These are ode’s of the form \(M dx + N dy=0\) where it become exact using integrating factor \(\mu \) to obtain \(\mu M dx + \mu N dy=0\). The integrating factor is found using three known methods. Number of problems in this table is 1335
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) |
|
\[ {}y^{\prime } = -\sin \left (x \right )-y \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.63 |
|
|
\[ {}y^{\prime } = x +y \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.374 |
|
|
\[ {}y^{\prime } = -\sin \left (x \right )+y \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.482 |
|
|
\[ {}y^{\prime } = x -y \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.379 |
|
|
\[ {}y^{\prime } = -x +y+1 \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.482 |
|
|
\[ {}y^{\prime } = x -y+1 \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.478 |
|
|
\[ {}y^{\prime } = x^{2}-y \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.381 |
|
|
\[ {}y^{\prime } = -2+x^{2}-y \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.549 |
|
|
\[ {}y^{\prime } = 3 \sqrt {x y} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
11.688 |
|
|
\[ {}y^{\prime } = 4 \left (x y\right )^{\frac {1}{3}} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
91.221 |
|
|
\[ {}-2 y+y^{\prime } = 3 \,{\mathrm e}^{2 x} \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.601 |
|
|
\[ {}y^{\prime }-2 x y = {\mathrm e}^{x^{2}} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.777 |
|
|
\[ {}2 y+x y^{\prime } = 3 x \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.953 |
|
|
\[ {}y+2 x y^{\prime } = 10 \sqrt {x} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.926 |
|
|
\[ {}y+2 x y^{\prime } = 10 \sqrt {x} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.698 |
|
|
\[ {}y+3 x y^{\prime } = 12 x \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.562 |
|
|
\[ {}-y+x y^{\prime } = x \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.707 |
|
|
\[ {}-3 y+2 x y^{\prime } = 9 x^{3} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.832 |
|
|
\[ {}3 y+x y^{\prime } = 2 x^{5} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.616 |
|
|
\[ {}y+y^{\prime } = {\mathrm e}^{x} \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.529 |
|
|
\[ {}-3 y+x y^{\prime } = x^{3} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.654 |
|
|
\[ {}x y^{\prime } = x^{3} \cos \left (x \right )+2 y \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.968 |
|
|
\[ {}\cot \left (x \right ) y+y^{\prime } = \cos \left (x \right ) \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.103 |
|
|
\[ {}x y^{\prime } = x^{4} \cos \left (x \right )+3 y \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.804 |
|
|
\[ {}y^{\prime } = 3 x^{2} {\mathrm e}^{x^{2}}+2 x y \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.689 |
|
|
\[ {}\left (2 x -3\right ) y+x y^{\prime } = 4 x^{4} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.961 |
|
|
\[ {}3 x^{3} y+\left (x^{2}+1\right ) y^{\prime } = 6 x \,{\mathrm e}^{-\frac {3 x^{2}}{2}} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
3.8 |
|
|
\[ {}2 x y y^{\prime } = x^{2}+y^{2} \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.878 |
|
|
\[ {}\left (2 y+x \right ) y^{\prime } = y \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.862 |
|
|
\[ {}x y^{2} y^{\prime } = x^{3}+y^{3} \] |
1 |
1 |
3 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.965 |
|
|
\[ {}x y y^{\prime } = x^{2}+3 y^{2} \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
2.107 |
|
|
\[ {}\left (x^{2}-y^{2}\right ) y^{\prime } = 2 x y \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
2.424 |
|
|
\[ {}y \left (3 x +y\right )+x \left (x +y\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
2.957 |
|
|
\[ {}\sqrt {x^{4}+1}\, y^{2} \left (x y^{\prime }+y\right ) = x \] |
1 |
1 |
3 |
[_Bernoulli] |
✓ |
✓ |
10.416 |
|
|
\[ {}y^{3}+3 y^{2} y^{\prime } = {\mathrm e}^{-x} \] |
1 |
1 |
3 |
[[_1st_order, _with_linear_symmetries], _Bernoulli] |
✓ |
✓ |
1.696 |
|
|
\[ {}3 x y^{2} y^{\prime } = 3 x^{4}+y^{3} \] |
1 |
1 |
3 |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
1.539 |
|
|
\[ {}x \,{\mathrm e}^{y} y^{\prime } = 2 \,{\mathrm e}^{y}+2 \,{\mathrm e}^{2 x} x^{3} \] |
1 |
1 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
✓ |
2.675 |
|
|
\[ {}2 x \cos \left (y\right ) \sin \left (y\right ) y^{\prime } = 4 x^{2}+\sin \left (y\right )^{2} \] |
1 |
1 |
2 |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
4.665 |
|
|
\[ {}x^{3}+3 y-x y^{\prime } = 0 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.321 |
|
|
\[ {}2 x^{2} y+x^{3} y^{\prime } = 1 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.77 |
|
|
\[ {}3 y+x y^{\prime } = \frac {3}{x^{\frac {3}{2}}} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.844 |
|
|
\[ {}\left (-1+x \right ) y+\left (x^{2}-1\right ) y^{\prime } = 1 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.962 |
|
|
\[ {}2 y+\left (1+x \right ) y^{\prime } = 3+3 x \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.444 |
|
|
\[ {}3 y+x^{3} y^{4}+3 x y^{\prime } = 0 \] |
1 |
1 |
3 |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
1.399 |
|
|
\[ {}y+\left (2 x +1\right ) y^{\prime } = \left (2 x +1\right )^{\frac {3}{2}} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.029 |
|
|
\[ {}3 y+y^{\prime } = {\mathrm e}^{-2 t}+t \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.925 |
|
|
\[ {}-2 y+y^{\prime } = {\mathrm e}^{2 t} t^{2} \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.835 |
|
|
\[ {}-2 y+y^{\prime } = 3 \,{\mathrm e}^{t} \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.859 |
|
|
\[ {}2 y+t y^{\prime } = \sin \left (t \right ) \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.026 |
|
|
\[ {}4 t y+\left (t^{2}+1\right ) y^{\prime } = \frac {1}{\left (t^{2}+1\right )^{2}} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.116 |
|
|
\[ {}y+2 y^{\prime } = 3 t \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.829 |
|
|
\[ {}-y+t y^{\prime } = t^{2} {\mathrm e}^{-t} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.972 |
|
|
\[ {}y+y^{\prime } = 5 \sin \left (2 t \right ) \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.095 |
|
|
\[ {}y+2 y^{\prime } = 3 t^{2} \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.847 |
|
|
\[ {}-y+y^{\prime } = 2 \,{\mathrm e}^{2 t} t \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.323 |
|
|
\[ {}2 y+t y^{\prime } = t^{2}-t +1 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.304 |
|
|
\[ {}-2 y+y^{\prime } = {\mathrm e}^{2 t} \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.156 |
|
|
\[ {}2 y+t y^{\prime } = \sin \left (t \right ) \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.485 |
|
|
\[ {}4 t^{2} y+t^{3} y^{\prime } = {\mathrm e}^{-t} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.281 |
|
|
\[ {}\left (t +1\right ) y+t y^{\prime } = t \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.574 |
|
|
\[ {}-\frac {y}{2}+y^{\prime } = 2 \cos \left (t \right ) \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.368 |
|
|
\[ {}-y+2 y^{\prime } = {\mathrm e}^{\frac {t}{3}} \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.177 |
|
|
\[ {}-2 y+3 y^{\prime } = {\mathrm e}^{-\frac {\pi t}{2}} \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.498 |
|
|
\[ {}\frac {y}{2}+y^{\prime } = 2 \cos \left (t \right ) \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.518 |
|
|
\[ {}\frac {2 y}{3}+y^{\prime } = -\frac {t}{2}+1 \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.88 |
|
|
\[ {}\frac {y}{4}+y^{\prime } = 3+2 \cos \left (2 t \right ) \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.701 |
|
|
\[ {}-y+y^{\prime } = 1+3 \sin \left (t \right ) \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.127 |
|
|
\[ {}-\frac {3 y}{2}+y^{\prime } = 2 \,{\mathrm e}^{t}+3 t \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.044 |
|
|
\[ {}y^{\prime } = \frac {x^{2}+3 y^{2}}{2 x y} \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.633 |
|
|
\[ {}y^{\prime } = \frac {x^{2}-3 y^{2}}{2 x y} \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.742 |
|
|
\[ {}y^{\prime } = \frac {3 y^{2}-x^{2}}{2 x y} \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.518 |
|
|
\[ {}\ln \left (t \right ) y+\left (t -3\right ) y^{\prime } = 2 t \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
3.69 |
|
|
\[ {}y \tan \left (t \right )+y^{\prime } = \sin \left (t \right ) \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.693 |
|
|
\[ {}2 t y+\left (-t^{2}+4\right ) y^{\prime } = 3 t^{2} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.746 |
|
|
\[ {}2 t y+\left (-t^{2}+4\right ) y^{\prime } = 3 t^{2} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.372 |
|
|
\[ {}y+\ln \left (t \right ) y^{\prime } = \cot \left (t \right ) \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.854 |
|
|
\[ {}y+\left (2 x -y \,{\mathrm e}^{y}\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
1.762 |
|
|
\[ {}2 x y+3 x^{2} y+y^{3}+\left (x^{2}+y^{2}\right ) y^{\prime } = 0 \] |
1 |
1 |
3 |
[[_homogeneous, ‘class D‘], _rational] |
✓ |
✓ |
3.155 |
|
|
\[ {}y^{\prime } = -1+{\mathrm e}^{2 x}+y \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.841 |
|
|
\[ {}y+\left (-{\mathrm e}^{-2 y}+2 x y\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_1st_order, _with_exponential_symmetries]] |
✓ |
✓ |
2.399 |
|
|
\[ {}{\mathrm e}^{x}+\left ({\mathrm e}^{x} \cot \left (y\right )+2 \csc \left (y\right ) y\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
3.892 |
|
|
\[ {}3 x y+y^{2}+\left (x^{2}+x y\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
3.201 |
|
|
\[ {}y^{\prime } = \frac {x^{3}-2 y}{x} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.846 |
|
|
\[ {}x y+x y^{\prime } = 1-y \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.539 |
|
|
\[ {}y+y^{\prime } = \frac {1}{1+{\mathrm e}^{x}} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.929 |
|
|
\[ {}y^{\prime } = \frac {-{\mathrm e}^{2 y} \cos \left (x \right )+\cos \left (y\right ) {\mathrm e}^{-x}}{2 \,{\mathrm e}^{2 y} \sin \left (x \right )-\sin \left (y\right ) {\mathrm e}^{-x}} \] |
1 |
1 |
1 |
[NONE] |
✓ |
✓ |
48.562 |
|
|
\[ {}y^{\prime } = {\mathrm e}^{2 x}+3 y \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.88 |
|
|
\[ {}2 y+y^{\prime } = {\mathrm e}^{-x^{2}-2 x} \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.011 |
|
|
\[ {}\left (t +1\right ) y+t y^{\prime } = {\mathrm e}^{2 t} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.082 |
|
|
\[ {}y^{\prime } = \frac {x}{x^{2}+y+y^{3}} \] |
1 |
1 |
1 |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
1.819 |
|
|
\[ {}3 t +2 y = -t y^{\prime } \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.25 |
|
|
\[ {}2 x y+3 y^{2}-\left (2 x y+x^{2}\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
2.812 |
|
|
\[ {}y^{\prime } = \frac {-3 x^{2} y-y^{2}}{2 x^{3}+3 x y} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
3.122 |
|
|
\[ {}y^{\prime } = \cos \left (x \right )-y \tan \left (x \right ) \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.645 |
|
|
\[ {}y^{\prime } = \frac {x^{2}-2 x^{2} y+2}{x^{3}} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.52 |
|
|
\[ {}y^{\prime }+\left (\frac {1}{x}-1\right ) y = -\frac {2}{x} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.088 |
|
|
\[ {}y^{\prime }+2 x y = x \,{\mathrm e}^{-x^{2}} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.0 |
|
|
\[ {}y^{\prime }+\frac {y}{x} = \frac {7}{x^{2}}+3 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.966 |
|
|
\[ {}y^{\prime }+\frac {4 y}{-1+x} = \frac {1}{\left (-1+x \right )^{5}}+\frac {\sin \left (x \right )}{\left (-1+x \right )^{4}} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
4.908 |
|
|
\[ {}x y^{\prime }+\left (2 x^{2}+1\right ) y = x^{3} {\mathrm e}^{-x^{2}} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.223 |
|
|
\[ {}2 y+x y^{\prime } = \frac {2}{x^{2}}+1 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.929 |
|
|
\[ {}y^{\prime }+y \tan \left (x \right ) = \cos \left (x \right ) \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.975 |
|
|
\[ {}\left (-2+x \right ) \left (-1+x \right ) y^{\prime }-\left (4 x -3\right ) y = \left (-2+x \right )^{3} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.288 |
|
|
\[ {}y^{\prime }+2 \sin \left (x \right ) \cos \left (x \right ) y = {\mathrm e}^{-\sin \left (x \right )^{2}} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
2.408 |
|
|
\[ {}x^{2} y^{\prime }+3 x y = {\mathrm e}^{x} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.018 |
|
|
\[ {}y^{\prime }+7 y = {\mathrm e}^{3 x} \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.433 |
|
|
\[ {}3 y+x y^{\prime } = \frac {2}{x \left (x^{2}+1\right )} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.601 |
|
|
\[ {}\cot \left (x \right ) y+y^{\prime } = \cos \left (x \right ) \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
2.142 |
|
|
\[ {}y^{\prime }+\frac {y}{x} = \frac {2}{x^{2}}+1 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.257 |
|
|
\[ {}\left (-1+x \right ) y^{\prime }+3 y = \frac {1}{\left (-1+x \right )^{3}}+\frac {\sin \left (x \right )}{\left (-1+x \right )^{2}} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
4.447 |
|
|
\[ {}2 y+x y^{\prime } = 8 x^{2} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.312 |
|
|
\[ {}x y^{\prime }-2 y = -x^{2} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.421 |
|
|
\[ {}\left (-1+x \right ) y^{\prime }+3 y = \frac {1+\left (-1+x \right ) \sec \left (x \right )^{2}}{\left (-1+x \right )^{3}} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
16.268 |
|
|
\[ {}\left (2+x \right ) y^{\prime }+4 y = \frac {2 x^{2}+1}{x \left (2+x \right )^{3}} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.597 |
|
|
\[ {}\left (x^{2}-1\right ) y^{\prime }-2 x y = x \left (x^{2}-1\right ) \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.576 |
|
|
\[ {}\frac {x y^{\prime }}{y}+2 \ln \left (y\right ) = 4 x^{2} \] |
1 |
1 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
4.343 |
|
|
\[ {}\frac {y^{\prime }}{\left (y+1\right )^{2}}-\frac {1}{x \left (y+1\right )} = -\frac {3}{x^{2}} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, _Riccati] |
✓ |
✓ |
2.29 |
|
|
\[ {}y+y^{\prime } = \frac {2 x \,{\mathrm e}^{-x}}{1+{\mathrm e}^{x} y} \] |
1 |
1 |
2 |
[[_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
2.789 |
|
|
\[ {}x y^{\prime }-2 y = \frac {x^{6}}{y+x^{2}} \] |
1 |
1 |
2 |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
8.738 |
|
|
\[ {}y^{\prime }-y = \frac {\left (1+x \right ) {\mathrm e}^{4 x}}{\left (y+{\mathrm e}^{x}\right )^{2}} \] |
1 |
1 |
3 |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
3.855 |
|
|
\[ {}-2 y+y^{\prime } = \frac {x \,{\mathrm e}^{2 x}}{1-y \,{\mathrm e}^{-2 x}} \] |
1 |
1 |
2 |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.913 |
|
|
\[ {}y^{\prime } = \frac {x +y}{x} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.011 |
|
|
\[ {}y^{\prime } = \frac {y^{2}+2 x y}{x^{2}} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.347 |
|
|
\[ {}x y^{3} y^{\prime } = y^{4}+x^{4} \] |
1 |
1 |
4 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.851 |
|
|
\[ {}x y y^{\prime } = x^{2}+2 y^{2} \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.96 |
|
|
\[ {}y^{\prime } = \frac {x^{3}+y^{3}}{x y^{2}} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.781 |
|
|
\[ {}x y y^{\prime }+x^{2}+y^{2} = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
2.448 |
|
|
\[ {}x y y^{\prime } = 3 x^{2}+4 y^{2} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
2.984 |
|
|
\[ {}\left (-y+x y^{\prime }\right ) \left (\ln \left (y\right )-\ln \left (x \right )\right ) = x \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘]] |
✓ |
✓ |
4.368 |
|
|
\[ {}y^{\prime } = \frac {y^{3}+2 x y^{2}+x^{2} y+x^{3}}{x \left (x +y\right )^{2}} \] |
1 |
1 |
3 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
1.686 |
|
|
\[ {}y^{\prime } = \frac {y}{-2 x +y} \] |
1 |
1 |
3 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.826 |
|
|
\[ {}y^{\prime } = \frac {x^{3}+x^{2} y+3 y^{3}}{x^{3}+3 x y^{2}} \] |
1 |
1 |
3 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
1.707 |
|
|
\[ {}3 x y^{2} y^{\prime } = y^{3}+x \] |
1 |
1 |
3 |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
1.648 |
|
|
\[ {}x y y^{\prime } = 3 x^{6}+6 y^{2} \] |
1 |
1 |
2 |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
1.386 |
|
|
\[ {}2 x \left (y+2 \sqrt {x}\right ) y^{\prime } = \left (y+\sqrt {x}\right )^{2} \] |
1 |
1 |
2 |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
2.043 |
|
|
\[ {}\left (y+{\mathrm e}^{x^{2}}\right ) y^{\prime } = 2 x \left (y^{2}+y \,{\mathrm e}^{x^{2}}+{\mathrm e}^{2 x^{2}}\right ) \] |
1 |
1 |
2 |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
3.753 |
|
|
\[ {}y^{\prime }+\frac {2 y}{x} = \frac {3 x^{2} y^{2}+6 x y+2}{x^{2} \left (2 x y+3\right )} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
16.555 |
|
|
\[ {}y^{\prime }+\frac {3 y}{x} = \frac {3 x^{4} y^{2}+10 x^{2} y+6}{x^{3} \left (2 x^{2} y+5\right )} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
12.26 |
|
|
\[ {}3 y \cos \left (x \right )+4 x \,{\mathrm e}^{x}+2 x^{3} y+\left (3 \sin \left (x \right )+3\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
153.251 |
|
|
\[ {}y^{\prime }+\frac {2 y}{x} = -\frac {2 x y}{x^{2}+2 x^{2} y+1} \] |
1 |
1 |
1 |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
5.012 |
|
|
\[ {}y^{\prime }-\frac {3 y}{x} = \frac {2 x^{4} \left (4 x^{3}-3 y\right )}{3 x^{5}+3 x^{3}+2 y} \] |
1 |
1 |
1 |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
2.682 |
|
|
\[ {}y^{\prime }+2 x y = -\frac {{\mathrm e}^{-x^{2}} \left (3 x +2 y \,{\mathrm e}^{x^{2}}\right )}{2 x +3 y \,{\mathrm e}^{x^{2}}} \] |
1 |
1 |
1 |
[[_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
44.569 |
|
|
\[ {}5 x y+2 y+5+2 x y^{\prime } = 0 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.224 |
|
|
\[ {}x y+x +2 y+1+\left (1+x \right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.129 |
|
|
\[ {}27 x y^{2}+8 y^{3}+\left (18 x^{2} y+12 x y^{2}\right ) y^{\prime } = 0 \] |
1 |
1 |
16 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
4.234 |
|
|
\[ {}6 x y^{2}+2 y+\left (12 x^{2} y+6 x +3\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
1.299 |
|
|
\[ {}y^{2}+\left (x y^{2}+6 x y+\frac {1}{y}\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
2.101 |
|
|
\[ {}12 x^{3} y+24 x^{2} y^{2}+\left (9 x^{4}+32 x^{3} y+4 y\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
2.471 |
|
|
\[ {}\cos \left (x \right ) \cos \left (y\right )+\left (\sin \left (x \right ) \cos \left (y\right )-\sin \left (x \right ) \sin \left (y\right )+y\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
42.992 |
|
|
\[ {}a \cos \left (x \right ) y-y^{2} \sin \left (x \right )+\left (b \cos \left (x \right ) y-x \sin \left (x \right ) y\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[_linear] |
✓ |
✓ |
33.192 |
|
|
\[ {}x^{4} y^{3}+y+\left (x^{5} y^{2}-x \right ) y^{\prime } = 0 \] |
1 |
1 |
3 |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
3.156 |
|
|
\[ {}3 x y+2 y^{2}+y+\left (x^{2}+2 x y+x +2 y\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class D‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
2.622 |
|
|
\[ {}12 x y+6 y^{3}+\left (9 x^{2}+10 x y^{2}\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
3.186 |
|
|
\[ {}3 x^{2} y^{2}+2 y+2 x y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
1.291 |
|
|
\[ {}x^{2} \left (y^{\prime }+y^{2}\right )-7 x y+7 = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
✓ |
3.356 |
|
|
\[ {}y+y^{\prime } = {\mathrm e}^{t} t \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.158 |
|
|
\[ {}t^{2} y+y^{\prime } = 1 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.704 |
|
|
\[ {}\frac {t y}{t^{2}+1}+y^{\prime } = 1-\frac {t^{3} y}{t^{4}+1} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
2.548 |
|
|
\[ {}y^{\prime }+t y = t +1 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
2.361 |
|
|
\[ {}y+y^{\prime } = \frac {1}{t^{2}+1} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
4.212 |
|
|
\[ {}y^{\prime }-2 t y = 1 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.676 |
|
|
\[ {}t y+\left (t^{2}+1\right ) y^{\prime } = \left (t^{2}+1\right )^{\frac {5}{2}} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.741 |
|
|
\[ {}2 t y y^{\prime } = 3 y^{2}-t^{2} \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
2.518 |
|
|
\[ {}{\mathrm e}^{\frac {t}{y}} \left (-t +y\right ) y^{\prime }+y \left (1+{\mathrm e}^{\frac {t}{y}}\right ) = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
2.985 |
|
|
