right )}{\cos \left (2 y\right )}+\frac {\ln \left (y\right ) y^{\prime }}{\ln \left (t \right )} = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
30.221 |
|
|
\[ {}\sqrt {t^{2}+1}+y y^{\prime } = 0 \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
3.096 |
|
|
\[ {}y+\left (t +y\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
3.825 |
|
|
\[ {}\left (t^{2}-y^{2}\right ) y^{\prime }+y^{2}+t y = 0 \] |
1 |
1 |
3 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
3.86 |
|
|
\[ {}5 t +2 y+1+\left (2 t +y+1\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
4.359 |
|
|
\[ {}y^{\prime }-\frac {2 y}{x} = -x^{2} y \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.704 |
|
|
\[ {}y^{\prime } = \frac {2 t^{5}}{5 y^{2}} \] |
1 |
1 |
3 |
[_separable] |
✓ |
✓ |
7.595 |
|
|
\[ {}\cos \left (4 x \right )-8 \sin \left (y\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.574 |
|
|
\[ {}y^{\prime }-\frac {y}{t} = \frac {y^{2}}{t} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.98 |
|
|
\[ {}y^{\prime } = \frac {{\mathrm e}^{8 y}}{t} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.113 |
|
|
\[ {}y^{\prime } = \frac {{\mathrm e}^{5 t}}{y^{4}} \] |
1 |
1 |
5 |
[_separable] |
✓ |
✓ |
0.912 |
|
|
\[ {}-\frac {1}{x^{5}}+\frac {1}{x^{3}} = \left (2 y^{4}-6 y^{9}\right ) y^{\prime } \] |
1 |
1 |
10 |
[_separable] |
✓ |
✓ |
1.445 |
|
|
\[ {}y^{\prime } = \frac {y \,{\mathrm e}^{-2 t}}{\ln \left (y\right )} \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
1.911 |
|
|
\[ {}y^{\prime } = \frac {\left (4-7 x \right ) \left (2 y-3\right )}{\left (-1+x \right ) \left (2 x -5\right )} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.785 |
|
|
\[ {}y-t +\left (t +y\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.921 |
|
|
\[ {}t^{2}-y+\left (-t +y\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.964 |
|
|
\[ {}t^{2} y+\sin \left (t \right )+\left (\frac {t^{3}}{3}-\cos \left (y\right )\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_exact] |
✓ |
✓ |
9.555 |
|
|
\[ {}\tan \left (y\right )-t +\left (t \sec \left (y\right )^{2}+1\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_exact] |
✓ |
✓ |
4.931 |
|
|
\[ {}t \ln \left (y\right )+\left (\frac {t^{2}}{2 y}+1\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_exact, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
1.882 |
|
|
\[ {}y^{\prime }+t y = t \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.487 |
|
|
\[ {}x^{\prime }+\frac {x}{y} = y^{2} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.267 |
|
|
\[ {}t r^{\prime }+r = t \cos \left (t \right ) \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.18 |
|
|
\[ {}2 x -y-2+\left (2 y-x \right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
7.896 |
|
|
\[ {}\cos \left (t -y\right )+\left (1-\cos \left (t -y\right )\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _exact, _dAlembert] |
✓ |
✓ |
9.635 |
|
|
\[ {}{\mathrm e}^{t y} y-2 t +t \,{\mathrm e}^{t y} y^{\prime } = 0 \] |
1 |
1 |
1 |
[_exact, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
2.181 |
|
|
\[ {}\sin \left (y\right )-y \cos \left (t \right )+\left (t \cos \left (y\right )-\sin \left (t \right )\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_exact] |
✓ |
✓ |
11.48 |
|
|
\[ {}y^{2}+\left (2 t y-2 \cos \left (y\right ) \sin \left (y\right )\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_exact, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
2.804 |
|
|
\[ {}\frac {y}{t}+\ln \left (y\right )+\left (\frac {t}{y}+\ln \left (t \right )\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_exact] |
✓ |
✓ |
3.188 |
|
|
\[ {}y^{\prime } = t y^{3} \] |
1 |
0 |
1 |
[_separable] |
✓ |
✓ |
1.024 |
|
|
\[ {}y^{\prime } = \frac {t}{y^{3}} \] |
1 |
1 |
4 |
[_separable] |
✓ |
✓ |
2.13 |
|
|
\[ {}y^{\prime } = -\frac {y}{t -2} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.637 |
|
|
\[ {}y^{\prime } = \frac {x}{y} \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
2.51 |
|
|
\[ {}x y^{\prime }+y = \cos \left (x \right ) \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.331 |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime }+x y = 2 x \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
3.665 |
|
|