\[ {}\frac {y^{2}}{2}-2 \,{\mathrm e}^{t} y+\left (-{\mathrm e}^{t}+y\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_1st_order, _with_linear_symmetries], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
4.016 |
|
|
\[ {}3 t y+y^{2}+\left (t^{2}+t y\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
7.145 |
|
|
\[ {}x +y = x y^{\prime } \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.223 |
|
|
\[ {}x^{2}+y^{2} = x y y^{\prime } \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.809 |
|
|
\[ {}x y^{\prime }+y = 2 \sqrt {x y} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
18.583 |
|
|
\[ {}x^{2}+y^{2} = 2 x y y^{\prime } \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
2.511 |
|
|
\[ {}\left (\frac {x}{y}+\frac {y}{x}\right ) y^{\prime }+1 = 0 \] |
1 |
1 |
4 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
4.8 |
|
|
\[ {}2 x y-\left (x^{2}+y^{2}\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
4.753 |
|
|
\[ {}x y^{\prime }+\ln \left (x \right )-y = 0 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.441 |
|
|
\[ {}x y+\left (y+x^{2}\right ) y^{\prime } = 0 \] |
1 |
1 |
9 |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
3.876 |
|
|
\[ {}x y^{3}-1+x^{2} y^{2} y^{\prime } = 0 \] |
1 |
1 |
3 |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
2.648 |
|
|
\[ {}\left (x^{3} y^{3}-1\right ) y^{\prime }+x^{2} y^{4} = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
2.335 |
|
|
\[ {}y \left (y-x^{2}\right )+x^{3} y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
1.716 |
|
|
\[ {}y+x y^{2}+\left (x -x^{2} y\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
2.576 |
|
|
\[ {}2 x y+\left (y-x^{2}\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.267 |
|
|
\[ {}y = x \left (x^{2} y-1\right ) y^{\prime } \] |
1 |
1 |
2 |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
4.134 |
|
|
\[ {}{\mathrm e}^{x} y^{\prime } = 2 x y^{2}+{\mathrm e}^{x} y \] |
1 |
1 |
1 |
[_Bernoulli] |
✓ |
✓ |
1.677 |
|
|
\[ {}\left (2 x +3 x^{2} y\right ) y^{\prime }+y+2 x y^{2} = 0 \] |
1 |
1 |
3 |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
4.182 |
|
|
\[ {}2 x^{2} y y^{\prime }+{\mathrm e}^{x} x^{4}-2 x y^{2} = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class D‘], _Bernoulli] |
✓ |
✓ |
2.105 |
|
|
\[ {}y \left (1-x^{4} y^{2}\right )+x y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
1.967 |
|
|
\[ {}x^{2} y^{2}-y+\left (2 x^{3} y+x \right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
5.316 |
|
|
\[ {}\left (x^{2}+y^{2}-2 y\right ) y^{\prime } = 2 x \] |
1 |
1 |
0 |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
2.453 |
|
|
\[ {}2 y+x y^{\prime } = x^{2} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.292 |
|
|
\[ {}y^{\prime }-x y = {\mathrm e}^{\frac {x^{2}}{2}} \cos \left (x \right ) \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.634 |
|
|
\[ {}y^{\prime }+2 x y = 2 x \,{\mathrm e}^{-x^{2}} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.285 |
|
|
\[ {}y^{\prime } = y+3 x^{2} {\mathrm e}^{x} \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.171 |
|
|
\[ {}x^{\prime }+x = {\mathrm e}^{-y} \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.164 |
|
|
\[ {}y x^{\prime }+\left (1+y \right ) x = {\mathrm e}^{y} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.446 |
|
|
\[ {}y+\left (2 x -3 y\right ) y^{\prime } = 0 \] |
1 |
1 |
3 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
4.38 |
|
|
\[ {}x y^{\prime }-2 x^{4}-2 y = 0 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.245 |
|
|
\[ {}1 = \left (x +{\mathrm e}^{y}\right ) y^{\prime } \] |
1 |
1 |
1 |
[[_1st_order, _with_exponential_symmetries]] |
✓ |
✓ |
1.615 |
|
|
\[ {}y^{2} x^{\prime }+\left (y^{2}+2 y \right ) x = 1 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.394 |
|
|
\[ {}x y^{\prime } = 5 y+x +1 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
2.558 |
|
|
\[ {}x^{2} y^{\prime }+y-2 x y-2 x^{2} = 0 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.525 |
|
|
\[ {}\cos \left (y\right )^{2}+\left (x -\tan \left (y\right )\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
8.594 |
|
|
\[ {}2 y = \left (y^{4}+x \right ) y^{\prime } \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
3.933 |
|
|
\[ {}\cos \left (\theta \right ) r^{\prime } = 2+2 r \sin \left (\theta \right ) \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
2.42 |
|
|
\[ {}\sin \left (\theta \right ) r^{\prime }+1+r \tan \left (\theta \right ) = \cos \left (\theta \right ) \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
9.127 |
|
|
\[ {}y x^{\prime } = 2 y \,{\mathrm e}^{3 y}+x \left (3 y +2\right ) \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.64 |
|
|
\[ {}y^{\prime }+\cot \left (x \right ) y-\sec \left (x \right ) = 0 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.962 |
|
|
\[ {}y+y^{3}+4 \left (x y^{2}-1\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
3.215 |
|
|
\[ {}2 y-x y-3+x y^{\prime } = 0 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
2.361 |
|
|
\[ {}y+2 \left (x -2 y^{2}\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
5.5 |
|
|
\[ {}\left (x^{2}-1\right ) y^{\prime }+\left (x^{2}-1\right )^{2}+4 y = 0 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
2.448 |
|
|
\[ {}3 y^{2} y^{\prime }-x y^{3} = {\mathrm e}^{\frac {x^{2}}{2}} \cos \left (x \right ) \] |
1 |
1 |
3 |
[_Bernoulli] |
✓ |
✓ |
3.883 |
|
|
\[ {}y^{3} y^{\prime }+y^{4} x = x \,{\mathrm e}^{-x^{2}} \] |
1 |
1 |
4 |
[_Bernoulli] |
✓ |
✓ |
2.7 |
|
|
\[ {}\cosh \left (y\right ) y^{\prime }+\sinh \left (y\right )-{\mathrm e}^{-x} = 0 \] |
1 |
1 |
1 |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
3.327 |
|
|
\[ {}\sin \left (\theta \right ) \theta ^{\prime }+\cos \left (\theta \right )-t \,{\mathrm e}^{-t} = 0 \] |
1 |
1 |
1 |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
3.487 |
|
|
\[ {}x y y^{\prime } = x^{2}-y^{2} \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
2.55 |
|
|
\[ {}t x^{\prime }+x \left (1-x^{2} t^{4}\right ) = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
2.024 |
|
|
\[ {}\csc \left (y\right ) \cot \left (y\right ) y^{\prime } = \csc \left (y\right )+{\mathrm e}^{x} \] |
1 |
1 |
1 |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
3.766 |
|
|
\[ {}x y^{\prime }+y = y^{2} x^{2} \cos \left (x \right ) \] |
1 |
1 |
1 |
[_Bernoulli] |
✓ |
✓ |
3.555 |
|
|
\[ {}3 y^{\prime }+\frac {2 y}{1+x} = \frac {x}{y^{2}} \] |
1 |
1 |
3 |
[_rational, _Bernoulli] |
✓ |
✓ |
3.15 |
|
|
\[ {}x \ln \left (x \right ) y^{\prime }+y-x = 0 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.645 |
|
|
\[ {}2 \,{\mathrm e}^{x}-t^{2}+t \,{\mathrm e}^{x} x^{\prime } = 0 \] |
1 |
1 |
1 |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
3.315 |
|
|
\[ {}x^{2} y-\left (x^{3}+y^{3}\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
2.58 |
|
|
\[ {}2 x y+y^{4}+\left (x y^{3}-2 x^{2}\right ) y^{\prime } = 0 \] |
1 |
1 |
3 |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
4.268 |
|
|
\[ {}y+\left (3 x -2 y\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
6.609 |
|
|
\[ {}2 x^{3}-y^{3}-3 x +3 x y^{2} y^{\prime } = 0 \] |
1 |
1 |
3 |
[_rational, _Bernoulli] |
✓ |
✓ |
2.457 |
|
|
\[ {}y^{\prime }+x +\cot \left (x \right ) y = 0 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.445 |
|
|
\[ {}2 x y^{\prime }-y+\frac {x^{2}}{y^{2}} = 0 \] |
1 |
1 |
3 |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
2.127 |
|
|
\[ {}\sec \left (y\right )^{2} y^{\prime } = \tan \left (y\right )+2 x \,{\mathrm e}^{x} \] |
1 |
1 |
0 |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
4.887 |
|
|
\[ {}y \cos \left (\frac {x}{y}\right )-\left (y+x \cos \left (\frac {x}{y}\right )\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
4.761 |
|
|
\[ {}x y^{\prime } = x^{4}+4 y \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.769 |
|
|
\[ {}x y^{\prime }+y = x^{3} y^{6} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
2.024 |
|
|
\[ {}x^{2}+y^{2} = 2 x y y^{\prime } \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
3.538 |
|
|
\[ {}3 x y+\left (3 x^{2}+y^{2}\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
6.322 |
|
|
\[ {}2 y+y^{\prime } = 3 \,{\mathrm e}^{2 x} \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.713 |
|
|
\[ {}2 x y-2 y+1+x \left (-1+x \right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
2.252 |
|
|
\[ {}y^{\prime }+P \left (x \right ) y = Q \left (x \right ) \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.581 |
|
|
\[ {}y^{\prime } = 2 y+{\mathrm e}^{-3 t} \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.663 |
|
|
\[ {}y^{\prime } = 2 y+{\mathrm e}^{2 t} \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.45 |
|
|
\[ {}y^{\prime } = t -y \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.454 |
|
|
\[ {}2 y+t y^{\prime } = \sin \left (t \right ) \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.585 |
|
|
\[ {}y^{\prime } = y \tan \left (t \right )+\sec \left (t \right ) \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.578 |
|
|
\[ {}y^{\prime } = \frac {2 t y}{t^{2}+1}+t +1 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.637 |
|
|
\[ {}y^{\prime } = y \tan \left (t \right )+\sec \left (t \right )^{3} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.651 |
|
|
\[ {}t y^{\prime } = y+t^{3} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.724 |
|
|
\[ {}y^{\prime } = -y \tan \left (t \right )+\sec \left (t \right ) \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.819 |
|
|
\[ {}y^{\prime }+4 \tan \left (2 t \right ) y = \tan \left (2 t \right ) \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.954 |
|
|
\[ {}t \ln \left (t \right ) y^{\prime } = \ln \left (t \right ) t -y \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.948 |
|
|
\[ {}y^{\prime } = \frac {2 y}{-t^{2}+1}+3 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.002 |
|
|
\[ {}y^{\prime } = -\cot \left (t \right ) y+6 \cos \left (t \right )^{2} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.224 |
|
|
\[ {}2 x y^{\prime }+3 x +y = 0 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.684 |
|
|
\[ {}\left (\cos \left (x \right )^{2}+y \sin \left (2 x \right )\right ) y^{\prime }+y^{2} = 0 \] |
1 |
1 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
3.886 |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime }+4 x y = \left (-x^{2}+1\right )^{\frac {3}{2}} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.754 |
|
|
\[ {}y^{\prime }-\cot \left (x \right ) y+\frac {1}{\sin \left (x \right )} = 0 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.731 |
|
|
\[ {}\left (y^{3}+x \right ) y^{\prime } = y \] |
1 |
1 |
3 |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
0.571 |
|
|
\[ {}y^{\prime } = -\frac {2 x^{2}+y^{2}+x}{x y} \] |
1 |
1 |
2 |
[_rational, _Bernoulli] |
✓ |
✓ |
0.653 |
|
|
\[ {}y^{\prime } = \frac {1}{x +2 y+1} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
✓ |
0.549 |
|
|
\[ {}y^{\prime }+\frac {x y}{a^{2}+x^{2}} = x \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.648 |
|
|
\[ {}y^{\prime }-\frac {y}{x} = 1 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.706 |
|
|
\[ {}y^{\prime }-y \tan \left (x \right ) = 1 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.865 |
|
|
\[ {}\sin \left (x \right ) y^{\prime }+2 y \cos \left (x \right ) = 1 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.245 |
|
|
\[ {}x y^{\prime }+y-\frac {y^{2}}{x^{\frac {3}{2}}} = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
1.586 |
|
|
\[ {}\left (2 \sin \left (y\right )-x \right ) y^{\prime } = \tan \left (y\right ) \] |
1 |
1 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
6.582 |
|
|
\[ {}\left (2 \sin \left (y\right )-x \right ) y^{\prime } = \tan \left (y\right ) \] |
1 |
1 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
6.447 |
|
|
\[ {}y^{\prime } = \frac {x^{2} y-32}{-x^{2}+16}+32 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.852 |
|
|
\[ {}y^{\prime }-y = {\mathrm e}^{2 x} \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.464 |
|
|
\[ {}x^{2} y^{\prime }-4 x y = x^{7} \sin \left (x \right ) \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.71 |
|
|
\[ {}y^{\prime }+2 x y = 2 x^{3} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.51 |
|
|
\[ {}y^{\prime }+\frac {2 x y}{x^{2}+1} = \frac {4}{\left (x^{2}+1\right )^{2}} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.65 |
|
|
\[ {}2 \cos \left (x \right )^{2} y^{\prime }+y \sin \left (2 x \right ) = 4 \cos \left (x \right )^{4} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.946 |
|
|
\[ {}y^{\prime }+\frac {y}{x \ln \left (x \right )} = 9 x^{2} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.669 |
|
|
\[ {}y^{\prime }-y \tan \left (x \right ) = 8 \sin \left (x \right )^{3} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.744 |
|
|
\[ {}t x^{\prime }+2 x = 4 \,{\mathrm e}^{t} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.585 |
|
|
\[ {}y^{\prime } = \sin \left (x \right ) \left (y \sec \left (x \right )-2\right ) \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.757 |
|
|
\[ {}1-y \sin \left (x \right )-y^{\prime } \cos \left (x \right ) = 0 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.935 |
|
|
\[ {}y^{\prime }-\frac {y}{x} = 2 \ln \left (x \right ) x^{2} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.595 |
|
|
\[ {}y^{\prime }+\alpha y = {\mathrm e}^{\beta x} \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.541 |
|
|
\[ {}\left (3 x -y\right ) y^{\prime } = 3 y \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
0.94 |
|
|
\[ {}\sin \left (\frac {y}{x}\right ) \left (-y+x y^{\prime }\right ) = x \cos \left (\frac {y}{x}\right ) \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
1.482 |
|
|
\[ {}y^{\prime } = \frac {x^{2} \left (1-y^{2}\right )+y \,{\mathrm e}^{\frac {y}{x}}}{x \left ({\mathrm e}^{\frac {y}{x}}+2 x^{2} y\right )} \] |
1 |
1 |
1 |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
37.297 |
|
|
\[ {}y^{\prime } = \sin \left (x \right ) \left (y \sec \left (x \right )-2\right ) \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.619 |
|
|
\[ {}\sin \left (x \right ) y^{\prime }-y \cos \left (x \right ) = \sin \left (2 x \right ) \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.749 |
|
|
\[ {}x^{\prime }+\frac {2 x}{4-t} = 5 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.122 |
|
|
\[ {}y-{\mathrm e}^{x}+y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.675 |
|
|
\[ {}y+y^{\prime } = {\mathrm e}^{-2 x} \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.488 |
|
|
\[ {}\cot \left (x \right ) y+y^{\prime } = 2 \cos \left (x \right ) \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.724 |
|
|
\[ {}-y+x y^{\prime } = \ln \left (x \right ) x^{2} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.58 |
|
|
\[ {}y^{\prime }-\frac {y}{x} = \frac {4 x^{2} \cos \left (x \right )}{y} \] |
1 |
1 |
2 |
[[_homogeneous, ‘class D‘], _Bernoulli] |
✓ |
✓ |
2.286 |
|
|
\[ {}y^{\prime }+\frac {2 y}{x} = 6 x^{4} y^{2} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
0.689 |
|
|
\[ {}y^{\prime }-\frac {y}{\left (\pi -1\right ) x} = \frac {3 x y^{\pi }}{1-\pi } \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
0.887 |
|
|
\[ {}2 y^{\prime }+\cot \left (x \right ) y = \frac {8 \cos \left (x \right )^{3}}{y} \] |
1 |
1 |
2 |
[_Bernoulli] |
✓ |
✓ |
14.635 |
|
|
\[ {}y^{\prime } = \frac {y \left (\ln \left (x y\right )-1\right )}{x} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
1.297 |
|
|
\[ {}y^{\prime }+\frac {2 y}{x}-y^{2} = -\frac {2}{x^{2}} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
✓ |
1.568 |
|
|
\[ {}y^{\prime }+\frac {7 y}{x}-3 y^{2} = \frac {3}{x^{2}} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
✓ |
0.924 |
|
|
\[ {}\frac {y^{\prime }}{y}+p \left (x \right ) \ln \left (y\right ) = q \left (x \right ) \] |
1 |
1 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
1.563 |
|
|
\[ {}\frac {y^{\prime }}{y}-\frac {2 \ln \left (y\right )}{x} = \frac {1-2 \ln \left (x \right )}{x} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
1.614 |
|
|
\[ {}5 x y+4 y^{2}+1+\left (2 x y+x^{2}\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
1.361 |
|
|
\[ {}2 x \tan \left (y\right )+\left (x -x^{2} \tan \left (y\right )\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_1st_order, _with_exponential_symmetries]] |
✓ |
✓ |
1.694 |
|
|
\[ {}4 x y^{2}+6 y+\left (5 x^{2} y+8 x \right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
2.534 |
|
|
\[ {}y^{\prime } = \frac {-2 x +y}{x} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.744 |
|
|
\[ {}x^{3}+y^{3}-x y^{2} y^{\prime } = 0 \] |
1 |
1 |
3 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.392 |
|
|
\[ {}y+y^{\prime } = x^{2}+2 \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.616 |
|
|
\[ {}y^{\prime }-y \tan \left (x \right ) = x \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.106 |
|
|
\[ {}x y^{\prime } = x +y \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.824 |
|
|
\[ {}y^{\prime }-3 y = {\mathrm e}^{3 x}+{\mathrm e}^{-3 x} \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.085 |
|
|
\[ {}2 y+x y^{\prime } = \left (3 x +2\right ) {\mathrm e}^{3 x} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.03 |
|
|
\[ {}y^{\prime } \cos \left (x \right )+y \sin \left (x \right ) = 1 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.556 |
|
|
\[ {}y^{\prime }-y = x^{3} \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.611 |
|
|
\[ {}\cot \left (x \right ) y+y^{\prime } = x \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.836 |
|
|
\[ {}\cot \left (x \right ) y+y^{\prime } = \tan \left (x \right ) \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.89 |
|
|
\[ {}y^{\prime }+y \tan \left (x \right ) = \cot \left (x \right ) \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.938 |
|
|
\[ {}y^{\prime }+y \ln \left (x \right ) = x^{-x} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.793 |
|
|
\[ {}-y+x y^{\prime } = x^{3} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.661 |
|
|
\[ {}x y^{\prime }+n y = x^{n} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.861 |
|
|
\[ {}x y^{\prime }-n y = x^{n} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.794 |
|
|
\[ {}\left (x^{3}+x \right ) y^{\prime }+y = x \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.812 |
|
|
\[ {}\cot \left (x \right ) y^{\prime }+y = x \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.232 |
|
|
\[ {}\cot \left (x \right ) y^{\prime }+y = \tan \left (x \right ) \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.333 |
|
|
\[ {}\tan \left (x \right ) y^{\prime }+y = \cot \left (x \right ) \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.52 |
|
|
\[ {}\tan \left (x \right ) y^{\prime } = y-\cos \left (x \right ) \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.854 |
|
|
\[ {}y^{\prime }+y \cos \left (x \right ) = \sin \left (2 x \right ) \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.105 |
|
|
\[ {}y^{\prime } \cos \left (x \right )+y = \sin \left (2 x \right ) \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
2.73 |
|
|
\[ {}y^{\prime }+y \sin \left (x \right ) = \sin \left (2 x \right ) \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.109 |
|
|
\[ {}\sin \left (x \right ) y^{\prime }+y = \sin \left (2 x \right ) \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
2.414 |
|
|
\[ {}\sqrt {x^{2}+1}\, y^{\prime }+y = 2 x \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.059 |
|
|
\[ {}\sqrt {x^{2}+1}\, y^{\prime }-y = 2 \sqrt {x^{2}+1} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.352 |
|
|
\[ {}\sqrt {\left (x +a \right ) \left (x +b \right )}\, \left (2 y^{\prime }-3\right )+y = 0 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
3.551 |
|
|
\[ {}\sqrt {\left (x +a \right ) \left (x +b \right )}\, y^{\prime }+y = \sqrt {x +a}-\sqrt {x +b} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
2.407 |
|
|
\[ {}x y y^{\prime } = 2 x^{2}-y^{2} \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.446 |
|
|
\[ {}x^{2}-y^{2}+x y y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.035 |
|
|
\[ {}x^{2} y^{\prime }-2 x y-2 y^{2} = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
0.959 |
|
|
\[ {}x \sin \left (\frac {y}{x}\right ) y^{\prime } = y \sin \left (\frac {y}{x}\right )+x \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
1.435 |
|
|
\[ {}\sin \left (x \right ) \tan \left (y\right )+1+\cos \left (x \right ) \sec \left (y\right )^{2} y^{\prime } = 0 \] |
1 |
1 |
0 |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
33.48 |
|
|
\[ {}\left (3 x^{2}-y^{2}\right ) y^{\prime }-2 x y = 0 \] |
1 |
1 |
3 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
2.34 |
|
|
\[ {}x y-1+\left (x^{2}-x y\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
1.131 |
|
|
\[ {}\left (x +3 x^{3} y^{4}\right ) y^{\prime }+y = 0 \] |
1 |
1 |
4 |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
2.339 |
|
|
\[ {}\left (x -1-y^{2}\right ) y^{\prime }-y = 0 \] |
1 |
1 |
2 |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
✓ |
0.852 |
|
|
\[ {}-3 y+x y^{\prime } = x^{4} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.685 |
|
|
\[ {}y+y^{\prime } = \frac {1}{1+{\mathrm e}^{2 x}} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.835 |
|
|
\[ {}y+y^{\prime } = 2 x \,{\mathrm e}^{-x}+x^{2} \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.165 |
|
|
\[ {}\cot \left (x \right ) y+y^{\prime } = 2 x \csc \left (x \right ) \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.387 |
|
|
\[ {}2 y-x^{3} = x y^{\prime } \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.095 |
|
|
\[ {}\left (1-x y\right ) y^{\prime } = y^{2} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
1.646 |
|
|
\[ {}y+x^{2} = x y^{\prime } \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.75 |
|
|
\[ {}y^{\prime }+2 x y = {\mathrm e}^{-x^{2}} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.701 |
|
|
\[ {}y^{2}-3 x y-2 x^{2} = \left (x^{2}-x y\right ) y^{\prime } \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
2.286 |
|
|
\[ {}{\mathrm e}^{x} \left (1+x \right ) = \left (x \,{\mathrm e}^{x}-y \,{\mathrm e}^{y}\right ) y^{\prime } \] |
1 |
1 |
1 |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
1.777 |
|
|
\[ {}x y+\left (x^{2}+y^{2}\right ) y^{\prime } = 0 \] |
1 |
1 |
4 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
2.681 |
|
|
\[ {}y+2 = \left (-4+2 x +y\right ) y^{\prime } \] |
1 |
1 |
2 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
3.103 |
|
|
\[ {}x^{2}-\sin \left (y\right )^{2}+x \sin \left (2 y\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
2.751 |
|
|
\[ {}y \left (2 x -y+2\right )+2 \left (x -y\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class D‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.152 |
|
|
\[ {}4 x y+3 y^{2}-x +x \left (2 y+x \right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
1.569 |
|
|
\[ {}y+x \left (y^{2}+\ln \left (x \right )\right ) y^{\prime } = 0 \] |
1 |
1 |
3 |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
3.78 |
|
|
\[ {}x^{2}+2 x +y+\left (3 x^{2} y-x \right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
1.695 |
|
|
\[ {}y^{2}+\left (x y+y^{2}-1\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
✓ |
1.128 |
|
|
\[ {}3 x^{2}+3 y^{2}+x \left (x^{2}+3 y^{2}+6 y\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_rational] |
✓ |
✓ |
1.726 |
|
|
\[ {}2 y \left (x +y+2\right )+\left (y^{2}-x^{2}-4 x -1\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
✓ |
2.742 |
|
|
\[ {}2+y^{2}+2 x +2 y y^{\prime } = 0 \] |
1 |
1 |
2 |
[_rational, _Bernoulli] |
✓ |
✓ |
1.158 |
|
|
\[ {}2 x y^{2}-y+\left (y^{2}+x +y\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_rational] |
✓ |
✓ |
1.935 |
|
|
\[ {}y \left (x +y\right )+\left (x +2 y-1\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.661 |
|
|
\[ {}2 x \left (x^{2}-\sin \left (y\right )+1\right )+\left (x^{2}+1\right ) \cos \left (y\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
3.445 |
|
|
\[ {}y \sqrt {1+y^{2}}+\left (x \sqrt {1+y^{2}}-y\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
2.106 |
|
|
\[ {}y^{2}-\left (x y+x^{3}\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
2.819 |
|
|
\[ {}2 x^{2} y^{2}+y+\left (x^{3} y-x \right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
1.677 |
|
|
\[ {}y^{2}+\left (x y+\tan \left (x y\right )\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
32.595 |
|
|
\[ {}1-\left (1+2 x \tan \left (y\right )\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
2.132 |
|
|
\[ {}\left (y^{3}+\frac {x}{y}\right ) y^{\prime } = 1 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
1.215 |
|
|
\[ {}1+\left (x -y^{2}\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_1st_order, _with_exponential_symmetries]] |
✓ |
✓ |
0.944 |
|
|
\[ {}y^{2}+\left (x y+y^{2}-1\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
✓ |
1.112 |
|
|
\[ {}y = \left ({\mathrm e}^{y}+2 x y-2 x \right ) y^{\prime } \] |
1 |
1 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
1.802 |
|
|
\[ {}y+\left (y^{2} {\mathrm e}^{y}-x \right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
1.271 |
|
|
\[ {}y^{\prime } = \frac {4 x^{3} y^{2}}{x^{4} y+2} \] |
1 |
1 |
2 |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
2.477 |
|
|
\[ {}x y^{2} \left (x y^{\prime }+y\right ) = 1 \] |
1 |
1 |
3 |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
2.256 |
|
|
\[ {}2 \sqrt {x y}-y-x y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
13.593 |
|
|
\[ {}y^{\prime } = x +\sin \left (x \right )+y \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.786 |
|
|
\[ {}y^{\prime } = x^{2}+3 \cosh \left (x \right )+2 y \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
2.769 |
|
|
\[ {}y^{\prime } = a +b x +c y \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.579 |
|
|
\[ {}y^{\prime } = a \cos \left (b x +c \right )+k y \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
2.238 |
|
|
\[ {}y^{\prime } = a \sin \left (b x +c \right )+k y \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
2.006 |
|
|
\[ {}y^{\prime } = a +b \,{\mathrm e}^{k x}+c y \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.674 |
|
|
\[ {}y^{\prime } = x \left (x^{2}-y\right ) \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.328 |
|
|
\[ {}y^{\prime } = x \left ({\mathrm e}^{-x^{2}}+a y\right ) \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.71 |
|
|
\[ {}y^{\prime } = x^{2} \left (a \,x^{3}+b y\right ) \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.734 |
|
|
\[ {}y^{\prime } = \sin \left (x \right ) \cos \left (x \right )+y \cos \left (x \right ) \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
2.138 |
|
|
\[ {}y^{\prime } = {\mathrm e}^{\sin \left (x \right )}+y \cos \left (x \right ) \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.684 |
|
|
\[ {}y^{\prime } = 1-\cot \left (x \right ) y \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.454 |
|
|
\[ {}y^{\prime } = x \csc \left (x \right )-\cot \left (x \right ) y \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.486 |
|
|
\[ {}y^{\prime } = \sec \left (x \right )-\cot \left (x \right ) y \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.72 |
|
|
\[ {}y^{\prime } = {\mathrm e}^{x} \sin \left (x \right )+\cot \left (x \right ) y \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
2.099 |
|
|
\[ {}y^{\prime }+\csc \left (x \right )+2 \cot \left (x \right ) y = 0 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.667 |
|
|
\[ {}y^{\prime } = 4 \csc \left (x \right ) x \sec \left (x \right )^{2}-2 y \cot \left (2 x \right ) \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
4.425 |
|
|
\[ {}y^{\prime } = 2 \cot \left (x \right )^{2} \cos \left (2 x \right )-2 y \csc \left (2 x \right ) \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.731 |
|
|
\[ {}y^{\prime } = 4 \csc \left (x \right ) x \left (\sin \left (x \right )^{3}+y\right ) \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
8.142 |
|
|
\[ {}y^{\prime } = 4 \csc \left (x \right ) x \left (1-\tan \left (x \right )^{2}+y\right ) \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
76.021 |
|
|
\[ {}y^{\prime }+\tan \left (x \right ) = \left (1-y\right ) \sec \left (x \right ) \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.483 |
|
|
\[ {}y^{\prime } = \cos \left (x \right )+y \tan \left (x \right ) \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.931 |
|
|
\[ {}y^{\prime } = \cos \left (x \right )-y \tan \left (x \right ) \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.838 |
|
|
\[ {}y^{\prime } = \sec \left (x \right )-y \tan \left (x \right ) \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.866 |
|
|
\[ {}y^{\prime } = \sin \left (2 x \right )+y \tan \left (x \right ) \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.98 |
|
|
\[ {}y^{\prime } = \sin \left (2 x \right )-y \tan \left (x \right ) \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.915 |
|
|
\[ {}y^{\prime } = \sin \left (x \right )+2 y \tan \left (x \right ) \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.968 |
|
|
\[ {}y^{\prime } = 2+2 \sec \left (2 x \right )+2 y \tan \left (2 x \right ) \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.793 |
|
|
|
||||||||
|
\[ {}y^{\prime } = \csc \left (x \right )+3 y \tan \left (x \right ) \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.534 |
|
|
\[ {}y^{\prime } = 6 \,{\mathrm e}^{2 x}-y \tanh \left (x \right ) \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.088 |
|
|
\[ {}y^{\prime } = f \left (x \right ) f^{\prime }\left (x \right )+f^{\prime }\left (x \right ) y \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.803 |
|
|
\[ {}y^{\prime } = f \left (x \right )+g \left (x \right ) y \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.711 |
|
|
\[ {}y^{\prime } = \sin \left (x \right ) \left (2 \sec \left (x \right )^{2}-y\right ) \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.546 |
|
|
\[ {}y^{\prime } = y \sec \left (x \right )+\left (\sin \left (x \right )-1\right )^{2} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
2.793 |
|
|
\[ {}y^{\prime } = \left (a +b x y\right ) y^{2} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _Abel] |
✓ |
✓ |
8.756 |
|
|
\[ {}y^{\prime } = \sec \left (x \right )^{2}+y \sec \left (x \right ) \operatorname {Csx} \left (x \right ) \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.252 |
|
|
\[ {}x y^{\prime }+x^{2}-y = 0 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.603 |
|
|
\[ {}x y^{\prime } = 1+x^{3}+y \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.631 |
|
|
\[ {}x y^{\prime } = x^{m}+y \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.914 |
|
|
\[ {}x y^{\prime } = x^{2} \sin \left (x \right )+y \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.682 |
|
|
\[ {}x y^{\prime } = \sin \left (x \right )-2 y \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.685 |
|
|
\[ {}x y^{\prime } = 1+x +a y \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.866 |
|
|
\[ {}x y^{\prime } = x a +b y \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.046 |
|
|
\[ {}x y^{\prime } = x^{2} a +b y \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.842 |
|
|
\[ {}x y^{\prime } = a +b \,x^{n}+c y \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.005 |
|
|
\[ {}x y^{\prime }+2+\left (-x +3\right ) y = 0 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.68 |
|
|
\[ {}x y^{\prime }+x +\left (x a +2\right ) y = 0 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.884 |
|
|
\[ {}x y^{\prime } = x^{3}+\left (-2 x^{2}+1\right ) y \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.874 |
|
|
\[ {}x y^{\prime } = x a -\left (-b \,x^{2}+1\right ) y \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.952 |
|
|
\[ {}x y^{\prime }+x +\left (-x^{2} a +2\right ) y = 0 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.012 |
|
|
\[ {}x y^{\prime }+\left (1-x y\right ) y = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
0.727 |
|
|
\[ {}x y^{\prime } = \left (1-x y\right ) y \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
0.707 |
|
|
\[ {}x y^{\prime } = \left (1+x y\right ) y \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
0.716 |
|
|
\[ {}x y^{\prime } = y \left (1+2 x y\right ) \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
0.711 |
|
|
\[ {}x y^{\prime }+\left (1-a y \ln \left (x \right )\right ) y = 0 \] |
1 |
1 |
1 |
[_Bernoulli] |
✓ |
✓ |
0.99 |
|
|
\[ {}x y^{\prime }+\left (1-x y^{2}\right ) y = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
0.803 |
|
|
\[ {}x y^{\prime }+y = a \left (x^{2}+1\right ) y^{3} \] |
1 |
1 |
2 |
[_rational, _Bernoulli] |
✓ |
✓ |
0.915 |
|
|
\[ {}x y^{\prime }+\left (\sin \left (y\right )-3 x^{2} \cos \left (y\right )\right ) \cos \left (y\right ) = 0 \] |
1 |
1 |
1 |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
1.823 |
|
|
\[ {}x y^{\prime }+y+2 x \sec \left (x y\right ) = 0 \] |
1 |
1 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
3.558 |
|
|
\[ {}x y^{\prime } = \left (1+\ln \left (x \right )-\ln \left (y\right )\right ) y \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
1.326 |
|
|
\[ {}\left (1+x \right ) y^{\prime } = x^{3} \left (3 x +4\right )+y \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.649 |
|
|
\[ {}\left (1+x \right ) y^{\prime } = \left (1+x \right )^{4}+2 y \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.658 |
|
|
\[ {}\left (1+x \right ) y^{\prime } = {\mathrm e}^{x} \left (1+x \right )^{n +1}+n y \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.98 |
|
|
\[ {}\left (x +a \right ) y^{\prime } = b x +y \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.889 |
|
|
\[ {}\left (x +a \right ) y^{\prime } = 2 \left (x +a \right )^{5}+3 y \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.908 |
|
|
\[ {}\left (x +a \right ) y^{\prime } = b x +c y \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.96 |
|
|
\[ {}2 x y^{\prime } = 2 x^{3}-y \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.668 |
|
|
\[ {}\left (1-2 x \right ) y^{\prime } = 16+32 x -6 y \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.954 |
|
|
\[ {}2 \left (1-x \right ) y^{\prime } = 4 x \sqrt {1-x}+y \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.608 |
|
|
\[ {}3 x y^{\prime } = \left (1+3 x y^{3} \ln \left (x \right )\right ) y \] |
1 |
1 |
3 |
[_Bernoulli] |
✓ |
✓ |
1.441 |
|
|
\[ {}x^{2} y^{\prime } = a +b x +c \,x^{2}+x y \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.619 |
|
|
\[ {}x^{2} y^{\prime } = a +b x +c \,x^{2}-x y \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.617 |
|
|
\[ {}x^{2} y^{\prime }+\left (1-2 x \right ) y = x^{2} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.543 |
|
|
\[ {}x^{2} y^{\prime } = a +b x y \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.555 |
|
|
\[ {}x^{2} y^{\prime }+x \left (2+x \right ) y = x \left (1-{\mathrm e}^{-2 x}\right )-2 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.626 |
|
|
\[ {}x^{2} y^{\prime }+2 x \left (1-x \right ) y = {\mathrm e}^{x} \left (2 \,{\mathrm e}^{x}-1\right ) \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.617 |
|
|
\[ {}x^{2} y^{\prime }+2+x y \left (4+x y\right ) = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
✓ |
1.003 |
|
|
\[ {}x^{2} y^{\prime } = a +b \,x^{2} y^{2} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational, [_Riccati, _special]] |
✓ |
✓ |
1.735 |
|
|
\[ {}x^{2} y^{\prime } = a +b x y+c \,x^{2} y^{2} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
✓ |
2.024 |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime } = 1-x^{2}+y \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.68 |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime }+1 = x y \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.638 |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime } = 5-x y \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.663 |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime }+a +x y = 0 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.552 |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime }+a -x y = 0 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.687 |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime }+a -x y = 0 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.573 |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime }-x^{2}+x y = 0 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.615 |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime }+x^{2}+x y = 0 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.617 |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime } = \left (x^{2}+1\right ) x -x y \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.511 |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime } = x \left (3 x^{2}-y\right ) \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.514 |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime } = 2 x \left (x^{2}+1\right )^{2}+2 x y \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.504 |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime } = a +4 x y \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.566 |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime } = 1+x^{2}-y \,\operatorname {arccot}\left (x \right ) \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.236 |
|
|
\[ {}\left (a^{2}+x^{2}\right ) y^{\prime } = b +x y \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.928 |
|
|
\[ {}x \left (1-x \right ) y^{\prime } = a +\left (1+x \right ) y \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.7 |
|
|
\[ {}x \left (1-x \right ) y^{\prime } = 2+2 x y \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.61 |
|
|
\[ {}x \left (1-x \right ) y^{\prime } = 2 x y-2 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.554 |
|
|
\[ {}x \left (1-x \right ) y^{\prime }+\left (2 x +1\right ) y = a \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.641 |
|
|
\[ {}x \left (1-x \right ) y^{\prime } = a +2 \left (2-x \right ) y \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.671 |
|
|
\[ {}x \left (1-x \right ) y^{\prime }+2-3 x y+y = 0 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.667 |
|
|
\[ {}x \left (1+x \right ) y^{\prime } = \left (1+x \right ) \left (x^{2}-1\right )+\left (x^{2}+x -1\right ) y \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.694 |
|
|
\[ {}\left (-2+x \right ) \left (x -3\right ) y^{\prime }+x^{2}-8 y+3 x y = 0 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.669 |
|
|
\[ {}\left (x -a \right ) \left (x -b \right ) y^{\prime } = \left (x -a \right ) \left (x -b \right )+\left (2 x -a -b \right ) y \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.894 |
|
|
\[ {}2 x^{2} y^{\prime }+x \cot \left (x \right )-1+2 x^{2} y \cot \left (x \right ) = 0 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.017 |
|
|
\[ {}2 x^{2} y^{\prime }+1+2 x y-x^{2} y^{2} = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
✓ |
0.979 |
|
|
\[ {}2 \left (-x^{2}+1\right ) y^{\prime } = \sqrt {-x^{2}+1}+\left (1+x \right ) y \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.693 |
|
|
\[ {}x \left (1-2 x \right ) y^{\prime } = 4 x -\left (1+4 x \right ) y+y^{2} \] |
1 |
1 |
1 |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
✓ |
1.909 |
|
|
\[ {}2 x \left (1-x \right ) y^{\prime }+x +\left (1-2 x \right ) y = 0 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.797 |
|
|
\[ {}2 \left (x^{2}+x +1\right ) y^{\prime } = 1+8 x^{2}-\left (2 x +1\right ) y \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.979 |
|
|
\[ {}4 \left (x^{2}+1\right ) y^{\prime }-4 x y-x^{2} = 0 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.651 |
|
|
\[ {}x^{3} y^{\prime } = a +b \,x^{2} y \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.656 |
|
|
\[ {}x^{3} y^{\prime } = 3-x^{2}+x^{2} y \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.605 |
|
|
\[ {}x^{3} y^{\prime } = y \left (y+x^{2}\right ) \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
0.691 |
|
|
\[ {}x \left (x^{2}+1\right ) y^{\prime } = x^{2} a +y \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.743 |
|
|
\[ {}x \left (-x^{2}+1\right ) y^{\prime } = x^{2} a +y \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.806 |
|
|
\[ {}x \left (x^{2}+1\right ) y^{\prime } = a \,x^{3}+y \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.788 |
|
|
\[ {}x \left (x^{2}+1\right ) y^{\prime } = a -x^{2} y \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.709 |
|
|
\[ {}x \left (-x^{2}+1\right ) y^{\prime } = a \,x^{3}+\left (-2 x^{2}+1\right ) y \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.964 |
|
|
\[ {}x \left (-x^{2}+1\right ) y^{\prime } = x^{3} \left (-x^{2}+1\right )+\left (-2 x^{2}+1\right ) y \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.645 |
|
|
\[ {}x \left (x^{2}+1\right ) y^{\prime } = 2-4 x^{2} y \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.67 |
|
|
\[ {}x \left (x^{2}+1\right ) y^{\prime } = x -\left (5 x^{2}+3\right ) y \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.613 |
|
|
\[ {}2 x^{3} y^{\prime } = \left (3 x^{2}+a y^{2}\right ) y \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
0.921 |
|
|
\[ {}x^{5} y^{\prime } = 1-3 x^{4} y \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.605 |
|
|
\[ {}x^{n} y^{\prime } = a +b \,x^{n -1} y \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.692 |
|
|
\[ {}\sqrt {x^{2}+1}\, y^{\prime } = 2 x -y \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.746 |
|
|
\[ {}y^{\prime } \sqrt {a^{2}+x^{2}}+x +y = \sqrt {a^{2}+x^{2}} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.826 |
|
|
\[ {}y^{\prime } x \ln \left (x \right ) = a x \left (1+\ln \left (x \right )\right )-y \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.815 |