\[ {}y^{\prime } = \left (y-1\right ) x \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.275 |
|
|
\[ {}y^{\prime } = \frac {y+1}{-1+x} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.953 |
|
|
\[ {}y^{\prime } = -\frac {y}{x} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.709 |
|
|
\[ {}x y^{\prime } = 2 x -y \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
2.59 |
|
|
\[ {}1+y^{2}+\left (x^{2}+1\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.477 |
|
|
\[ {}1+y^{2}+x y y^{\prime } = 0 \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
3.681 |
|
|
\[ {}y^{\prime } \sin \left (x \right )-y \cos \left (x \right ) = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
3.12 |
|
|
\[ {}1+y^{2} = x y^{\prime } \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.455 |
|
|
\[ {}x \sqrt {1+y^{2}}+y y^{\prime } \sqrt {x^{2}+1} = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.202 |
|
|
\[ {}x \sqrt {1-y^{2}}+y \sqrt {-x^{2}+1}\, y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
3.635 |
|
|
\[ {}y \ln \left (y\right )+x y^{\prime } = 1 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
11.04 |
|
|
\[ {}y^{\prime } = a^{x +y} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.565 |
|
|
\[ {}{\mathrm e}^{y} \left (x^{2}+1\right ) y^{\prime }-2 x \left (1+{\mathrm e}^{y}\right ) = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.532 |
|
|
\[ {}2 x \sqrt {1-y^{2}} = \left (x^{2}+1\right ) y^{\prime } \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.034 |
|
|
\[ {}{\mathrm e}^{x} \sin \left (y\right )^{3}+\left (1+{\mathrm e}^{2 x}\right ) \cos \left (y\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
4.908 |
|
|
\[ {}y^{2} \sin \left (x \right )+\cos \left (x \right )^{2} \ln \left (y\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
4.586 |
|
|
\[ {}a^{2}+y^{2}+2 x \sqrt {x a -x^{2}}\, y^{\prime } = 0 \] |
1 |
0 |
1 |
[_separable] |
✓ |
✓ |
5.954 |
|
|
\[ {}y^{\prime } = \frac {y}{x} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.441 |
|
|
\[ {}x^{2} y^{\prime } \cos \left (y\right )+1 = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✗ |
6.134 |
|
|
\[ {}x^{2} y^{\prime }+\cos \left (2 y\right ) = 1 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✗ |
10.013 |
|
|
\[ {}x^{3} y^{\prime }-\sin \left (y\right ) = 1 \] |
1 |
1 |
0 |
[_separable] |
✓ |
✓ |
5.432 |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime }-\frac {\cos \left (2 y\right )^{2}}{2} = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
5.362 |
|
|
\[ {}\left (1+x \right ) y^{\prime } = y-1 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.071 |
|
|
\[ {}y^{\prime } = 2 x \left (\pi +y\right ) \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.981 |
|
|
\[ {}x^{2} y^{\prime }+\sin \left (2 y\right ) = 1 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✗ |
32.723 |
|
|
\[ {}4 x -3 y+\left (2 y-3 x \right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
5.026 |
|
|
\[ {}y-x +\left (x +y\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
3.454 |
|
|
\[ {}x +y-2+\left (-y+4+x \right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
4.743 |
|
|
\[ {}x +y+\left (x -y-2\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
4.56 |
|
|
\[ {}2 x +3 y-5+\left (3 x +2 y-5\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
3.665 |
|
|
\[ {}8 x +4 y+1+\left (4 x +2 y+1\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.536 |
|
|
\[ {}x +y+\left (x +y-1\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.97 |
|
|
\[ {}x^{2}-x y^{\prime } = y \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.849 |
|
|
\[ {}y^{\prime } \cos \left (x \right )-y \sin \left (x \right ) = 2 x \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
2.506 |
|
|
\[ {}y^{\prime }+y \cos \left (x \right ) = \cos \left (x \right ) \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.506 |
|
|
\[ {}y^{\prime } = \frac {y}{2 y \ln \left (y\right )+y-x} \] |
1 |
1 |
1 |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
3.484 |
|
|
\[ {}x y^{\prime }+y = 2 x \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
2.009 |
|
|
\[ {}y^{\prime } \sin \left (x \right )+y \cos \left (x \right ) = 1 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.679 |
|
|