|
|
\[ {}y y^{\prime }+4 \left (1+x \right ) x +y^{2} = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
1.223 |
|
|
\[ {}y y^{\prime } = x a +b y^{2} \] |
1 |
1 |
2 |
[_rational, _Bernoulli] |
✓ |
✓ |
0.854 |
|
|
\[ {}y y^{\prime } = b \cos \left (x +c \right )+a y^{2} \] |
1 |
1 |
2 |
[_Bernoulli] |
✓ |
✓ |
1.502 |
|
|
\[ {}y y^{\prime } = \csc \left (x \right )^{2}-y^{2} \cot \left (x \right ) \] |
1 |
1 |
2 |
[_Bernoulli] |
✓ |
✓ |
21.66 |
|
|
\[ {}\left (x -y\right ) y^{\prime } = y \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
0.863 |
|
|
\[ {}1-y^{\prime } = x +y \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.459 |
|
|
\[ {}\left (x -y\right ) y^{\prime } = y \left (1+2 x y\right ) \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.059 |
|
|
\[ {}\left (x +y\right ) y^{\prime }+\tan \left (y\right ) = 0 \] |
1 |
1 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
1.849 |
|
|
\[ {}\left (3+2 x -y\right ) y^{\prime }+2 = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
✓ |
0.776 |
|
|
\[ {}\left (x^{2}-y\right ) y^{\prime }+x = 0 \] |
1 |
1 |
1 |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
0.72 |
|
|
\[ {}\left (x^{2}-y\right ) y^{\prime } = 4 x y \] |
1 |
1 |
2 |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.272 |
|
|
\[ {}\left (y-\cot \left (x \right ) \csc \left (x \right )\right ) y^{\prime }+\csc \left (x \right ) \left (1+y \cos \left (x \right )\right ) y = 0 \] |
1 |
1 |
2 |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
41.14 |
|
|
\[ {}2 y y^{\prime }+2 x +x^{2}+y^{2} = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
1.248 |
|
|
\[ {}2 y y^{\prime } = x y^{2}+x^{3} \] |
1 |
1 |
2 |
[_rational, _Bernoulli] |
✓ |
✓ |
0.678 |
|
|
\[ {}\left (x -2 y\right ) y^{\prime } = y \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
0.911 |
|
|
\[ {}\left (x \,{\mathrm e}^{-x}-2 y\right ) y^{\prime } = 2 x \,{\mathrm e}^{-2 x}-\left ({\mathrm e}^{-x}+x \,{\mathrm e}^{-x}-2 y\right ) y \] |
1 |
1 |
2 |
[[_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
1.798 |
|
|
\[ {}\left (x a +b y\right ) y^{\prime }+y = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.525 |
|
|
\[ {}x y y^{\prime } = x +y^{2} \] |
1 |
1 |
2 |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
0.72 |
|
|
\[ {}x y y^{\prime }+x^{2}+y^{2} = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
0.955 |
|
|
\[ {}x y y^{\prime }+x^{4}-y^{2} = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
0.75 |
|
|
\[ {}x y y^{\prime } = a \,x^{3} \cos \left (x \right )+y^{2} \] |
1 |
1 |
2 |
[[_homogeneous, ‘class D‘], _Bernoulli] |
✓ |
✓ |
0.971 |
|
|
\[ {}x y y^{\prime } = a \,x^{n}+b y^{2} \] |
1 |
1 |
2 |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
1.063 |
|
|
\[ {}\left (1+x y\right ) y^{\prime }+y^{2} = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
0.757 |
|
|
\[ {}\left (2+3 x -x y\right ) y^{\prime }+y = 0 \] |
1 |
1 |
1 |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
0.839 |
|
|
\[ {}x \left (x -y\right ) y^{\prime }+2 x^{2}+3 x y-y^{2} = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
1.451 |
|
|
\[ {}2 x y y^{\prime }+1-2 x^{3}-y^{2} = 0 \] |
1 |
1 |
2 |
[_rational, _Bernoulli] |
✓ |
✓ |
0.704 |
|
|
\[ {}2 x y y^{\prime } = x a +y^{2} \] |
1 |
1 |
2 |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
0.686 |
|
|
\[ {}2 x y y^{\prime } = x^{2}+y^{2} \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
0.924 |
|
|
\[ {}2 x y y^{\prime } = 4 x^{2} \left (2 x +1\right )+y^{2} \] |
1 |
1 |
2 |
[_rational, _Bernoulli] |
✓ |
✓ |
0.618 |
|
|
\[ {}2 x y y^{\prime }+x^{2} \left (a \,x^{3}+1\right ) = 6 y^{2} \] |
1 |
1 |
2 |
[_rational, _Bernoulli] |
✓ |
✓ |
0.755 |
|
|
\[ {}x \left (x -2 y\right ) y^{\prime }+y^{2} = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
2.421 |
|
|
\[ {}x \left (1+x -2 y\right ) y^{\prime }+\left (1-2 x +y\right ) y = 0 \] |
1 |
1 |
3 |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
1.194 |
|
|
\[ {}x \left (1-x -2 y\right ) y^{\prime }+\left (2 x +y+1\right ) y = 0 \] |
1 |
1 |
3 |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
1.174 |
|
|
\[ {}x \left (2 x +3 y\right ) y^{\prime }+3 \left (x +y\right )^{2} = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
2.763 |
|
|
\[ {}a x y y^{\prime } = x^{2}+y^{2} \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.403 |
|
|
\[ {}a x y y^{\prime }+x^{2}-y^{2} = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.078 |
|
|
\[ {}x \left (x -a y\right ) y^{\prime } = y \left (-x a +y\right ) \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
3.023 |
|
|
\[ {}x \left (1-x y\right ) y^{\prime }+\left (1+x y\right ) y = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
1.041 |
|
|
\[ {}x \left (2-x y\right ) y^{\prime }+2 y-x y^{2} \left (1+x y\right ) = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
0.848 |
|
|
\[ {}x \left (3-x y\right ) y^{\prime } = y \left (x y-1\right ) \] |
1 |
1 |
3 |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
1.184 |
|
|
\[ {}\left (-x^{2}+1\right ) y y^{\prime }+2 x^{2}+x y^{2} = 0 \] |
1 |
1 |
2 |
[_rational, _Bernoulli] |
✓ |
✓ |
0.832 |
|
|
\[ {}2 x^{2} y y^{\prime } = x^{2} \left (2 x +1\right )-y^{2} \] |
1 |
1 |
2 |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
1.65 |
|
|
\[ {}x \left (1-2 x y\right ) y^{\prime }+y \left (1+2 x y\right ) = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
1.144 |
|
|
\[ {}x \left (1+2 x y\right ) y^{\prime }+\left (2+3 x y\right ) y = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
2.707 |
|
|
\[ {}x \left (1+2 x y\right ) y^{\prime }+\left (1+2 x y-x^{2} y^{2}\right ) y = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
0.883 |
|
|
\[ {}3 x^{2} y y^{\prime }+1+2 x y^{2} = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
0.836 |
|
|
\[ {}\left (1-x^{3} y\right ) y^{\prime } = x^{2} y^{2} \] |
1 |
1 |
9 |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
2.39 |
|
|
\[ {}3 x^{4} y y^{\prime } = 1-2 x^{3} y^{2} \] |
1 |
1 |
2 |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
0.97 |
|
|
\[ {}x y+\left (x^{2}+y^{2}\right ) y^{\prime } = 0 \] |
1 |
1 |
4 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
2.749 |
|
|
\[ {}\left (x^{2}+y^{2}\right ) y^{\prime } = x y \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
0.924 |
|
|
\[ {}\left (x^{2}-y^{2}\right ) y^{\prime } = 2 x y \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
2.559 |
|
|
\[ {}\left (3 x^{2}-y^{2}\right ) y^{\prime } = 2 x y \] |
1 |
1 |
3 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
2.833 |
|
|
\[ {}\left (x^{4}+y^{2}\right ) y^{\prime } = 4 x^{3} y \] |
1 |
1 |
2 |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
2.571 |
|
|
\[ {}\left (x^{2}+2 y+y^{2}\right ) y^{\prime }+2 x = 0 \] |
1 |
1 |
1 |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
0.951 |
|
|
\[ {}\left (1+y+x y+y^{2}\right ) y^{\prime }+1+y = 0 \] |
1 |
1 |
1 |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
✓ |
2.296 |
|
|
\[ {}3 y^{2} y^{\prime } = 1+x +a y^{3} \] |
1 |
1 |
3 |
[_rational, _Bernoulli] |
✓ |
✓ |
1.469 |
|
|
\[ {}3 \left (x^{2}-y^{2}\right ) y^{\prime }+3 \,{\mathrm e}^{x}+6 x y \left (1+x \right )-2 y^{3} = 0 \] |
1 |
1 |
3 |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
1.554 |
|
|
\[ {}\left (x^{2}+a y^{2}\right ) y^{\prime } = x y \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
1.386 |
|
|
\[ {}x \left (1-x^{2}+y^{2}\right ) y^{\prime }+\left (1+x^{2}-y^{2}\right ) y = 0 \] |
1 |
1 |
2 |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
5.356 |
|
|
\[ {}x \left (a -x^{2}-y^{2}\right ) y^{\prime }+\left (a +x^{2}+y^{2}\right ) y = 0 \] |
1 |
1 |
2 |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
5.602 |
|
|
\[ {}x \left (x^{2}-x y-y^{2}\right ) y^{\prime } = \left (x^{2}+x y-y^{2}\right ) y \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
1.309 |
|
|
\[ {}x \left (x^{2}+a x y+y^{2}\right ) y^{\prime } = \left (x^{2}+b x y+y^{2}\right ) y \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
1.513 |
|
|
\[ {}x \left (x^{2}-2 y^{2}\right ) y^{\prime } = \left (2 x^{2}-y^{2}\right ) y \] |
1 |
1 |
6 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
4.329 |
|
|
\[ {}\left (1-4 x +3 x y^{2}\right ) y^{\prime } = \left (2-y^{2}\right ) y \] |
1 |
1 |
1 |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
1.402 |
|
|
\[ {}3 x \left (x +y^{2}\right ) y^{\prime }+x^{3}-3 x y-2 y^{3} = 0 \] |
1 |
1 |
3 |
[_rational] |
✓ |
✓ |
1.22 |
|
|
\[ {}x \left (3 x -7 y^{2}\right ) y^{\prime }+\left (5 x -3 y^{2}\right ) y = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
3.315 |
|
|
\[ {}\left (1-x^{2} y^{2}\right ) y^{\prime } = x y^{3} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
0.975 |
|
|
\[ {}\left (1-x^{2} y^{2}\right ) y^{\prime } = \left (1+x y\right ) y^{2} \] |
1 |
1 |
2 |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
0.971 |
|
|
\[ {}x \left (1+x y^{2}\right ) y^{\prime }+y = 0 \] |
1 |
1 |
4 |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
3.185 |
|
|
\[ {}x \left (1-x y\right )^{2} y^{\prime }+\left (1+x^{2} y^{2}\right ) y = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
1.223 |
|
|
\[ {}\left (1-x^{4} y^{2}\right ) y^{\prime } = x^{3} y^{3} \] |
1 |
1 |
4 |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
3.205 |
|
|
\[ {}\left (x^{3}-y^{3}\right ) y^{\prime }+x^{2} y = 0 \] |
1 |
1 |
10 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
3.447 |
|
|
\[ {}\left (x^{3}+a y^{3}\right ) y^{\prime } = x^{2} y \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
1.381 |
|
|
\[ {}x \left (2 x^{3}-y^{3}\right ) y^{\prime } = \left (x^{3}-2 y^{3}\right ) y \] |
1 |
1 |
3 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
5.336 |
|
|
\[ {}x \left (x^{3}-2 y^{3}\right ) y^{\prime } = \left (2 x^{3}-y^{3}\right ) y \] |
1 |
1 |
3 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
3.612 |
|
|
\[ {}x \left (x^{4}-2 y^{3}\right ) y^{\prime }+\left (2 x^{4}+y^{3}\right ) y = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
5.208 |
|
|
\[ {}\left (5 x -y-7 x y^{3}\right ) y^{\prime }+5 y-y^{4} = 0 \] |
1 |
1 |
1 |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
1.248 |
|
|
\[ {}x \left (1-2 x y^{3}\right ) y^{\prime }+\left (1-2 x^{3} y\right ) y = 0 \] |
1 |
1 |
3 |
[_rational] |
✓ |
✓ |
1.28 |
|
|
\[ {}x \left (a +b x y^{3}\right ) y^{\prime }+\left (a +c \,x^{3} y\right ) y = 0 \] |
1 |
1 |
3 |
[_rational] |
✓ |
✓ |
1.53 |
|
|
\[ {}x \left (1-2 y^{3} x^{2}\right ) y^{\prime }+\left (1-2 x^{3} y^{2}\right ) y = 0 \] |
1 |
1 |
3 |
[_rational] |
✓ |
✓ |
1.236 |
|
|
\[ {}x \left (1-x y\right ) \left (1-x^{2} y^{2}\right ) y^{\prime }+\left (1+x y\right ) \left (1+x^{2} y^{2}\right ) y = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
1.201 |
|
|
\[ {}\left (x^{2}-y^{4}\right ) y^{\prime } = x y \] |
1 |
1 |
4 |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
3.335 |
|
|
\[ {}\left (x^{3}-y^{4}\right ) y^{\prime } = 3 x^{2} y \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
3.968 |
|
|
\[ {}2 \left (x -y^{4}\right ) y^{\prime } = y \] |
1 |
1 |
4 |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
3.197 |
|
|
\[ {}\left (4 x -x y^{3}-2 y^{4}\right ) y^{\prime } = \left (2+y^{3}\right ) y \] |
1 |
1 |
1 |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
1.21 |
|
|
\[ {}2 x \left (x^{3}+y^{4}\right ) y^{\prime } = \left (x^{3}+2 y^{4}\right ) y \] |
1 |
1 |
8 |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
3.709 |
|
|
\[ {}x \left (1-x^{2} y^{4}\right ) y^{\prime }+y = 0 \] |
1 |
1 |
4 |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
3.585 |
|
|
\[ {}\left (x^{2}-y^{5}\right ) y^{\prime } = 2 x y \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
3.212 |
|
|
\[ {}x \left (x^{3}+y^{5}\right ) y^{\prime } = \left (x^{3}-y^{5}\right ) y \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
3.368 |
|
|
\[ {}x^{3} \left (1+5 x^{3} y^{7}\right ) y^{\prime }+\left (3 x^{5} y^{5}-1\right ) y^{3} = 0 \] |
1 |
1 |
1 |
[_rational] |
✓ |
✓ |
1.467 |
|
|
\[ {}\left (x +\cos \left (x \right ) \sec \left (y\right )\right ) y^{\prime }+\tan \left (y\right )-y \sin \left (x \right ) \sec \left (y\right ) = 0 \] |
1 |
1 |
1 |
[NONE] |
✓ |
✓ |
18.316 |
|
|
\[ {}\left (1+\left (x +y\right ) \tan \left (y\right )\right ) y^{\prime }+1 = 0 \] |
1 |
1 |
1 |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
1.122 |
|
|
\[ {}\left (1-2 x -\ln \left (y\right )\right ) y^{\prime }+2 y = 0 \] |
1 |
1 |
1 |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
1.09 |
|
|
\[ {}y^{\prime } = \frac {x y}{x^{2}-y^{2}} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
1.12 |
|
|
\[ {}y^{\prime }-\frac {2 y}{1+x} = \left (1+x \right )^{2} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.708 |
|
|
\[ {}y+x y^{2}-x y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
0.744 |
|
|
\[ {}\left (y-x \right ) y^{\prime }+y = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.105 |
|
|
\[ {}x -y \cos \left (\frac {y}{x}\right )+x \cos \left (\frac {y}{x}\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
1.442 |
|
|
\[ {}y^{\prime }+\frac {x y}{x^{2}+1} = \frac {1}{2 x \left (x^{2}+1\right )} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.835 |
|
|
\[ {}x \left (-x^{2}+1\right ) y^{\prime }+\left (2 x^{2}-1\right ) y = a \,x^{3} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.347 |
|
|
\[ {}y^{\prime }+\frac {y}{\left (-x^{2}+1\right )^{\frac {3}{2}}} = \frac {x +\sqrt {-x^{2}+1}}{\left (-x^{2}+1\right )^{2}} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
4.732 |
|
|
\[ {}y^{\prime }+y \cos \left (x \right ) = \frac {\sin \left (2 x \right )}{2} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.525 |
|
|
|
||||||||
|
\[ {}\left (x^{2}+1\right ) y^{\prime }+y = \arctan \left (x \right ) \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.905 |
|
|
\[ {}3 z^{2} z^{\prime }-a z^{3} = 1+x \] |
1 |
1 |
3 |
[_rational, _Bernoulli] |
✓ |
✓ |
1.86 |
|
|
\[ {}x y^{\prime }+y = y^{2} \ln \left (x \right ) \] |
1 |
1 |
1 |
[_Bernoulli] |
✓ |
✓ |
1.004 |
|
|
\[ {}\left (x^{2} y^{2}+x y\right ) y+\left (x^{2} y^{2}-1\right ) x y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
1.265 |
|
|
\[ {}\left (x^{3} y^{3}+x^{2} y^{2}+x y+1\right ) y+\left (x^{3} y^{3}-x^{2} y^{2}-x y+1\right ) x y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
1.514 |
|
|
\[ {}\frac {y \cos \left (\frac {y}{x}\right )}{x}-\left (\frac {x \sin \left (\frac {y}{x}\right )}{y}+\cos \left (\frac {y}{x}\right )\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
2.806 |
|
|
\[ {}2 y \,{\mathrm e}^{\frac {x}{y}}+\left (y-2 x \,{\mathrm e}^{\frac {x}{y}}\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
1.985 |
|
|
\[ {}x^{2}+y^{2} = 2 x y y^{\prime } \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.574 |
|
|
\[ {}y+7+\left (2 x +y+3\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
4.445 |
|
|
\[ {}x y^{\prime }+y = y^{2} \ln \left (x \right ) \] |
1 |
1 |
1 |
[_Bernoulli] |
✓ |
✓ |
1.133 |
|
|
\[ {}x^{\prime }+2 y x = {\mathrm e}^{-y^{2}} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.774 |
|
|
\[ {}r^{\prime } = \left (r+{\mathrm e}^{-\theta }\right ) \tan \left (\theta \right ) \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.231 |
|
|
\[ {}y^{\prime }-\frac {2 x y}{x^{2}+1} = 1 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.866 |
|
|
\[ {}\tan \left (\theta \right ) r^{\prime }-r = \tan \left (\theta \right )^{2} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.508 |
|
|
\[ {}y^{\prime }+2 y = 3 \,{\mathrm e}^{-2 x} \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.737 |
|
|
\[ {}y^{\prime }+2 y = \frac {3 \,{\mathrm e}^{-2 x}}{4} \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.778 |
|
|
\[ {}y^{\prime }+2 y = \sin \left (x \right ) \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.939 |
|
|
\[ {}y^{\prime }+y \cos \left (x \right ) = {\mathrm e}^{2 x} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.483 |
|
|
\[ {}y^{\prime }+y \cos \left (x \right ) = \frac {\sin \left (2 x \right )}{2} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.425 |
|
|
\[ {}-y+x y^{\prime } = x^{2} \sin \left (x \right ) \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.083 |
|
|
\[ {}x y^{\prime }+x y^{2}-y = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
0.94 |
|
|
\[ {}x y^{\prime }-y \left (2 y \ln \left (x \right )-1\right ) = 0 \] |
1 |
1 |
1 |
[_Bernoulli] |
✓ |
✓ |
1.199 |
|
|
\[ {}y^{\prime }-y = {\mathrm e}^{x} \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.975 |
|
|
\[ {}\left (x -\cos \left (y\right )\right ) y^{\prime }+\tan \left (y\right ) = 0 \] |
1 |
1 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
12.745 |
|
|
\[ {}y^{\prime } = \frac {1}{x^{2}}-\frac {y}{x}-y^{2} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
✓ |
2.769 |
|
|
\[ {}2 x y y^{\prime }+\left (1+x \right ) y^{2} = {\mathrm e}^{x} \] |
1 |
1 |
2 |
[_Bernoulli] |
✓ |
✓ |
1.655 |
|
|
\[ {}\cos \left (y\right ) y^{\prime }+\sin \left (y\right ) = x^{2} \] |
1 |
1 |
1 |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
1.981 |
|
|
\[ {}{\mathrm e}^{y} \left (1+y^{\prime }\right ) = {\mathrm e}^{x} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
1.761 |
|
|
\[ {}\left (x^{2}-y^{2}\right ) y^{\prime } = 2 x y \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
3.274 |
|
|
\[ {}x y^{\prime }+y = x^{2} \left (1+{\mathrm e}^{x}\right ) y^{2} \] |
1 |
1 |
1 |
[_Bernoulli] |
✓ |
✓ |
1.166 |
|
|
\[ {}y^{\prime }+a y = k \,{\mathrm e}^{b x} \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.028 |
|
|
\[ {}y^{\prime }+a y = b \sin \left (k x \right ) \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.237 |
|
|
\[ {}\left (y^{2}+a \sin \left (x \right )\right ) y^{\prime } = \cos \left (x \right ) \] |
1 |
1 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
2.471 |
|
|
\[ {}y^{\prime }+y \cos \left (x \right ) = {\mathrm e}^{-\sin \left (x \right )} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.011 |
|
|
\[ {}x y^{\prime }-y \left (\ln \left (x y\right )-1\right ) = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
3.353 |
|
|
\[ {}x^{3} y^{\prime }-y^{2}-x^{2} y = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
1.043 |
|
|
\[ {}x y^{\prime }+a y+b \,x^{n} = 0 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.145 |
|
|
\[ {}y^{2}-3 x y-2 x^{2}+\left (x y-x^{2}\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
3.047 |
|
|
\[ {}y^{\prime } \cos \left (x \right )+y+\left (\sin \left (x \right )+1\right ) \cos \left (x \right ) = 0 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
3.275 |
|
|
\[ {}\left (x^{2}-y\right ) y^{\prime }+x = 0 \] |
1 |
1 |
1 |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
1.16 |
|
|
\[ {}\left (x^{2}-y\right ) y^{\prime }-4 x y = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
3.718 |
|
|
\[ {}x y y^{\prime }+x^{2}+y^{2} = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
2.011 |
|
|
\[ {}2 x y y^{\prime }+3 x^{2}-y^{2} = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.442 |
|
|
\[ {}\left (2 x y^{3}-x^{4}\right ) y^{\prime }+2 x^{3} y-y^{4} = 0 \] |
1 |
1 |
3 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
10.768 |
|
|
\[ {}\left (x y-1\right )^{2} x y^{\prime }+\left (1+x^{2} y^{2}\right ) y = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
1.541 |
|
|
\[ {}a x y^{3}+b y^{2}+y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _Abel] |
✓ |
✓ |
4.519 |
|
|
\[ {}y^{\prime } = {\mathrm e}^{x a}+a y \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.368 |
|
|
\[ {}y^{\prime }+\frac {y}{x} = 2 x^{\frac {3}{2}} \sqrt {y} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
3.696 |
|
|
\[ {}x y+\left (-x^{2}+y^{2}\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
1.023 |
|
|
\[ {}x^{2} y^{\prime }-x y = \frac {1}{x} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.643 |
|
|
\[ {}3 x^{3} y^{2} y^{\prime }-y^{3} x^{2} = 1 \] |
1 |
1 |
3 |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
1.158 |
|
|
\[ {}y+2 x -x y^{\prime } = 0 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.604 |
|
|
\[ {}\left (x \cos \left (y\right )-{\mathrm e}^{-\sin \left (y\right )}\right ) y^{\prime }+1 = 0 \] |
1 |
1 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
1.866 |
|
|
\[ {}\sin \left (\theta \right ) \cos \left (\theta \right ) r^{\prime }-\sin \left (\theta \right )^{2} = r \cos \left (\theta \right )^{2} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
2.109 |
|
|
\[ {}-y+x y^{\prime } = x^{2} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.856 |
|
|
\[ {}x^{2} y^{\prime }+\sin \left (x \right )-y = 0 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.517 |
|
|
\[ {}3 t = {\mathrm e}^{t} y^{\prime }+y \ln \left (t \right ) \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
4.544 |
|
|
\[ {}3 r = r^{\prime }-\theta ^{3} \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.584 |
|
|
\[ {}y^{\prime }-y-{\mathrm e}^{3 x} = 0 \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.553 |
|
|
\[ {}y^{\prime } = \frac {y}{x}+2 x +1 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.583 |
|
|
\[ {}r^{\prime }+r \tan \left (\theta \right ) = \sec \left (\theta \right ) \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.714 |
|
|
\[ {}x y^{\prime }+2 y = \frac {1}{x^{3}} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.576 |
|
|
\[ {}t +y+1-y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.528 |
|
|
\[ {}y^{\prime } = x^{2} {\mathrm e}^{-4 x}-4 y \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.579 |
|
|
\[ {}x y^{\prime }+3 y+3 x^{2} = \frac {\sin \left (x \right )}{x} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.75 |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime }-x^{2} y = \left (1+x \right ) \sqrt {-x^{2}+1} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
2.342 |
|
|
\[ {}y^{\prime }-\frac {y}{x} = x \,{\mathrm e}^{x} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.122 |
|
|
\[ {}y^{\prime }+4 y-{\mathrm e}^{-x} = 0 \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.069 |
|
|
\[ {}t^{2} x^{\prime }+3 x t = t^{4} \ln \left (t \right )+1 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.249 |
|
|
\[ {}y^{\prime }+\frac {3 y}{x}+2 = 3 x \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.112 |
|
|
\[ {}y^{\prime } \cos \left (x \right )+y \sin \left (x \right ) = 2 \cos \left (x \right )^{2} x \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
2.098 |
|
|
\[ {}y^{\prime }+y \sqrt {1+\sin \left (x \right )^{2}} = x \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
19.125 |
|
|
\[ {}\left ({\mathrm e}^{4 y}+2 x \right ) y^{\prime }-1 = 0 \] |
1 |
1 |
2 |
[[_1st_order, _with_exponential_symmetries]] |
✓ |
✓ |
4.855 |
|
|
\[ {}y^{\prime }+2 y = \frac {x}{y^{2}} \] |
1 |
1 |
3 |
[_rational, _Bernoulli] |
✓ |
✓ |
1.266 |
|
|
\[ {}y^{\prime }+\frac {3 y}{x} = x^{2} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.552 |
|
|
\[ {}x^{\prime } = \alpha -\beta \cos \left (\frac {\pi t}{12}\right )-k x \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.755 |
|
|
\[ {}x^{2} y+x^{4} \cos \left (x \right )-x^{3} y^{\prime } = 0 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.118 |
|
|
\[ {}x^{\frac {10}{3}}-2 y+x y^{\prime } = 0 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.59 |
|
|
\[ {}y^{\prime }-4 y = 32 x^{2} \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.918 |
|
|
\[ {}y^{\prime }+\frac {3 y}{x} = x^{2}-4 x +3 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.97 |
|
|
\[ {}y^{\prime }-y = {\mathrm e}^{2 x} \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.553 |
|
|
\[ {}y+y^{\prime } = \left (1+x \right )^{2} \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.194 |
|
|
\[ {}y^{\prime }+\frac {y}{1-x}+2 x -x^{2} = 0 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.63 |
|
|
\[ {}y^{\prime }+\frac {y}{1-x}+x -x^{2} = 0 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.593 |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime } = 1+x y \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.216 |
|
|
\[ {}y^{\prime }-\frac {2 y}{x}-x^{2} = 0 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.561 |
|
|
\[ {}y^{\prime }+\frac {2 y}{x}-x^{3} = 0 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.548 |
|
|
\[ {}y^{\prime }+2 y = {\mathrm e}^{3 x} \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.583 |
|
|
\[ {}-y+x y^{\prime } = x^{2} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.578 |
|
|
\[ {}y^{\prime }+y \tanh \left (x \right ) = 2 \sinh \left (x \right ) \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.762 |
|
|
\[ {}x y^{\prime }-2 y = x^{3} \cos \left (x \right ) \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.692 |
|
|
\[ {}y^{\prime }+\frac {y}{x} = y^{3} \] |
1 |
1 |
2 |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
1.257 |
|
|
\[ {}x -x y^{2} = \left (x +x^{2} y\right ) y^{\prime } \] |
1 |
1 |
1 |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
8.067 |
|
|
\[ {}\left (1+x y\right ) y+x \left (1+x y+x^{2} y^{2}\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
1.46 |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime } = 1+x y \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.256 |
|
|
\[ {}y^{\prime }-y \tan \left (x \right ) = \cos \left (x \right )-2 x \sin \left (x \right ) \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.78 |
|
|
\[ {}y^{\prime } = \frac {y^{2}+2 x y}{2 x y+x^{2}} \] |
1 |
1 |
3 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
2.571 |
|
|
\[ {}x y^{\prime }+2 y = 3 x -1 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.792 |
|
|
\[ {}\left (-x^{3}+1\right ) y^{\prime }+x^{2} y = x^{2} \left (-x^{3}+1\right ) \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.234 |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime }+x y = \left (x^{2}+1\right )^{\frac {3}{2}} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.305 |
|
|
\[ {}y^{\prime }+\cot \left (x \right ) y = \cos \left (x \right ) \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.926 |
|
|
\[ {}y^{\prime }+\frac {y}{x} = x y^{2} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
1.179 |
|
|
\[ {}y^{\prime }-5 y = \left (-1+x \right ) \sin \left (x \right )+\left (1+x \right ) \cos \left (x \right ) \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.505 |
|
|
\[ {}y^{\prime }-5 y = 3 \,{\mathrm e}^{x}-2 x +1 \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.664 |
|
|
\[ {}y^{\prime }-5 y = x^{2} {\mathrm e}^{x}-x \,{\mathrm e}^{5 x} \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.688 |
|
|
\[ {}y^{\prime }-y = {\mathrm e}^{x} \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.525 |
|
|
\[ {}y^{\prime }-y = {\mathrm e}^{2 x} x +1 \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.573 |
|
|
\[ {}y^{\prime }-y = \sin \left (x \right )+\cos \left (2 x \right ) \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.557 |
|
|
\[ {}y^{\prime }+\frac {4 y}{x} = x^{4} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.617 |
|
|
\[ {}y^{\prime }-\frac {y}{x} = x^{2} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.075 |
|
|
\[ {}2 x^{3} y^{\prime } = y \left (y^{2}+3 x^{2}\right ) \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.546 |
|
|
\[ {}x y^{2}+y+\left (x^{2} y-x \right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
1.543 |
|
|
\[ {}x \sin \left (\frac {y}{x}\right )-y \cos \left (\frac {y}{x}\right )+x \cos \left (\frac {y}{x}\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
1.992 |
|
|
\[ {}y^{2}-x^{2}+x y y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.685 |
|
|
\[ {}y \left (1+2 x y\right )+x \left (1-x y\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
1.641 |
|
|
\[ {}x y y^{\prime }+x^{2}+y^{2} = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
2.356 |
|
|
\[ {}x y y^{\prime }+x^{2}+y^{2} = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.536 |
|
|
\[ {}y+y^{\prime } = 2 x +2 \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.349 |
|
|
\[ {}-3 y-\left (-2+x \right ) {\mathrm e}^{x}+x y^{\prime } = 0 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.332 |
|
|
\[ {}i^{\prime }-6 i = 10 \sin \left (2 t \right ) \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.397 |
|
|
\[ {}y+\left (x y+x -3 y\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
1.443 |
|
|
\[ {}x y^{\prime }+y-x^{3} y^{6} = 0 \] |
1 |
1 |
5 |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
2.846 |
|
|
\[ {}r^{\prime }+2 r \cos \left (\theta \right )+\sin \left (2 \theta \right ) = 0 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.566 |
|
|
\[ {}y \left (1+y^{2}\right ) = 2 \left (1-2 x y^{2}\right ) y^{\prime } \] |
1 |
1 |
1 |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
1.914 |
|
|
\[ {}2 x^{\prime }-\frac {x}{y}+x^{3} \cos \left (y \right ) = 0 \] |
1 |
1 |
2 |
[_Bernoulli] |
✓ |
✓ |
4.125 |
|
|
\[ {}x y^{\prime } = y \left (1-x \tan \left (x \right )\right )+x^{2} \cos \left (x \right ) \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
15.706 |
|
|
\[ {}2+y^{2}-\left (x y+2 y+y^{3}\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
6.585 |
|
|
\[ {}1+y^{2} = \left (\arctan \left (y\right )-x \right ) y^{\prime } \] |
1 |
1 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
10.002 |
|
|
\[ {}1+\sin \left (y\right ) = \left (2 y \cos \left (y\right )-x \left (\sec \left (y\right )+\tan \left (y\right )\right )\right ) y^{\prime } \] |
1 |
1 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
31.581 |
|
|
\[ {}x y^{\prime } = 2 y+x^{3} {\mathrm e}^{x} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.503 |
|
|
\[ {}L i^{\prime }+R i = E \sin \left (2 t \right ) \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.95 |
|
|
\[ {}x^{2} \cos \left (y\right ) y^{\prime } = 2 x \sin \left (y\right )-1 \] |
1 |
1 |
1 |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
2.265 |
|
|
\[ {}x y^{3}-y^{3}-x^{2} {\mathrm e}^{x}+3 x y^{2} y^{\prime } = 0 \] |
1 |
1 |
3 |
[_Bernoulli] |
✓ |
✓ |
1.971 |
|
|
\[ {}y+{\mathrm e}^{y}-{\mathrm e}^{-x}+\left (1+{\mathrm e}^{y}\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
2.033 |
|
|
\[ {}x y^{\prime } = 1-x +2 y \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.968 |
|
|
\[ {}y^{\prime }+x y = \frac {1}{x^{3}} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.727 |
|
|
\[ {}y^{\prime }-y = 2 x -3 \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.591 |
|
|
\[ {}\left (2 y+x \right ) y^{\prime } = 1 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
✓ |
1.563 |
|
|
\[ {}y+y^{\prime } = 2 x +1 \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.585 |
|
|
\[ {}y+2 = \left (-4+2 x +y\right ) y^{\prime } \] |
1 |
1 |
2 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.622 |
|
|
\[ {}y^{\prime } = \frac {y}{2 x}+\frac {x^{2}}{2 y} \] |
1 |
1 |
2 |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
1.115 |
|
|
\[ {}\left (1+x^{2} y^{2}\right ) y+\left (x^{2} y^{2}-1\right ) x y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
1.478 |
|
|
\[ {}2 x^{3} y^{2}-y+\left (2 y^{3} x^{2}-x \right ) y^{\prime } = 0 \] |
1 |
1 |
3 |
[_rational] |
✓ |
✓ |
1.302 |
|
|
\[ {}x^{2}+y^{2}-2 x y y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.446 |
|
|
\[ {}x^{2}-y^{2}+2 x y y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
0.927 |
|
|
\[ {}y^{\prime }+y \cos \left (x \right ) = \sin \left (x \right ) \cos \left (x \right ) \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.023 |
|
|
\[ {}y+y^{\prime } = {\mathrm e}^{x} \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.675 |
|
|
\[ {}y^{\prime }-2 y = x^{2}+x \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.69 |
|
|
\[ {}3 y^{\prime }+y = 2 \,{\mathrm e}^{-x} \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.788 |
|
|
\[ {}y^{\prime }+3 y = {\mathrm e}^{i x} \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.707 |
|
|
\[ {}y^{\prime }+i y = x \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.693 |
|
|
\[ {}L y^{\prime }+R y = E \sin \left (\omega x \right ) \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.498 |
|
|
\[ {}L y^{\prime }+R y = E \,{\mathrm e}^{i \omega x} \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.25 |
|
|
\[ {}y^{\prime }+a y = b \left (x \right ) \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.949 |
|
|
\[ {}y^{\prime }-y \tan \left (x \right ) = {\mathrm e}^{\sin \left (x \right )} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.961 |
|
|
\[ {}y^{\prime }+2 x y = x \,{\mathrm e}^{-x^{2}} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.701 |
|
|
\[ {}y^{\prime }+y \cos \left (x \right ) = {\mathrm e}^{-\sin \left (x \right )} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.123 |
|
|
\[ {}y^{\prime }+2 y = b \left (x \right ) \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.91 |
|
|
\[ {}y^{\prime } = \frac {x y}{x^{2}+y^{2}} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
1.279 |
|
|
\[ {}2 x y y^{\prime } = x^{2}+y^{2} \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.457 |
|
|
\[ {}\left (y \cos \left (y\right )-\sin \left (y\right )+x \right ) y^{\prime } = y \] |
1 |
1 |
1 |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
1.437 |
|
|
\[ {}y^{\prime } = 1+2 x y \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.773 |
|
|
\[ {}y^{\prime } = \frac {2 x y^{2}}{1-x^{2} y} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
1.313 |
|
|
\[ {}x y^{\prime }+y = x^{4} y^{3} \] |
1 |
1 |
2 |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
1.231 |
|
|
\[ {}x y^{2} y^{\prime }+y^{3} = x \cos \left (x \right ) \] |
1 |
1 |
3 |
[_Bernoulli] |
✓ |
✓ |
8.563 |
|
|
\[ {}x y^{\prime }+y = x y^{2} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
1.415 |
|
|
\[ {}y-x y^{\prime } = y^{\prime } y^{2} {\mathrm e}^{y} \] |
1 |
1 |
1 |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
1.62 |
|
|
\[ {}y^{\prime } \sin \left (2 x \right ) = 2 y+2 \cos \left (x \right ) \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
4.145 |
|
|
\[ {}2 x +3 y-1-4 \left (1+x \right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
2.355 |
|
|
\[ {}y^{\prime } = \frac {1-x y^{2}}{2 x^{2} y} \] |
1 |
1 |
2 |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
1.75 |
|
|
\[ {}y^{\prime } = \frac {2+3 x y^{2}}{4 x^{2} y} \] |
1 |
1 |
2 |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
2.215 |
|
|
\[ {}y^{\prime } = \frac {y-x y^{2}}{x +x^{2} y} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
2.674 |
|
|
\[ {}x^{2} y^{\prime }+y = x^{2} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.694 |
|
|
\[ {}-y+x y^{\prime } = 2 x \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
2.21 |
|
|
\[ {}x^{2} y^{\prime }-2 y = 3 x^{2} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
23.692 |
|
|
\[ {}y+y^{\prime } = \cos \left (x \right ) \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
2.008 |
|
|
\[ {}y^{\prime }-y = x^{2} \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.397 |
|
|
\[ {}y^{\prime }-\frac {y}{x} = x^{2} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.743 |
|
|
\[ {}y^{\prime } = x -y \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.708 |
|
|
\[ {}y^{\prime }-2 y = x^{2} \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.412 |
|
|
\[ {}y^{\prime }+\frac {2 y}{x} = 5 x^{2} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.654 |
|
|
\[ {}t x^{\prime }+2 x = 4 \,{\mathrm e}^{t} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.777 |
|
|
\[ {}y^{\prime }+\frac {2 y}{x} = 6 x^{4} y^{2} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
1.166 |
|
|
\[ {}y^{\prime } = x +\frac {\sec \left (x \right ) y}{x} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
4.544 |
|
|
\[ {}y^{\prime } = \frac {-x y-1}{4 x^{3} y-2 x^{2}} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
2.513 |
|
|
\[ {}v v^{\prime } = \frac {2 v^{2}}{r^{3}}+\frac {\lambda r}{3} \] |
1 |
1 |
2 |
[_rational, _Bernoulli] |
✓ |
✓ |
1.752 |
|
|
\[ {}y^{\prime } = x a +y \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.982 |
|
|
\[ {}y^{\prime } = x a +b y \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.067 |
|
|
\[ {}c y^{\prime } = x a +y \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.201 |
|
|
\[ {}c y^{\prime } = x a +b y \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.153 |
|
|
\[ {}c y^{\prime } = \frac {x a +b y^{2}}{y} \] |
1 |
1 |
2 |
[_rational, _Bernoulli] |
✓ |
✓ |
1.917 |
|
|
\[ {}y^{\prime } = \sin \left (x \right )+y \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.249 |
|
|
\[ {}y^{\prime } = \cos \left (x \right )+\frac {y}{x} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.673 |
|
|
\[ {}y^{\prime }+\cot \left (x \right ) y = 2 \cos \left (x \right ) \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.737 |
|
|
\[ {}2 x y^{2}-y+\left (y^{2}+x +y\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_rational] |
✓ |
✓ |
2.504 |
|
|
\[ {}y^{\prime }+a y-c \,{\mathrm e}^{b x} = 0 \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.124 |
|
|
\[ {}y^{\prime }+a y-b \sin \left (c x \right ) = 0 \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.301 |
|
|
\[ {}y^{\prime }+2 x y-x \,{\mathrm e}^{-x^{2}} = 0 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.869 |
|
|
\[ {}y^{\prime }+y \cos \left (x \right )-{\mathrm e}^{2 x} = 0 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.787 |
|
|
\[ {}y^{\prime }+y \cos \left (x \right )-\frac {\sin \left (2 x \right )}{2} = 0 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.807 |
|
|
|
||||||||
|
\[ {}y^{\prime }+y \cos \left (x \right )-{\mathrm e}^{-\sin \left (x \right )} = 0 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.965 |
|
|
\[ {}y^{\prime }+y \tan \left (x \right )-\sin \left (2 x \right ) = 0 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.166 |
|
|
\[ {}y^{\prime }+f^{\prime }\left (x \right ) y-f \left (x \right ) f^{\prime }\left (x \right ) = 0 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.095 |
|
|
\[ {}y^{\prime }+f \left (x \right ) y-g \left (x \right ) = 0 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.904 |
|
|
\[ {}a x y^{3}+b y^{2}+y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _Abel] |
✓ |
✓ |
9.667 |
|
|
\[ {}y^{\prime }-\sqrt {\frac {a y^{2}+b y+c}{x^{2} a +b x +c}} = 0 \] |
1 |
1 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
293.068 |
|
|
\[ {}y^{\prime }-\sqrt {\frac {y^{3}+1}{x^{3}+1}} = 0 \] |
1 |
1 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
43.512 |
|
|
\[ {}y^{\prime }-\sqrt {\frac {a y^{4}+b y^{2}+1}{a \,x^{4}+b \,x^{2}+1}} = 0 \] |
1 |
1 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
5.464 |
|
|
\[ {}y^{\prime }-\sqrt {\left (b_{4} y^{4}+b_{3} y^{3}+b_{2} y^{2}+b_{1} y+b_{0} \right ) \left (a_{4} x^{4}+a_{3} x^{3}+a_{2} x^{2}+a_{1} x +a_{0} \right )} = 0 \] |
1 |
1 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✗ |
57.172 |
|
|
\[ {}y^{\prime }-\sqrt {\frac {a_{4} x^{4}+a_{3} x^{3}+a_{2} x^{2}+a_{1} x +a_{0}}{b_{4} y^{4}+b_{3} y^{3}+b_{2} y^{2}+b_{1} y+b_{0}}} = 0 \] |
1 |
1 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✗ |
47.033 |
|
|
\[ {}y^{\prime }-\sqrt {\frac {b_{4} y^{4}+b_{3} y^{3}+b_{2} y^{2}+b_{1} y+b_{0}}{a_{4} x^{4}+a_{3} x^{3}+a_{2} x^{2}+a_{1} x +a_{0}}} = 0 \] |
1 |
1 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✗ |
43.478 |
|
|
\[ {}y^{\prime }-\left (\frac {a_{3} x^{3}+a_{2} x^{2}+a_{1} x +a_{0}}{a_{3} y^{3}+a_{2} y^{2}+a_{1} y+a_{0}}\right )^{\frac {2}{3}} = 0 \] |
1 |
1 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
6.01 |
|
|
\[ {}x y^{\prime }-y-\frac {x}{\ln \left (x \right )} = 0 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.069 |
|
|
\[ {}x y^{\prime }-y-x^{2} \sin \left (x \right ) = 0 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.191 |
|
|
\[ {}x y^{\prime }-y-\frac {x \cos \left (\ln \left (\ln \left (x \right )\right )\right )}{\ln \left (x \right )} = 0 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
3.878 |
|
|
\[ {}x y^{\prime }+a y+b \,x^{n} = 0 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.228 |
|
|
\[ {}x y^{\prime }+x y^{2}-y = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
1.065 |
|
|
\[ {}x y^{\prime }-y^{2} \ln \left (x \right )+y = 0 \] |
1 |
1 |
1 |
[_Bernoulli] |
✓ |
✓ |
1.306 |
|
|
\[ {}x y^{\prime }-y \left (2 y \ln \left (x \right )-1\right ) = 0 \] |
1 |
1 |
1 |
[_Bernoulli] |
✓ |
✓ |
1.316 |
|
|
\[ {}x y^{\prime }-y \left (\ln \left (x y\right )-1\right ) = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
1.928 |
|
|
\[ {}x y^{\prime }+\left (\sin \left (y\right )-3 x^{2} \cos \left (y\right )\right ) \cos \left (y\right ) = 0 \] |
1 |
1 |
1 |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
3.234 |
|
|
\[ {}x y^{\prime }-y f \left (x y\right ) = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
1.169 |
|
|
\[ {}2 x y^{\prime }-y-2 x^{3} = 0 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.897 |
|
|
\[ {}3 x y^{\prime }-3 x \ln \left (x \right ) y^{4}-y = 0 \] |
1 |
1 |
3 |
[_Bernoulli] |
✓ |
✓ |
2.128 |
|
|
\[ {}x^{2} y^{\prime }+y-x = 0 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.943 |
|
|
\[ {}x^{2} y^{\prime }-y+x^{2} {\mathrm e}^{x -\frac {1}{x}} = 0 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.091 |
|
|
\[ {}x^{2} \left (y^{\prime }+y^{2}\right )+4 x y+2 = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
✓ |
1.753 |
|
|
\[ {}x^{2} \left (y^{\prime }+y^{2}\right )+a x y+b = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
✓ |
2.507 |
|
|
\[ {}x^{2} \left (y^{\prime }+a y^{2}\right )-b = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational, [_Riccati, _special]] |
✓ |
✓ |