\[ {}y^{\prime } \cos \left (x \right )-y \sin \left (x \right ) = -\sin \left (2 x \right ) \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
3.099 |
|
|
\[ {}y^{\prime }+2 x y = 2 x y^{2} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
3.732 |
|
|
\[ {}y^{\prime }+3 x y = y \,{\mathrm e}^{x^{2}} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.742 |
|
|
\[ {}y^{\prime }-y \cos \left (x \right ) = y^{2} \cos \left (x \right ) \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
4.376 |
|
|
\[ {}x \left (2 x^{2}+y^{2}\right )+y \left (x^{2}+2 y^{2}\right ) y^{\prime } = 0 \] |
1 |
1 |
4 |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
3.869 |
|
|
\[ {}3 x^{2}+6 x y^{2}+\left (6 x^{2} y+4 y^{3}\right ) y^{\prime } = 0 \] |
1 |
1 |
4 |
[_exact, _rational] |
✓ |
✓ |
1.825 |
|
|
\[ {}\frac {x}{\sqrt {x^{2}+y^{2}}}+\frac {1}{x}+\frac {1}{y}+\left (\frac {y}{\sqrt {x^{2}+y^{2}}}+\frac {1}{y}-\frac {x}{y^{2}}\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_exact] |
✓ |
✓ |
30.911 |
|
|
\[ {}3 x^{2} \tan \left (y\right )-\frac {2 y^{3}}{x^{3}}+\left (x^{3} \sec \left (y\right )^{2}+4 y^{3}+\frac {3 y^{2}}{x^{2}}\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_exact] |
✓ |
✓ |
51.631 |
|
|
\[ {}2 x +\frac {x^{2}+y^{2}}{x^{2} y} = \frac {\left (x^{2}+y^{2}\right ) y^{\prime }}{x y^{2}} \] |
1 |
1 |
2 |
[[_homogeneous, ‘class D‘], _exact, _rational] |
✓ |
✓ |
2.423 |
|
|
\[ {}\frac {\sin \left (2 x \right )}{y}+x +\left (y-\frac {\sin \left (x \right )^{2}}{y^{2}}\right ) y^{\prime } = 0 \] |
1 |
1 |
3 |
[_exact] |
✓ |
✓ |
11.772 |
|
|
|
||||||||
|
\[ {}3 x^{2}-2 x -y+\left (2 y-x +3 y^{2}\right ) y^{\prime } = 0 \] |
1 |
1 |
3 |
[_exact, _rational] |
✓ |
✓ |
22.627 |
|
|
\[ {}\frac {x y}{\sqrt {x^{2}+1}}+2 x y-\frac {y}{x}+\left (\sqrt {x^{2}+1}+x^{2}-\ln \left (x \right )\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
37.151 |
|
|
\[ {}\sin \left (y\right )+y \sin \left (x \right )+\frac {1}{x}+\left (x \cos \left (y\right )-\cos \left (x \right )+\frac {1}{y}\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_exact] |
✓ |
✓ |
41.57 |
|
|
\[ {}\frac {y+\sin \left (x \right ) \cos \left (x y\right )^{2}}{\cos \left (x y\right )^{2}}+\left (\frac {x}{\cos \left (x y\right )^{2}}+\sin \left (y\right )\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_exact] |
✓ |
✓ |
62.519 |
|
|
\[ {}\frac {2 x}{y^{3}}+\frac {\left (y^{2}-3 x^{2}\right ) y^{\prime }}{y^{4}} = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
6.991 |
|
|
\[ {}y \left (x^{2}+y^{2}+a^{2}\right ) y^{\prime }+x \left (x^{2}+y^{2}-a^{2}\right ) = 0 \] |
1 |
1 |
4 |
[_exact, _rational] |
✓ |
✓ |
2.072 |
|
|
\[ {}3 x^{2} y+y^{3}+\left (x^{3}+3 x y^{2}\right ) y^{\prime } = 0 \] |
1 |
1 |
3 |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
4.919 |
|
|
\[ {}x^{3}-3 x y^{2}+\left (y^{3}-3 x^{2} y\right ) y^{\prime } = 0 \] |
1 |
1 |
4 |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
1.65 |
|
|
\[ {}5 x y-4 y^{2}-6 x^{2}+\left (y^{2}-8 x y+\frac {5 x^{2}}{2}\right ) y^{\prime } = 0 \] |
1 |
1 |
3 |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
1.411 |
|
|
\[ {}3 x y^{2}-x^{2}+\left (3 x^{2} y-6 y^{2}-1\right ) y^{\prime } = 0 \] |
1 |
1 |
3 |
[_exact, _rational] |
✓ |
✓ |
1.541 |
|
|
\[ {}2 x y \,{\mathrm e}^{x^{2}}-x \sin \left (x \right )+{\mathrm e}^{x^{2}} y^{\prime } = 0 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.996 |
|
|
\[ {}y^{\prime }+\cos \left (\frac {x}{2}+\frac {y}{2}\right ) = \cos \left (\frac {x}{2}-\frac {y}{2}\right ) \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.551 |
|
|
\[ {}y^{\prime } \left (3 x^{2}-2 x \right )-y \left (6 x -2\right ) = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.583 |
|
|
\[ {}1+{\mathrm e}^{\frac {x}{y}}+{\mathrm e}^{\frac {x}{y}} \left (1-\frac {x}{y}\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _exact, _dAlembert] |
✓ |
✓ |
7.802 |
|
|
\[ {}\left (-1+x \right ) \left (y^{2}-y+1\right ) = \left (y-1\right ) \left (x^{2}+x +1\right ) y^{\prime } \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.444 |
|
|
\[ {}\sin \left (\ln \left (x \right )\right )-\cos \left (\ln \left (y\right )\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
59.475 |
|
|
|
||||||||
|
|
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|
|