2.336 |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime }+x y-1 = 0 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.001 |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime }+x y-\left (x^{2}+1\right ) x = 0 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.016 |
|
|
\[ {}\left (x^{2}-1\right ) y^{\prime }-x y+a = 0 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.601 |
|
|
\[ {}\left (x^{2}-5 x +6\right ) y^{\prime }+3 x y-8 y+x^{2} = 0 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.147 |
|
|
\[ {}x \left (2 x -1\right ) y^{\prime }+y^{2}-\left (1+4 x \right ) y+4 x = 0 \] |
1 |
1 |
1 |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
✓ |
3.405 |
|
|
\[ {}x^{3} y^{\prime }-y^{2}-x^{2} y = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
1.181 |
|
|
\[ {}x \left (x^{2}-1\right ) y^{\prime }-\left (2 x^{2}-1\right ) y+a \,x^{3} = 0 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.795 |
|
|
\[ {}y^{\prime } \sqrt {a^{2}+x^{2}}+y-\sqrt {a^{2}+x^{2}}+x = 0 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.701 |
|
|
\[ {}y^{\prime } x \ln \left (x \right )+y-a x \left (1+\ln \left (x \right )\right ) = 0 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.624 |
|
|
\[ {}y^{\prime } \cos \left (x \right )+y+\left (\sin \left (x \right )+1\right ) \cos \left (x \right ) = 0 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
3.306 |
|
|
\[ {}\sin \left (x \right ) \cos \left (x \right ) y^{\prime }-y-\sin \left (x \right )^{3} = 0 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
4.431 |
|
|
\[ {}y y^{\prime }+y^{2}+4 \left (1+x \right ) x = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
2.217 |
|
|
\[ {}y y^{\prime }+a y^{2}-b \cos \left (x +c \right ) = 0 \] |
1 |
1 |
2 |
[_Bernoulli] |
✓ |
✓ |
3.21 |
|
|
\[ {}\left (y-x^{2}\right ) y^{\prime }-x = 0 \] |
1 |
1 |
1 |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
1.368 |
|
|
\[ {}\left (y-x^{2}\right ) y^{\prime }+4 x y = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.253 |
|
|
\[ {}2 y y^{\prime }-x y^{2}-x^{3} = 0 \] |
1 |
1 |
2 |
[_rational, _Bernoulli] |
✓ |
✓ |
1.375 |
|
|
\[ {}a y y^{\prime }+b y^{2}+f \left (x \right ) = 0 \] |
1 |
1 |
2 |
[_Bernoulli] |
✓ |
✓ |
1.867 |
|
|
\[ {}x y y^{\prime }+x^{2}+y^{2} = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.885 |
|
|
\[ {}x y y^{\prime }-y^{2}+a \,x^{3} \cos \left (x \right ) = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class D‘], _Bernoulli] |
✓ |
✓ |
1.794 |
|
|
\[ {}\left (x y+a \right ) y^{\prime }+b y = 0 \] |
1 |
1 |
1 |
[[_1st_order, _with_exponential_symmetries], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
1.537 |
|
|
\[ {}y^{2}-3 x y-2 x^{2}+\left (x y-x^{2}\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
2.605 |
|
|
\[ {}2 x y y^{\prime }-y^{2}+x a = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
1.388 |
|
|
\[ {}2 x y y^{\prime }-y^{2}+x^{2} a = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.811 |
|
|
\[ {}x \left (x +2 y-1\right ) y^{\prime }-\left (2 x +y+1\right ) y = 0 \] |
1 |
1 |
3 |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
2.121 |
|
|
\[ {}x \left (2 y-x -1\right ) y^{\prime }+y \left (2 x -y-1\right ) = 0 \] |
1 |
1 |
3 |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
2.125 |
|
|
\[ {}x \left (2 x +3 y\right ) y^{\prime }+3 \left (x +y\right )^{2} = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
2.754 |
|
|
\[ {}x \left (x y-2\right ) y^{\prime }+y^{3} x^{2}+x y^{2}-2 y = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
1.533 |
|
|
\[ {}x \left (x y-3\right ) y^{\prime }+x y^{2}-y = 0 \] |
1 |
1 |
3 |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
1.989 |
|
|
\[ {}2 x^{2} y y^{\prime }+y^{2}-2 x^{3}-x^{2} = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
2.801 |
|
|
\[ {}2 x^{2} y y^{\prime }-y^{2}-x^{2} {\mathrm e}^{x -\frac {1}{x}} = 0 \] |
1 |
1 |
2 |
[_Bernoulli] |
✓ |
✓ |
1.458 |
|
|
\[ {}\left (2 x^{2} y+x \right ) y^{\prime }-y^{3} x^{2}+2 x y^{2}+y = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
1.589 |
|
|
\[ {}\left (2 x^{2} y-x \right ) y^{\prime }-2 x y^{2}-y = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
1.831 |
|
|
\[ {}2 x^{3}+y y^{\prime }+3 x^{2} y^{2}+7 = 0 \] |
1 |
1 |
2 |
[_rational, _Bernoulli] |
✓ |
✓ |
3.064 |
|
|
\[ {}f \left (x \right ) y y^{\prime }+g \left (x \right ) y^{2}+h \left (x \right ) = 0 \] |
1 |
1 |
2 |
[_Bernoulli] |
✓ |
✓ |
1.951 |
|
|
\[ {}\left (-x^{2}+y^{2}\right ) y^{\prime }+2 x y = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
2.542 |
|
|
\[ {}\left (y^{2}+x^{4}\right ) y^{\prime }-4 x^{3} y = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
2.52 |
|
|
\[ {}\left (y^{2}+4 \sin \left (x \right )\right ) y^{\prime }-\cos \left (x \right ) = 0 \] |
1 |
1 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
2.526 |
|
|
\[ {}3 \left (-x^{2}+y^{2}\right ) y^{\prime }+2 y^{3}-6 x y \left (1+x \right )-3 \,{\mathrm e}^{x} = 0 \] |
1 |
1 |
3 |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
2.594 |
|
|
\[ {}\left (4 y^{2}+x^{2}\right ) y^{\prime }-x y = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
1.81 |
|
|
\[ {}x \left (y^{2}+x^{2}-a \right ) y^{\prime }-\left (a +x^{2}+y^{2}\right ) y = 0 \] |
1 |
1 |
2 |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
5.089 |
|
|
\[ {}x \left (y^{2}+x y-x^{2}\right ) y^{\prime }-y^{3}+x y^{2}+x^{2} y = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
1.986 |
|
|
\[ {}\left (x^{2} y^{2}+x \right ) y^{\prime }+y = 0 \] |
1 |
1 |
4 |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
2.464 |
|
|
\[ {}\left (x y-1\right )^{2} x y^{\prime }+\left (1+x^{2} y^{2}\right ) y = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
1.829 |
|
|
\[ {}\left (10 x^{3} y^{2}+x^{2} y+2 x \right ) y^{\prime }+5 y^{3} x^{2}+x y^{2} = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
3.185 |
|
|
\[ {}\left (y^{3}-x^{3}\right ) y^{\prime }-x^{2} y = 0 \] |
1 |
1 |
10 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
2.938 |
|
|
\[ {}x y^{3} y^{\prime }+y^{4}-x \sin \left (x \right ) = 0 \] |
1 |
1 |
4 |
[_Bernoulli] |
✓ |
✓ |
7.618 |
|
|
\[ {}\left (2 x y^{3}-x^{4}\right ) y^{\prime }+2 x^{3} y-y^{4} = 0 \] |
1 |
1 |
3 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
3.033 |
|
|
\[ {}\left (2 x y^{3}+y\right ) y^{\prime }+2 y^{2} = 0 \] |
1 |
1 |
3 |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
1.514 |
|
|
\[ {}\left (3 x y^{3}-4 x y+y\right ) y^{\prime }+y^{2} \left (y^{2}-2\right ) = 0 \] |
1 |
1 |
2 |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
2.52 |
|
|
\[ {}\left (7 x y^{3}+y-5 x \right ) y^{\prime }+y^{4}-5 y = 0 \] |
1 |
1 |
1 |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
1.996 |
|
|
\[ {}\left (a x y^{3}+c \right ) x y^{\prime }+\left (b \,x^{3} y+c \right ) y = 0 \] |
1 |
1 |
3 |
[_rational] |
✓ |
✓ |
2.47 |
|
|
\[ {}\left (2 x^{3} y^{3}-x \right ) y^{\prime }+2 x^{3} y^{3}-y = 0 \] |
1 |
1 |
3 |
[_rational] |
✓ |
✓ |
1.992 |
|
|
\[ {}\left (\sqrt {x y}-1\right ) x y^{\prime }-\left (\sqrt {x y}+1\right ) y = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
5.008 |
|
|
\[ {}\left (2 x^{\frac {5}{2}} y^{\frac {3}{2}}+x^{2} y-x \right ) y^{\prime }-x^{\frac {3}{2}} y^{\frac {5}{2}}+x y^{2}-y = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
191.197 |
|
|
\[ {}\left (\frac {\operatorname {e1} \left (x +a \right )}{\left (\left (x +a \right )^{2}+y^{2}\right )^{\frac {3}{2}}}+\frac {\operatorname {e2} \left (x -a \right )}{\left (\left (x -a \right )^{2}+y^{2}\right )^{\frac {3}{2}}}\right ) y^{\prime }-y \left (\frac {\operatorname {e1}}{\left (\left (x +a \right )^{2}+y^{2}\right )^{\frac {3}{2}}}+\frac {\operatorname {e2}}{\left (\left (x -a \right )^{2}+y^{2}\right )^{\frac {3}{2}}}\right ) = 0 \] |
1 |
1 |
0 |
unknown |
✓ |
✓ |
67.142 |
|
|
\[ {}x \left (3 \,{\mathrm e}^{x y}+2 \,{\mathrm e}^{-x y}\right ) \left (x y^{\prime }+y\right )+1 = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
35.467 |
|
|
\[ {}\left (\ln \left (y\right )+x \right ) y^{\prime }-1 = 0 \] |
1 |
1 |
1 |
[[_1st_order, _with_exponential_symmetries]] |
✓ |
✓ |
1.513 |
|
|
\[ {}\left (\ln \left (y\right )+2 x -1\right ) y^{\prime }-2 y = 0 \] |
1 |
1 |
1 |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
2.277 |
|
|
\[ {}x \left (2 x^{2} y \ln \left (y\right )+1\right ) y^{\prime }-2 y = 0 \] |
1 |
1 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
1.725 |
|
|
\[ {}x \left (y \ln \left (x y\right )+y-x a \right ) y^{\prime }-y \left (a x \ln \left (x y\right )-y+x a \right ) = 0 \] |
1 |
1 |
1 |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
2.546 |
|
|
\[ {}\left (x \sin \left (y\right )-1\right ) y^{\prime }+\cos \left (y\right ) = 0 \] |
1 |
1 |
2 |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
13.398 |
|
|
\[ {}\left (x^{2} y \sin \left (x y\right )-4 x \right ) y^{\prime }+x y^{2} \sin \left (x y\right )-y = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
33.174 |
|
|
\[ {}\left (-y+x y^{\prime }\right ) \cos \left (\frac {y}{x}\right )^{2}+x = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
4.676 |
|
|
\[ {}\left (y \sin \left (\frac {y}{x}\right )-x \cos \left (\frac {y}{x}\right )\right ) x y^{\prime }-\left (x \cos \left (\frac {y}{x}\right )+y \sin \left (\frac {y}{x}\right )\right ) y = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
4.265 |
|
|
\[ {}y^{\prime } = \frac {y}{x \left (-1+F \left (x y\right ) y\right )} \] |
1 |
1 |
3 |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
1.014 |
|
|
\[ {}y^{\prime } = \frac {\left (\ln \left (y\right )+x^{2}\right ) y}{x} \] |
1 |
1 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
1.096 |
|
|
\[ {}y^{\prime } = \frac {\left (\ln \left (y\right )+x^{3}\right ) y}{x} \] |
1 |
1 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
1.328 |
|
|
\[ {}y^{\prime } = \frac {-\sin \left (2 y\right )+\cos \left (2 y\right ) x^{2}+x^{2}}{2 x} \] |
1 |
1 |
1 |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
1.942 |
|
|
\[ {}y^{\prime } = \frac {y \left (-1+\ln \left (\left (1+x \right ) x \right ) y x^{4}-\ln \left (\left (1+x \right ) x \right ) x^{3}\right )}{x} \] |
1 |
1 |
1 |
[_Bernoulli] |
✓ |
✓ |
3.632 |
|
|
\[ {}y^{\prime } = \frac {-\sin \left (2 y\right )+\cos \left (2 y\right ) x^{3}+x^{3}}{2 x} \] |
1 |
1 |
1 |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
2.125 |
|
|
\[ {}y^{\prime } = \frac {\left (\ln \left (y\right )+x +x^{3}+x^{4}\right ) y}{x} \] |
1 |
1 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
1.543 |
|
|
\[ {}y^{\prime } = \frac {\left (\ln \left (y\right ) x +\ln \left (y\right )+x^{4}\right ) y}{x \left (1+x \right )} \] |
1 |
1 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
2.066 |
|
|
\[ {}y^{\prime } = \frac {\left (\ln \left (y\right ) x +\ln \left (y\right )+x \right ) y}{x \left (1+x \right )} \] |
1 |
1 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
1.83 |
|
|
\[ {}y^{\prime } = \frac {y \left (-1-\ln \left (\frac {\left (-1+x \right ) \left (1+x \right )}{x}\right )+\ln \left (\frac {\left (-1+x \right ) \left (1+x \right )}{x}\right ) x y\right )}{x} \] |
1 |
1 |
1 |
[_Bernoulli] |
✓ |
✓ |
12.734 |
|
|
\[ {}y^{\prime } = -\frac {y \left (1+x y\right )}{x \left (x y+1-y\right )} \] |
1 |
1 |
1 |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
2.964 |
|
|
\[ {}y^{\prime } = \frac {y}{x \left (-1+y+y^{3} x^{2}+x^{3} y^{4}\right )} \] |
1 |
1 |
5 |
[_rational] |
✓ |
✓ |
2.698 |
|
|
\[ {}y^{\prime } = \frac {y \left (-1-\cosh \left (\frac {1+x}{-1+x}\right ) x +\cosh \left (\frac {1+x}{-1+x}\right ) x^{2} y-\cosh \left (\frac {1+x}{-1+x}\right ) x^{2}+\cosh \left (\frac {1+x}{-1+x}\right ) x^{3} y\right )}{x} \] |
1 |
1 |
1 |
[_Bernoulli] |
✓ |
✓ |
34.423 |
|
|
\[ {}y^{\prime } = \frac {y \left (-1-{\mathrm e}^{\frac {1+x}{-1+x}} x +x^{2} {\mathrm e}^{\frac {1+x}{-1+x}} y-x^{2} {\mathrm e}^{\frac {1+x}{-1+x}}+x^{3} {\mathrm e}^{\frac {1+x}{-1+x}} y\right )}{x} \] |
1 |
1 |
1 |
[_Bernoulli] |
✓ |
✓ |
5.467 |
|
|
\[ {}y^{\prime } = \frac {y}{x \left (-1+x y+x y^{3}+y^{4} x \right )} \] |
1 |
1 |
1 |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
4.684 |
|
|
\[ {}y^{\prime } = \frac {y \left (1+x y\right )}{x \left (-x y-1+x^{3} y^{4}\right )} \] |
1 |
1 |
1 |
[_rational] |
✓ |
✓ |
2.575 |
|
|
\[ {}y^{\prime } = \frac {14 x y+12+2 x +x^{3} y^{3}+6 x^{2} y^{2}}{x^{2} \left (x y+2+x \right )} \] |
1 |
1 |
2 |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
3.396 |
|
|
\[ {}y^{\prime } = \frac {-\sin \left (2 y\right )+x \cos \left (2 y\right )+\cos \left (2 y\right ) x^{3}+\cos \left (2 y\right ) x^{4}+x +x^{3}+x^{4}}{2 x} \] |
1 |
1 |
1 |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
7.437 |
|
|
\[ {}y^{\prime } = \frac {y a^{2} x +a +x \,a^{2}+y^{3} a^{3} x^{3}+3 y^{2} a^{2} x^{2}+3 a x y+1}{a^{2} x^{2} \left (a x y+1+x a \right )} \] |
1 |
1 |
2 |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
3.69 |
|
|
\[ {}y^{\prime } = \frac {\left (y-a \ln \left (y\right ) x +x^{2}\right ) y}{\left (-y \ln \left (y\right )-y \ln \left (x \right )-y+x a \right ) x} \] |
1 |
1 |
1 |
[NONE] |
✓ |
✓ |
3.469 |
|
|
\[ {}y^{\prime } = \frac {-y \sin \left (\frac {y}{x}\right )+y \sin \left (\frac {3 y}{2 x}\right ) \cos \left (\frac {y}{2 x}\right )+y \cos \left (\frac {y}{2 x}\right ) \sin \left (\frac {y}{2 x}\right )+2 \sin \left (\frac {y}{x}\right ) x^{3} \cos \left (\frac {y}{2 x}\right ) \sin \left (\frac {y}{2 x}\right )}{2 \cos \left (\frac {y}{x}\right ) \cos \left (\frac {y}{2 x}\right ) \sin \left (\frac {y}{2 x}\right ) x} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘]] |
✓ |
✓ |
38.3 |
|
|
\[ {}y^{\prime } = \frac {-y \sin \left (\frac {y}{x}\right )+y \sin \left (\frac {3 y}{2 x}\right ) \cos \left (\frac {y}{2 x}\right )+y \cos \left (\frac {y}{2 x}\right ) \sin \left (\frac {y}{2 x}\right )+2 \sin \left (\frac {y}{x}\right ) x^{2} \sin \left (\frac {y}{2 x}\right ) \cos \left (\frac {y}{2 x}\right )}{2 \cos \left (\frac {y}{x}\right ) \cos \left (\frac {y}{2 x}\right ) \sin \left (\frac {y}{2 x}\right ) x} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘]] |
✓ |
✓ |
32.956 |
|
|
\[ {}y^{\prime } = \frac {-y \sin \left (\frac {y}{x}\right )+y \sin \left (\frac {3 y}{2 x}\right ) \cos \left (\frac {y}{2 x}\right )+y \cos \left (\frac {y}{2 x}\right ) \sin \left (\frac {y}{2 x}\right )+2 \sin \left (\frac {y}{x}\right ) \cos \left (\frac {y}{2 x}\right ) \sin \left (\frac {y}{2 x}\right ) x +2 \sin \left (\frac {y}{x}\right ) x^{3} \cos \left (\frac {y}{2 x}\right ) \sin \left (\frac {y}{2 x}\right )+2 \sin \left (\frac {y}{x}\right ) x^{4} \cos \left (\frac {y}{2 x}\right ) \sin \left (\frac {y}{2 x}\right )}{2 \cos \left (\frac {y}{x}\right ) \cos \left (\frac {y}{2 x}\right ) \sin \left (\frac {y}{2 x}\right ) x} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘]] |
✓ |
✓ |
54.065 |
|
|
\[ {}y^{\prime } = \frac {-\sin \left (\frac {y}{x}\right ) y x -y \sin \left (\frac {y}{x}\right )+y \sin \left (\frac {3 y}{2 x}\right ) \cos \left (\frac {y}{2 x}\right ) x +y \sin \left (\frac {3 y}{2 x}\right ) \cos \left (\frac {y}{2 x}\right )+y \cos \left (\frac {y}{2 x}\right ) \sin \left (\frac {y}{2 x}\right ) x +y \cos \left (\frac {y}{2 x}\right ) \sin \left (\frac {y}{2 x}\right )+2 \sin \left (\frac {y}{x}\right ) x^{4} \cos \left (\frac {y}{2 x}\right ) \sin \left (\frac {y}{2 x}\right )}{2 \cos \left (\frac {y}{x}\right ) \cos \left (\frac {y}{2 x}\right ) \sin \left (\frac {y}{2 x}\right ) x \left (1+x \right )} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘]] |
✓ |
✓ |
71.731 |
|
|
\[ {}y^{\prime } = \frac {y \sin \left (\frac {3 y}{2 x}\right ) \cos \left (\frac {y}{2 x}\right ) x +y \sin \left (\frac {3 y}{2 x}\right ) \cos \left (\frac {y}{2 x}\right )+y \cos \left (\frac {y}{2 x}\right ) \sin \left (\frac {y}{2 x}\right ) x +y \cos \left (\frac {y}{2 x}\right ) \sin \left (\frac {y}{2 x}\right )-\sin \left (\frac {y}{x}\right ) y x -y \sin \left (\frac {y}{x}\right )+2 \sin \left (\frac {y}{x}\right ) \cos \left (\frac {y}{2 x}\right ) \sin \left (\frac {y}{2 x}\right ) x}{2 \cos \left (\frac {y}{x}\right ) \sin \left (\frac {y}{2 x}\right ) x \cos \left (\frac {y}{2 x}\right ) \left (1+x \right )} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘]] |
✓ |
✓ |
47.311 |
|
|
\[ {}y^{\prime } = \frac {x^{3} y^{3}+6 x^{2} y^{2}+12 x y+8+2 x}{x^{3}} \] |
1 |
2 |
2 |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Abel] |
✓ |
✓ |
3.043 |
|
|
\[ {}y^{\prime } = \frac {y^{3} a^{3} x^{3}+3 y^{2} a^{2} x^{2}+3 a x y+1+x \,a^{2}}{x^{3} a^{3}} \] |
1 |
2 |
2 |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Abel] |
✓ |
✓ |
3.145 |
|
|
\[ {}g \left (x \right ) y^{\prime } = f_{1} \left (x \right ) y+f_{0} \left (x \right ) \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.224 |
|
|
\[ {}x^{2} y^{\prime } = a \,x^{2} y^{2}+b \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational, [_Riccati, _special]] |
✓ |
✓ |
4.039 |
|
|
\[ {}x^{2} y^{\prime } = a \,x^{2} y^{2}+b x y+c \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
✓ |
4.879 |
|
|
\[ {}y^{\prime } = a \ln \left (x \right )^{n} y-a b x \ln \left (x \right )^{n +1} y+b \ln \left (x \right )+b \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
2.198 |
|
|
\[ {}x +y \cos \left (\frac {y}{x}\right )-x \cos \left (\frac {y}{x}\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
1.654 |
|
|
\[ {}y+2 x y^{2}-y^{3} x^{2}+2 x^{2} y y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
✓ |
1.801 |
|
|
\[ {}2 y+3 x y^{2}+\left (2 x^{2} y+x \right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
2.91 |
|
|
\[ {}y+x y^{2}+\left (x -x^{2} y\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
1.565 |
|
|
\[ {}y^{\prime }+\cot \left (x \right ) y = \sec \left (x \right ) \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.151 |
|
|
\[ {}x y^{\prime }+\left (1+x \right ) y = {\mathrm e}^{x} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.905 |
|
|
\[ {}y^{\prime }-\frac {2 y}{1+x} = \left (1+x \right )^{3} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.865 |
|
|
\[ {}\left (x^{3}+x \right ) y^{\prime }+4 x^{2} y = 2 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.918 |
|
|
\[ {}x^{2} y^{\prime }+\left (1-2 x \right ) y = x^{2} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.898 |
|
|
\[ {}\frac {-y+x y^{\prime }}{\sqrt {x^{2}-y^{2}}} = x y^{\prime } \] |
1 |
1 |
1 |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
2.869 |
|
|
\[ {}x^{2}+y^{2}-2 x y y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.666 |
|
|
\[ {}x -y^{2}+2 x y y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
0.887 |
|
|
\[ {}3 x^{2}+6 x y+3 y^{2}+\left (2 x^{2}+3 x y\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
3.418 |
|
|
\[ {}\left (x^{2}+2 y+y^{2}\right ) y^{\prime }+2 x = 0 \] |
1 |
1 |
1 |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
1.183 |
|
|
\[ {}y^{4}+2 y+\left (x y^{3}+2 y^{4}-4 x \right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
1.352 |
|
|
\[ {}x y^{\prime }-y+2 x^{2} y-x^{3} = 0 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.48 |
|
|
\[ {}\left (x +y\right ) y^{\prime }-1 = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
✓ |
0.92 |
|
|
\[ {}y^{\prime }-x^{2} y = x^{5} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.726 |
|
|
\[ {}x y^{\prime }+y+x^{4} y^{4} {\mathrm e}^{x} = 0 \] |
1 |
1 |
3 |
[_Bernoulli] |
✓ |
✓ |
1.786 |
|
|
\[ {}\left (y-x \right ) y^{\prime }+y = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.315 |
|
|
\[ {}x \sin \left (\frac {y}{x}\right )-y \cos \left (\frac {y}{x}\right )+x \cos \left (\frac {y}{x}\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
2.359 |
|
|
\[ {}y^{\prime }+\frac {y}{\left (-x^{2}+1\right )^{\frac {3}{2}}} = \frac {x +\sqrt {-x^{2}+1}}{\left (-x^{2}+1\right )^{2}} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
5.35 |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime }+y = \arctan \left (x \right ) \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.999 |
|
|
\[ {}5 x y-3 y^{3}+\left (3 x^{2}-7 x y^{2}\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
2.938 |
|
|
\[ {}y^{\prime }+y \cos \left (x \right ) = \frac {\sin \left (2 x \right )}{2} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.682 |
|
|
\[ {}y+x y^{2}-x y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
0.929 |
|
|
\[ {}y^{3}-2 x^{2} y+\left (2 x y^{2}-x^{3}\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
4.365 |
|
|
\[ {}2 x^{3} y^{2}-y+\left (2 y^{3} x^{2}-x \right ) y^{\prime } = 0 \] |
1 |
1 |
3 |
[_rational] |
✓ |
✓ |
1.448 |
|
|
\[ {}x y^{\prime }-y^{2} \ln \left (x \right )+y = 0 \] |
1 |
1 |
1 |
[_Bernoulli] |
✓ |
✓ |
1.163 |
|
|
\[ {}x^{\prime }+2 x = t^{2}+4 t +7 \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.774 |
|
|
\[ {}x^{\prime } = \frac {4 t^{2}+3 x^{2}}{2 x t} \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.906 |
|
|
\[ {}y^{\prime } = \frac {y^{2}+2 t y}{t^{2}} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.068 |
|
|
\[ {}x^{\prime } = 2 t^{3} x-6 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.665 |
|
|
\[ {}7 t^{2} x^{\prime } = 3 x-2 t \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.96 |
|
|
\[ {}x^{\prime } = -\frac {2 x}{t}+t \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.79 |
|
|
\[ {}y^{\prime }+y = {\mathrm e}^{t} \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.692 |
|
|
\[ {}x^{\prime }+2 x t = {\mathrm e}^{-t^{2}} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.746 |
|
|
\[ {}\theta ^{\prime } = -a \theta +{\mathrm e}^{b t} \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.01 |
|
|
\[ {}x^{\prime }+\frac {5 x}{t} = t +1 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.069 |
|
|
\[ {}R^{\prime }+\frac {R}{t} = \frac {2}{t^{2}+1} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.167 |
|
|
\[ {}N^{\prime } = N-9 \,{\mathrm e}^{-t} \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.785 |
|
|
\[ {}R^{\prime } = \frac {R}{t}+t \,{\mathrm e}^{-t} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.165 |
|
|
\[ {}y^{\prime }+a y = \sqrt {t +1} \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.173 |
|
|
\[ {}x^{\prime }+\frac {{\mathrm e}^{-t} x}{t} = t \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
2.41 |
|
|
\[ {}x^{\prime } = \frac {2 x}{3 t}+\frac {2 t}{x} \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.877 |
|
|
\[ {}y+y^{\prime } = 1+x \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.169 |
|
|
\[ {}x y^{\prime }+y = x^{3} y^{3} \] |
1 |
1 |
2 |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
1.318 |
|
|
\[ {}y^{\prime }+3 y = 3 x^{2} {\mathrm e}^{-3 x} \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.78 |
|
|
\[ {}y^{\prime }+2 y = 6 \,{\mathrm e}^{x}+4 x \,{\mathrm e}^{-2 x} \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.884 |
|
|
\[ {}y+y^{\prime } = 2 x \,{\mathrm e}^{-x} \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.011 |
|
|
\[ {}y+y^{\prime } = 2 x \,{\mathrm e}^{-x} \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.994 |
|
|
\[ {}\frac {x}{y^{2}}+x +\left (\frac {x^{2}}{y^{3}}+y\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
1.719 |
|
|
\[ {}4 x +3 y^{2}+2 x y y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
1.25 |
|
|
\[ {}y^{2}+2 x y-x^{2} y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.13 |
|
|
\[ {}x +y-x y^{\prime } = 0 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.896 |
|
|
\[ {}2 x y+3 y^{2}-\left (2 x y+x^{2}\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
3.822 |
|
|
\[ {}x^{3}+y^{2} \sqrt {x^{2}+y^{2}}-x y \sqrt {x^{2}+y^{2}}\, y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
2.595 |
|
|
\[ {}x^{2}+3 y^{2}-2 x y y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
2.539 |
|
|
\[ {}3 x^{2}+9 x y+5 y^{2}-\left (6 x^{2}+4 x y\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
5.463 |
|
|
\[ {}y^{\prime }+\frac {3 y}{x} = 6 x^{2} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.88 |
|
|
\[ {}x^{4} y^{\prime }+2 x^{3} y = 1 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.821 |
|
|
\[ {}y^{\prime }+3 y = 3 x^{2} {\mathrm e}^{-3 x} \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.774 |
|
|
\[ {}\left (x^{2}+x -2\right ) y^{\prime }+3 \left (1+x \right ) y = -1+x \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.022 |
|
|
\[ {}x y^{\prime }+x y+y-1 = 0 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.885 |
|
|
\[ {}y+\left (x y^{2}+x -y\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
1.348 |
|
|
\[ {}r^{\prime }+r \tan \left (t \right ) = \cos \left (t \right ) \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.154 |
|
|
\[ {}\cos \left (t \right ) r^{\prime }+r \sin \left (t \right )-\cos \left (t \right )^{4} = 0 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
2.248 |
|
|
\[ {}x y^{\prime }+y = -2 x^{6} y^{4} \] |
1 |
1 |
3 |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
2.023 |
|
|
\[ {}x y^{\prime }-2 y = 2 x^{4} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.138 |
|
|
\[ {}r^{\prime }+r \tan \left (t \right ) = \cos \left (t \right )^{2} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.6 |
|
|
\[ {}x^{\prime }-x = \sin \left (2 t \right ) \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.323 |
|
|
\[ {}y^{\prime }+\frac {y}{2 x} = \frac {x}{y^{3}} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
1.193 |
|
|
\[ {}x y^{\prime }+y = \left (x y\right )^{\frac {3}{2}} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
21.659 |
|
|
\[ {}a y^{\prime }+b y = k \,{\mathrm e}^{-\lambda x} \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.316 |
|
|
\[ {}y+y^{\prime } = 2 \sin \left (x \right )+5 \sin \left (2 x \right ) \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.592 |
|
|
\[ {}x^{2}-2 y+x y^{\prime } = 0 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.873 |
|
|
|
||||||||
|
\[ {}y^{\prime } = \frac {4 x^{3} y^{2}-3 x^{2} y}{x^{3}-2 x^{4} y} \] |
1 |
1 |
2 |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
4.252 |
|
|
\[ {}\left (1+x \right ) y^{\prime }+x y = {\mathrm e}^{-x} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.015 |
|
|
\[ {}y^{\prime } = \frac {2 x^{2}+y^{2}}{2 x y-x^{2}} \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
4.46 |
|
|
\[ {}x^{2}+y^{2}-2 x y y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
2.645 |
|
|
\[ {}5 x y+4 y^{2}+1+\left (2 x y+x^{2}\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
1.426 |
|
|
\[ {}2 x +\tan \left (y\right )+\left (x -x^{2} \tan \left (y\right )\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
✓ |
2.401 |
|
|
\[ {}\left (1+x \right ) y^{2}+y+\left (1+2 x y\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
1.314 |
|
|
\[ {}2 x y^{2}+y+\left (2 y^{3}-x \right ) y^{\prime } = 0 \] |
1 |
1 |
3 |
[_rational] |
✓ |
✓ |
2.313 |
|
|
\[ {}4 x y^{2}+6 y+\left (5 x^{2} y+8 x \right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
5.113 |
|
|
\[ {}z^{\prime } = z \tan \left (y \right )+\sin \left (y \right ) \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.334 |
|
|
\[ {}y^{\prime }+y \,{\mathrm e}^{-x} = 1 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.697 |
|
|
\[ {}x^{\prime }+x \tanh \left (t \right ) = 3 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.259 |
|
|
\[ {}y^{\prime }+2 \cot \left (x \right ) y = 5 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
2.536 |
|
|
\[ {}x^{\prime }+5 x = t \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.875 |
|
|
\[ {}x^{\prime }+\left (a +\frac {1}{t}\right ) x = b \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.571 |
|
|
\[ {}T^{\prime } = -k \left (T-\mu -a \cos \left (\omega \left (t -\phi \right )\right )\right ) \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
2.019 |
|
|
\[ {}{\mathrm e}^{-y} \sec \left (x \right )+2 \cos \left (x \right )-{\mathrm e}^{-y} y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
✓ |
3.376 |
|
|
\[ {}y-x y^{\prime } = x^{2} y y^{\prime } \] |
1 |
1 |
2 |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
3.868 |
|
|
\[ {}x^{\prime }+3 x = {\mathrm e}^{2 t} \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.984 |
|
|
\[ {}y^{\prime } \cos \left (x \right )+y \sin \left (x \right ) = 1 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.909 |
|
|
\[ {}x^{\prime } = x+\sin \left (t \right ) \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.2 |
|
|
\[ {}y^{\prime } = \frac {y}{x +y^{3}} \] |
1 |
1 |
3 |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
1.094 |
|
|
\[ {}y^{\prime }-\frac {y}{1+x}+y^{2} = 0 \] |
1 |
1 |
1 |
[[_1st_order, _with_linear_symmetries], _rational, _Bernoulli] |
✓ |
✓ |
1.172 |
|
|
\[ {}x^{\prime }+5 x = 10 t +2 \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
2.14 |
|
|
\[ {}x^{\prime } = \frac {x}{t}+\frac {x^{2}}{t^{3}} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
1.663 |
|
|
\[ {}x^{\prime }-x \cot \left (t \right ) = 4 \sin \left (t \right ) \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.496 |
|
|
\[ {}x^{2}-y+\left (x^{2} y^{2}+x \right ) y^{\prime } = 0 \] |
1 |
1 |
3 |
[_rational] |
✓ |
✓ |
1.532 |
|
|
\[ {}x y^{\prime }-y^{2} \ln \left (x \right )+y = 0 \] |
1 |
1 |
1 |
[_Bernoulli] |
✓ |
✓ |
1.475 |
|
|
\[ {}\left (-x^{2}+y^{2}\right ) y^{\prime }+2 x y = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
4.112 |
|
|
\[ {}x y^{\prime }+y = x y^{2} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
0.898 |
|
|
\[ {}y^{\prime } \cos \left (x \right )+y \,{\mathrm e}^{x^{2}} = \sinh \left (x \right ) \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
40.495 |
|
|
\[ {}{y^{\prime }}^{2} \sqrt {y} = \sin \left (x \right ) \] |
2 |
2 |
2 |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
4.825 |
|
|
\[ {}y^{\prime }+y \cos \left (x \right ) = \frac {\sin \left (2 x \right )}{2} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.242 |
|
|
\[ {}t -s+t s^{\prime } = 0 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.084 |
|
|
\[ {}x y^{2} y^{\prime } = x^{3}+y^{3} \] |
1 |
1 |
3 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.569 |
|
|
\[ {}x \cos \left (\frac {y}{x}\right ) \left (x y^{\prime }+y\right ) = y \sin \left (\frac {y}{x}\right ) \left (-y+x y^{\prime }\right ) \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
2.424 |
|
|
\[ {}x +2 y+1-\left (2 x -3\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.298 |
|
|
\[ {}\frac {y-x y^{\prime }}{\sqrt {x^{2}+y^{2}}} = m \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
25.151 |
|
|
\[ {}y^{\prime }-\frac {2 y}{1+x} = \left (1+x \right )^{3} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.171 |
|
|
\[ {}y^{\prime }-\frac {a y}{x} = \frac {1+x}{x} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.43 |
|
|
\[ {}\left (-x^{2}+x \right ) y^{\prime }+\left (2 x^{2}-1\right ) y-a \,x^{3} = 0 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.608 |
|
|
\[ {}s^{\prime } \cos \left (t \right )+s \sin \left (t \right ) = 1 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.543 |
|
|
\[ {}s^{\prime }+s \cos \left (t \right ) = \frac {\sin \left (2 t \right )}{2} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.783 |
|
|
\[ {}y^{\prime }-\frac {n y}{x} = {\mathrm e}^{x} x^{n} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.383 |
|
|
\[ {}y^{\prime }+\frac {n y}{x} = a \,x^{-n} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.881 |
|
|
\[ {}y+y^{\prime } = {\mathrm e}^{-x} \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.592 |
|
|
\[ {}y^{\prime }+\frac {\left (1-2 x \right ) y}{x^{2}}-1 = 0 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.192 |
|
|
\[ {}3 y^{2} y^{\prime }-a y^{3}-x -1 = 0 \] |
1 |
1 |
3 |
[_rational, _Bernoulli] |
✓ |
✓ |
1.909 |
|
|
\[ {}y^{\prime } = \frac {2 y}{x}-\sqrt {3} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.802 |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime }-x y-\alpha = 0 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.156 |
|
|
\[ {}x \cos \left (\frac {y}{x}\right ) y^{\prime } = y \cos \left (\frac {y}{x}\right )-x \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
1.165 |
|
|
\[ {}x y^{\prime }-y^{2} \ln \left (x \right )+y = 0 \] |
1 |
1 |
1 |
[_Bernoulli] |
✓ |
✓ |
0.868 |
|
|
\[ {}y^{\prime }-\frac {y}{x} = 1 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.638 |
|
|
\[ {}y+y^{\prime } = x^{2}+2 x -1 \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.628 |
|
|
\[ {}y^{\prime } = x +y \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.621 |
|
|
\[ {}y^{\prime } = \frac {3 y}{\left (x -5\right ) \left (x +3\right )}+{\mathrm e}^{-x} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.183 |
|
|
\[ {}y^{\prime } = \frac {x y}{x^{2}+y^{2}} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
1.0 |
|
|
\[ {}y^{\prime } = \left (x y\right )^{\frac {1}{3}} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
96.204 |
|
|
\[ {}y^{\prime } = \sqrt {\frac {y-4}{x}} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
3.463 |
|
|
\[ {}y^{\prime } = -\frac {y}{x}+y^{\frac {1}{4}} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
2.401 |
|
|
\[ {}y^{\prime } = x y+\frac {1}{x^{2}+1} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.97 |
|
|
\[ {}y^{\prime } = \frac {y}{x}+\cos \left (x \right ) \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.202 |
|
|
\[ {}y^{\prime } = \frac {y}{x}+\tan \left (x \right ) \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
5.545 |
|
|
\[ {}y^{\prime } = \frac {y}{-x^{2}+4}+\sqrt {x} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
3.967 |
|
|
\[ {}y^{\prime } = \frac {y}{-x^{2}+4}+\sqrt {x} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
7.509 |
|
|
\[ {}y^{\prime } = \cot \left (x \right ) y+\csc \left (x \right ) \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.372 |
|
|
\[ {}y^{\prime } = \frac {1-x y}{x^{2}} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.72 |
|
|
\[ {}y^{\prime } = \frac {y^{2}}{1-x y} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
1.053 |
|
|
\[ {}y^{\prime } = 2+x y \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.075 |
|
|
\[ {}y^{\prime } = \frac {y}{-1+x}+x^{2} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.954 |
|
|
\[ {}y^{\prime } = \frac {y}{x}+\sin \left (x^{2}\right ) \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.747 |
|
|
\[ {}y^{\prime } = \frac {2 y}{x}+{\mathrm e}^{x} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
13.245 |
|
|
\[ {}y^{\prime } = \cot \left (x \right ) y+\sin \left (x \right ) \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.187 |
|
|
\[ {}x^{2}-y+x y^{\prime } = 0 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.721 |
|
|
\[ {}y^{\prime } = x +y \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.783 |
|
|
\[ {}y^{\prime } = \frac {y}{-x^{2}+1}+\sqrt {x} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
3.382 |
|
|
\[ {}y^{\prime } = \frac {y}{-x^{2}+1}+\sqrt {x} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.951 |
|
|
\[ {}y^{\prime } = \frac {y}{-x^{2}+1}+\sqrt {x} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
2.293 |
|
|
\[ {}y^{\prime } = \frac {x y}{x^{2}+y^{2}} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
2.948 |
|
|
\[ {}y^{\prime } = \frac {x y}{x^{2}+y^{2}} \] |
1 |
0 |
1 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
1.625 |
|
|
\[ {}y^{\prime } = \frac {x y}{x^{2}+y^{2}} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
3.802 |
|
|
\[ {}y^{\prime } = y+t +1 \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.646 |
|
|
\[ {}y^{\prime } = 2 y-t \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.857 |
|
|
\[ {}v^{\prime } = 2 V \left (t \right )-2 v \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.837 |
|
|
\[ {}y^{\prime } = -4 y+9 \,{\mathrm e}^{-t} \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.707 |
|
|
\[ {}y^{\prime } = -4 y+3 \,{\mathrm e}^{-t} \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.689 |
|
|
\[ {}y^{\prime } = -3 y+4 \cos \left (2 t \right ) \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.989 |
|
|
\[ {}y^{\prime } = 2 y+\sin \left (2 t \right ) \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.91 |
|
|
\[ {}y^{\prime } = 3 y-4 \,{\mathrm e}^{3 t} \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.639 |
|
|
\[ {}y^{\prime } = \frac {y}{2}+4 \,{\mathrm e}^{\frac {t}{2}} \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.738 |
|
|
\[ {}y^{\prime }+2 y = {\mathrm e}^{\frac {t}{3}} \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.986 |
|
|
\[ {}y^{\prime }-2 y = 3 \,{\mathrm e}^{-2 t} \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.96 |
|
|
\[ {}y^{\prime }+y = \cos \left (2 t \right ) \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.137 |
|
|
\[ {}y^{\prime }+3 y = \cos \left (2 t \right ) \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.142 |
|
|
\[ {}y^{\prime }-2 y = 7 \,{\mathrm e}^{2 t} \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.913 |
|
|
\[ {}y^{\prime }+2 y = 3 t^{2}+2 t -1 \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.668 |
|
|
\[ {}y^{\prime }+2 y = t^{2}+2 t +1+{\mathrm e}^{4 t} \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.736 |
|
|
\[ {}y^{\prime }+y = t^{3}+\sin \left (3 t \right ) \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.999 |
|
|
\[ {}y^{\prime }-3 y = 2 t -{\mathrm e}^{4 t} \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.706 |
|
|
\[ {}y^{\prime }+y = \cos \left (2 t \right )+3 \sin \left (2 t \right )+{\mathrm e}^{-t} \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.089 |
|
|
\[ {}y^{\prime } = \frac {3 y}{t}+t^{5} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.684 |
|
|
\[ {}y^{\prime } = -2 t y+4 \,{\mathrm e}^{-t^{2}} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.711 |
|
|
\[ {}y^{\prime }-\frac {2 t y}{t^{2}+1} = 3 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.793 |
|
|
\[ {}y^{\prime }-\frac {2 y}{t} = {\mathrm e}^{t} t^{3} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.738 |
|
|
\[ {}y^{\prime } = \frac {y}{t +1}+4 t^{2}+4 t \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.939 |
|
|
\[ {}y^{\prime } = -2 t y+4 \,{\mathrm e}^{-t^{2}} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.893 |
|
|
\[ {}y^{\prime }-\frac {2 y}{t} = 2 t^{2} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.809 |
|
|
\[ {}y^{\prime }-\frac {3 y}{t} = 2 t^{3} {\mathrm e}^{2 t} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.991 |
|
|
\[ {}y^{\prime } = \sin \left (t \right ) y+4 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.56 |
|
|
\[ {}y^{\prime } = t^{2} y+4 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.383 |
|
|
\[ {}y^{\prime } = \frac {y}{t^{2}}+4 \cos \left (t \right ) \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.75 |
|
|
\[ {}y^{\prime } = y+4 \cos \left (t^{2}\right ) \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.403 |
|
|
\[ {}y^{\prime } = -y \,{\mathrm e}^{-t^{2}}+\cos \left (t \right ) \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
2.383 |
|
|
\[ {}y^{\prime } = \frac {y}{\sqrt {t^{3}-3}}+t \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
10.095 |
|
|
\[ {}y^{\prime } = a t y+4 \,{\mathrm e}^{-t^{2}} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.009 |
|
|
\[ {}y^{\prime } = t^{r} y+4 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
4.659 |
|
|
\[ {}v^{\prime }+\frac {2 v}{5} = 3 \cos \left (2 t \right ) \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.017 |
|
|
\[ {}y^{\prime } = -2 t y+4 \,{\mathrm e}^{-t^{2}} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.653 |
|
|
\[ {}y^{\prime }+2 y = 3 \,{\mathrm e}^{-2 t} \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.64 |
|
|
\[ {}y^{\prime } = y+{\mathrm e}^{-t} \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.622 |
|
|
\[ {}y^{\prime } = 3 y+{\mathrm e}^{7 t} \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.691 |
|
|
\[ {}y^{\prime } = -5 y+\sin \left (3 t \right ) \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.934 |
|
|
\[ {}y^{\prime } = t +\frac {2 y}{t +1} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.773 |
|
|
\[ {}y^{\prime } = -3 y+{\mathrm e}^{-2 t}+t^{2} \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.74 |
|
|
\[ {}y^{\prime } = 2 y+\cos \left (4 t \right ) \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.177 |
|
|
\[ {}y^{\prime } = 3 y+2 \,{\mathrm e}^{3 t} \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.948 |
|
|
\[ {}y^{\prime }+5 y = 3 \,{\mathrm e}^{-5 t} \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.929 |
|
|
\[ {}y^{\prime } = 2 t y+3 t \,{\mathrm e}^{t^{2}} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.978 |
|
|
\[ {}y^{\prime }+4 y = {\mathrm e}^{2 x} \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.718 |
|
|
\[ {}y^{\prime } = 3 x -y \sin \left (x \right ) \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.444 |
|
|
\[ {}y^{\prime }+4 y = x^{2} \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.684 |
|
|
\[ {}y y^{\prime } = 3 \sqrt {x y^{2}+9 x} \] |
1 |
1 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
2.664 |
|
|
\[ {}x^{2} y^{\prime }+3 x^{2} y = \sin \left (x \right ) \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.36 |
|
|
\[ {}y^{\prime } = 1+x y+3 y \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.843 |
|
|
\[ {}x y^{\prime }+\cos \left (x^{2}\right ) = 827 y \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
36.53 |
|
|
\[ {}y^{\prime }+2 y = 20 \,{\mathrm e}^{3 x} \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.733 |
|
|
\[ {}y^{\prime } = 4 y+16 x \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.691 |
|
|
\[ {}x y^{\prime }+3 y-10 x^{2} = 0 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.754 |
|
|
\[ {}x y^{\prime } = \sqrt {x}+3 y \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.779 |
|
|
\[ {}y^{\prime } \cos \left (x \right )+y \sin \left (x \right ) = \cos \left (x \right )^{2} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.528 |
|
|
\[ {}x y^{\prime }+\left (5 x +2\right ) y = \frac {20}{x} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.84 |
|
|
\[ {}2 \sqrt {x}\, y^{\prime }+y = 2 x \,{\mathrm e}^{-\sqrt {x}} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
3.005 |
|
|
\[ {}y^{\prime }+5 y = {\mathrm e}^{-3 x} \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.95 |
|
|
\[ {}x y^{\prime }+3 y = 20 x^{2} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.924 |
|
|
\[ {}x y^{\prime } = y+x^{2} \cos \left (x \right ) \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.349 |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime } = x \left (3+3 x^{2}-y\right ) \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.303 |
|
|
\[ {}y^{\prime }+6 x y = \sin \left (x \right ) \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.661 |
|
|
\[ {}x^{2} y^{\prime }+x y = \sqrt {x}\, \sin \left (x \right ) \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
5.733 |
|
|
\[ {}-y+x y^{\prime } = x^{2} {\mathrm e}^{-x^{2}} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.387 |
|
|
\[ {}y^{\prime } = \frac {\left (3 x -2 y\right )^{2}+1}{3 x -2 y}+\frac {3}{2} \] |
1 |
1 |
2 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.398 |
|
|
\[ {}y^{\prime } = \frac {y}{x}+\frac {x}{y} \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.075 |
|
|
\[ {}\cos \left (\frac {y}{x}\right ) \left (y^{\prime }-\frac {y}{x}\right ) = 1+\sin \left (\frac {y}{x}\right ) \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
2.826 |
|
|
\[ {}y^{\prime }-\frac {y}{x} = \frac {1}{y} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
1.112 |
|
|
\[ {}y^{\prime } = \frac {y}{x}+\frac {x^{2}}{y^{2}} \] |
1 |
1 |
3 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.426 |
|
|
\[ {}\left (y-x \right ) y^{\prime } = 1 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
✓ |
1.053 |
|
|
\[ {}\left (x +y\right ) y^{\prime } = y \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.184 |
|
|
\[ {}\left (2 x y+2 x^{2}\right ) y^{\prime } = x^{2}+2 x y+2 y^{2} \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
1.078 |
|
|
\[ {}y^{\prime }+\frac {y}{x} = y^{3} x^{2} \] |
1 |
1 |
2 |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
1.13 |
|
|
\[ {}y^{\prime }+3 y = \frac {28 \,{\mathrm e}^{2 x}}{y^{3}} \] |
1 |
1 |
4 |
[[_1st_order, _with_linear_symmetries], _Bernoulli] |
✓ |
✓ |
1.609 |
|
|
\[ {}\cos \left (y\right ) y^{\prime } = {\mathrm e}^{-x}-\sin \left (y\right ) \] |
1 |
1 |
1 |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
1.832 |
|
|
\[ {}y+\left (y^{4}-3 x \right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
4.097 |
|
|
\[ {}1+\left (1-x \tan \left (y\right )\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
1.204 |
|
|
\[ {}2 y^{3}+\left (4 x^{3} y^{3}-3 x y^{2}\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
6.408 |
|
|
\[ {}4 x y+\left (3 x^{2}+5 y\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.204 |
|
|
\[ {}6+12 x^{2} y^{2}+\left (7 x^{3} y+\frac {x}{y}\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
3.278 |
|
|
\[ {}x y^{\prime } = 2 y-6 x^{3} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.721 |
|
|
\[ {}4 x y-6+x^{2} y^{\prime } = 0 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.74 |
|
|
\[ {}x^{3}+y^{3}+x y^{2} y^{\prime } = 0 \] |
1 |
1 |
3 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
2.127 |
|
|
\[ {}3 y-x^{3}+x y^{\prime } = 0 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.747 |
|
|
\[ {}2+2 x^{2}-2 x y+\left (x^{2}+1\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.832 |
|
|
\[ {}x y y^{\prime } = 2 x^{2}+2 y^{2} \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.588 |
|
|
\[ {}1-\left (2 y+x \right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
✓ |
1.086 |
|
|
\[ {}y^{\prime }-3 y = 12 \,{\mathrm e}^{2 x} \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.749 |
|
|
\[ {}x y^{3} y^{\prime } = y^{4}-x^{2} \] |
1 |
1 |
4 |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
1.307 |
|
|
\[ {}y^{\prime } = 4 y-\frac {16 \,{\mathrm e}^{4 x}}{y^{2}} \] |
1 |
1 |
3 |
[[_1st_order, _with_linear_symmetries], _Bernoulli] |
✓ |
✓ |
1.252 |
|
|
\[ {}2 y-6 x +\left (1+x \right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.564 |
|
|
\[ {}y y^{\prime }-x y^{2} = 6 x \,{\mathrm e}^{4 x^{2}} \] |
1 |
1 |
2 |
[_Bernoulli] |
✓ |
✓ |
2.217 |
|
|
\[ {}y^{\prime }+2 y = \sin \left (x \right ) \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.923 |
|
|
\[ {}y^{\prime } = x \left (6 y+{\mathrm e}^{x^{2}}\right ) \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.832 |
|
|
\[ {}x^{2} y^{\prime }+3 x y = 6 \,{\mathrm e}^{-x^{2}} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.908 |
|
|
\[ {}x y^{\prime }+3 y = {\mathrm e}^{2 x} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.904 |
|
|
\[ {}y+y^{\prime } = \sin \left (x \right ) \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.62 |
|
|
\[ {}y^{\prime } = -\frac {2 y}{x}-3 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
2.029 |
|
|
\[ {}y^{\prime }+y = \sin \left (t \right ) \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
2.041 |
|
|
\[ {}y^{\prime } = \frac {y^{2}+2 x y}{x^{2}} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.803 |
|
|
\[ {}y^{\prime }-y = \sin \left (x \right ) \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.642 |
|
|
\[ {}y^{\prime }+2 y = x^{2} \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.708 |
|
|
\[ {}y^{\prime } = y+\frac {1}{1-t} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.396 |
|
|
\[ {}t^{3} y^{\prime }+t^{4} y = 2 t^{3} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
2.265 |
|
|
\[ {}2 y^{\prime }+t y = \ln \left (t \right ) \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
5.365 |
|
|
\[ {}y^{\prime }+y \sec \left (t \right ) = t \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
5.944 |
|
|
\[ {}y^{\prime }+\frac {y}{t -3} = \frac {1}{-1+t} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.927 |
|
|
\[ {}\left (t -2\right ) y^{\prime }+\left (t^{2}-4\right ) y = \frac {1}{2+t} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
8.855 |
|
|
\[ {}y^{\prime }+\frac {y}{\sqrt {-t^{2}+4}} = t \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
5.844 |
|
|
\[ {}y^{\prime }+\frac {y}{\sqrt {-t^{2}+4}} = t \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
7.891 |
|
|
\[ {}y^{\prime }+y \tan \left (t \right ) = \sin \left (t \right ) \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
2.844 |
|
|
\[ {}y^{\prime } = \frac {t^{3}}{y \sqrt {\left (1-y^{2}\right ) \left (t^{4}+9\right )}} \] |
1 |
1 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
3.423 |
|
|
\[ {}y^{\prime } = \sqrt {\frac {y}{t}} \] |
1 |
1 |
4 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
123.202 |
|
|
\[ {}y^{\prime }-y = 2 \,{\mathrm e}^{-t} \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.894 |
|
|
\[ {}y^{\prime }-y = 2 \cos \left (t \right ) \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.11 |
|
|
|
||||||||
|
\[ {}y^{\prime }-y = t^{2}-2 t \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.833 |
|
|
\[ {}y^{\prime }-y = 4 t \,{\mathrm e}^{-t} \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.948 |
|
|
\[ {}y^{\prime }-\frac {2 t y}{t^{2}+1} = 2 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.048 |
|
|
\[ {}y^{\prime }-\frac {4 t y}{4 t^{2}+1} = 4 t \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.078 |
|
|
\[ {}y^{\prime } = 2 x +\frac {x y}{x^{2}-1} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.14 |
|
|
\[ {}y^{\prime }+y \cot \left (t \right ) = \cos \left (t \right ) \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.421 |
|
|
\[ {}y^{\prime }-\frac {3 t y}{t^{2}-4} = t \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.097 |
|
|
\[ {}y^{\prime }-\frac {4 t y}{4 t^{2}-9} = t \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.108 |
|
|
\[ {}y^{\prime }-\frac {9 x y}{9 x^{2}+49} = x \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.084 |
|
|
\[ {}y^{\prime }+2 \cot \left (x \right ) y = \cos \left (x \right ) \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.288 |
|
|
\[ {}y^{\prime }+x y = x^{3} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.894 |
|
|
\[ {}y^{\prime } = \frac {1}{x +y^{2}} \] |
1 |
1 |
1 |
[[_1st_order, _with_exponential_symmetries]] |
✓ |
✓ |
0.976 |
|
|
\[ {}y^{\prime }-x = y \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.776 |
|
|
\[ {}y-\left (x +3 y^{2}\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
1.014 |
|
|
\[ {}p^{\prime } = t^{3}+\frac {p}{t} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.995 |
|
|
\[ {}v^{\prime }+v = {\mathrm e}^{-s} \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.904 |
|
|
\[ {}y^{\prime }-y = 4 \,{\mathrm e}^{t} \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.171 |
|
|
\[ {}y^{\prime }+y = {\mathrm e}^{-t} \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.116 |
|
|
\[ {}y^{\prime }+3 t^{2} y = {\mathrm e}^{-t^{3}} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.23 |
|
|
\[ {}x^{\prime } = x+t +1 \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.076 |
|
|
\[ {}y^{\prime } = {\mathrm e}^{2 t}+2 y \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.102 |
|
|
\[ {}y^{\prime }-\frac {y}{t} = \ln \left (t \right ) \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.043 |
|
|
\[ {}y^{\prime }-y = \sin \left (2 t \right ) \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.211 |
|
|
\[ {}y^{\prime }+y = 5 \,{\mathrm e}^{2 t} \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.919 |
|
|
\[ {}y^{\prime }+y = {\mathrm e}^{-t} \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.858 |
|
|
\[ {}y^{\prime }+y = 2-{\mathrm e}^{2 t} \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.918 |
|
|
\[ {}y^{\prime }-5 y = t \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.876 |
|
|
\[ {}y^{\prime }+3 y = 27 t^{2}+9 \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.898 |
|
|
\[ {}y^{\prime }-\frac {y}{2} = 5 \cos \left (t \right )+2 \,{\mathrm e}^{t} \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.453 |
|
|
\[ {}y^{\prime }+4 y = 8 \cos \left (4 t \right ) \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.347 |
|
|
\[ {}y^{\prime }+10 y = 2 \,{\mathrm e}^{t} \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.939 |
|
|
\[ {}y^{\prime }-3 y = 27 t^{2} \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.893 |
|
|
\[ {}y^{\prime }-y = 2 \,{\mathrm e}^{t} \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.849 |
|
|
\[ {}y^{\prime }+y = 4+3 \,{\mathrm e}^{t} \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.959 |
|
|
\[ {}y^{\prime }+y = 2 \cos \left (t \right )+t \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.183 |
|
|
\[ {}y^{\prime }+\frac {y}{2} = \sin \left (t \right ) \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.462 |
|
|
\[ {}y^{\prime }-\frac {y}{2} = \sin \left (t \right ) \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.385 |
|
|
\[ {}y^{\prime }+y = t \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.079 |
|
|
\[ {}y^{\prime }+y = \sin \left (t \right ) \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.336 |
|
|
\[ {}y^{\prime }+y = \cos \left (t \right ) \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.329 |
|
|
\[ {}y^{\prime }+y = {\mathrm e}^{t} \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.079 |
|
|
\[ {}y \sin \left (2 t \right )+\left (\sqrt {y}+\cos \left (2 t \right )\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
11.048 |
|
|
\[ {}y+\left (2 t -y \,{\mathrm e}^{y}\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
1.392 |
|
|
\[ {}2 t y+y^{2}-t^{2} y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.324 |
|
|
\[ {}y+2 t^{2}+\left (t^{2} y-t \right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
1.399 |
|
|
\[ {}5 t y+4 y^{2}+1+\left (t^{2}+2 t y\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
1.58 |
|
|
\[ {}2 t +\tan \left (y\right )+\left (t -t^{2} \tan \left (y\right )\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
✓ |
2.592 |
|
|
\[ {}y^{\prime }-\frac {y}{2} = \frac {t}{y} \] |
1 |
1 |
2 |
[_rational, _Bernoulli] |
✓ |
✓ |
1.296 |
|
|
\[ {}2 t y^{\prime }-y = 2 t y^{3} \cos \left (t \right ) \] |
1 |
1 |
2 |
[_Bernoulli] |
✓ |
✓ |
35.666 |
|
|
\[ {}y^{\prime }-2 y = \frac {\cos \left (t \right )}{\sqrt {y}} \] |
1 |
1 |
1 |
[_Bernoulli] |
✓ |
✓ |
10.556 |
|
|
\[ {}y^{\prime }-\frac {y}{t} = t y^{2} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
1.211 |
|
|
\[ {}\frac {2}{t}+\frac {1}{y}+\frac {t y^{\prime }}{y^{2}} = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.791 |
|
|
\[ {}2 y-3 t +t y^{\prime } = 0 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.466 |
|
|
\[ {}t y-y^{2}+t \left (t -3 y\right ) y^{\prime } = 0 \] |
1 |
1 |
3 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
3.457 |
|
|
\[ {}t^{3}+y^{3}-t y^{2} y^{\prime } = 0 \] |
1 |
1 |
3 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
2.089 |
|
|
\[ {}t -y+t y^{\prime } = 0 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.949 |
|
|
\[ {}y^{\prime } = \frac {4 y^{2}-t^{2}}{2 t y} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
2.464 |
|
|
\[ {}t +y-t y^{\prime } = 0 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.295 |
|
|
\[ {}t^{3}+y^{2} \sqrt {t^{2}+y^{2}}-t y \sqrt {t^{2}+y^{2}}\, y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
5.021 |
|
|
\[ {}y^{3}-t^{3}-t y^{2} y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.701 |
|
|
\[ {}y = t \left (y^{\prime }+1\right )+2 y^{\prime }+1 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.308 |
|
|
\[ {}y^{\prime } = \frac {y^{2}-t^{2}}{t y} \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.677 |
|
|
\[ {}y \sin \left (\frac {t}{y}\right )-\left (t +t \sin \left (\frac {t}{y}\right )\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
4.586 |
|
|
\[ {}y^{\prime }+3 y = -10 \sin \left (t \right ) \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.303 |
|
|
\[ {}y-x +y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.888 |
|
|
\[ {}r^{\prime } = \frac {r^{2}+t^{2}}{r t} \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.603 |
|
|
\[ {}x^{\prime } = \frac {5 t x}{x^{2}+t^{2}} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
5.543 |
|
|
\[ {}y^{\prime }+y = \frac {{\mathrm e}^{t}}{y^{2}} \] |
1 |
1 |
3 |
[[_1st_order, _with_linear_symmetries], _Bernoulli] |
✓ |
✓ |
1.687 |
|
|
\[ {}y-t y^{\prime } = 2 y^{2} \ln \left (t \right ) \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘], _Bernoulli] |
✓ |
✓ |
1.624 |
|
|
\[ {}y^{\prime }-4 y = t^{2} \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.99 |
|
|
\[ {}y^{\prime }+y = \cos \left (2 t \right ) \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.553 |
|
|
\[ {}y^{\prime }-y = {\mathrm e}^{4 t} \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.167 |
|
|
\[ {}y^{\prime }+4 y = {\mathrm e}^{-4 t} \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.237 |
|
|
\[ {}y^{\prime }+4 y = t \,{\mathrm e}^{-4 t} \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.985 |
|
|
\[ {}y^{\prime } = \frac {y+1}{x -y} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.871 |
|
|
\[ {}y^{\prime }+2 y = {\mathrm e}^{x} \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.125 |
|
|
\[ {}y^{\prime } = x +y \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.951 |
|
|
\[ {}y^{\prime } = y-x \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.972 |
|
|
\[ {}y^{\prime } = \frac {x}{2}-y+\frac {3}{2} \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.108 |
|
|
\[ {}y^{\prime } = y-x^{2} \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.992 |
|
|
\[ {}y^{\prime } = x^{2}+2 x -y \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.021 |
|
|
\[ {}y^{\prime } = 2 x -y \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.009 |
|
|
\[ {}y^{\prime } = y+x^{2} \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.995 |
|
|
\[ {}y^{\prime } = x +y \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.161 |
|
|
\[ {}y^{\prime } = 2 y-2 x^{2}-3 \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.28 |
|
|
\[ {}y^{\prime } = x a +b y+c \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.722 |
|
|
\[ {}x y^{\prime }+y = a \left (1+x y\right ) \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.595 |
|
|
\[ {}x -y+x y^{\prime } = 0 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.218 |
|
|
\[ {}x +y-2+\left (1-x \right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.473 |
|
|
\[ {}4 y^{6}+x^{3} = 6 x y^{5} y^{\prime } \] |
1 |
1 |
6 |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
2.838 |
|
|
\[ {}y^{\prime }+2 y = {\mathrm e}^{-x} \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.133 |
|
|
\[ {}y^{\prime }-2 x y = 2 x \,{\mathrm e}^{x^{2}} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.074 |
|
|
\[ {}y^{\prime }+2 x y = {\mathrm e}^{-x^{2}} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.083 |
|
|
\[ {}x y^{\prime }-2 y = x^{3} \cos \left (x \right ) \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.51 |
|
|
\[ {}y^{\prime }-y \tan \left (x \right ) = \frac {1}{\cos \left (x \right )^{3}} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
9.075 |
|
|
\[ {}y^{\prime } x \ln \left (x \right )-y = 3 x^{3} \ln \left (x \right )^{2} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.676 |
|
|
\[ {}\left (2 x -y^{2}\right ) y^{\prime } = 2 y \] |
1 |
1 |
2 |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
1.271 |
|
|
\[ {}\left (\frac {{\mathrm e}^{-y^{2}}}{2}-x y\right ) y^{\prime }-1 = 0 \] |
1 |
1 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
2.204 |
|
|
\[ {}y^{\prime }-{\mathrm e}^{x} y = 2 x \,{\mathrm e}^{{\mathrm e}^{x}} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.138 |
|
|
\[ {}y^{\prime }+x y \,{\mathrm e}^{x} = {\mathrm e}^{\left (1-x \right ) {\mathrm e}^{x}} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.222 |
|
|
\[ {}y^{\prime }-y \ln \left (2\right ) = 2^{\sin \left (x \right )} \left (\cos \left (x \right )-1\right ) \ln \left (2\right ) \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
2.681 |
|
|
\[ {}y^{\prime }-y = -2 \,{\mathrm e}^{-x} \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
3.295 |
|
|
\[ {}y^{\prime } \sin \left (x \right )-y \cos \left (x \right ) = -\frac {\sin \left (x \right )^{2}}{x^{2}} \] |
1 |
0 |
1 |
[_linear] |
✗ |
N/A |
4.23 |
|
|
\[ {}x^{2} y^{\prime } \cos \left (\frac {1}{x}\right )-y \sin \left (\frac {1}{x}\right ) = -1 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
5.698 |
|
|
\[ {}2 x y^{\prime }-y = 1-\frac {2}{\sqrt {x}} \] |
1 |
0 |
1 |
[_linear] |
✗ |
N/A |
2.308 |
|
|
\[ {}2 x y^{\prime }+y = \left (x^{2}+1\right ) {\mathrm e}^{x} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✗ |
4.82 |
|
|
\[ {}3 x y^{2} y^{\prime }-2 y^{3} = x^{3} \] |
1 |
1 |
3 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
2.863 |
|
|
\[ {}\left (x^{3}+{\mathrm e}^{y}\right ) y^{\prime } = 3 x^{2} \] |
1 |
1 |
1 |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
1.671 |
|
|
\[ {}2 y^{\prime } \ln \left (x \right )+\frac {y}{x} = \frac {\cos \left (x \right )}{y} \] |
1 |
1 |
2 |
[_Bernoulli] |
✓ |
✓ |
10.419 |
|
|
\[ {}\left (1+x^{2}+y^{2}\right ) y^{\prime }+x y = 0 \] |
1 |
1 |
4 |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
1.496 |
|
|
\[ {}y^{\prime }-\tan \left (y\right ) = \frac {{\mathrm e}^{x}}{\cos \left (y\right )} \] |
1 |
1 |
0 |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
3.112 |
|
|
\[ {}\cos \left (y\right ) y^{\prime }+\sin \left (y\right ) = 1+x \] |
1 |
1 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
4.095 |
|
|
\[ {}1-x^{2} y+x^{2} \left (y-x \right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
1.543 |
|
|
\[ {}x^{2}+y-x y^{\prime } = 0 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.183 |
|
|
\[ {}x +y^{2}-2 x y y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
1.652 |
|
|
\[ {}2 x^{2} y+2 y+5+\left (2 x^{3}+2 x \right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.444 |
|
|
\[ {}x^{4} \ln \left (x \right )-2 x y^{3}+3 x^{2} y^{2} y^{\prime } = 0 \] |
1 |
1 |
3 |
[_Bernoulli] |
✓ |
✓ |
1.855 |
|
|
\[ {}x +\sin \left (x \right )+\sin \left (y\right )+\cos \left (y\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
4.541 |
|
|
\[ {}2 x y^{2}-3 y^{3}+\left (7-3 x y^{2}\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[_rational] |
✓ |
✓ |
1.615 |
|
|
\[ {}x^{2}+y^{2}+1-2 x y y^{\prime } = 0 \] |
1 |
1 |
2 |
[_rational, _Bernoulli] |
✓ |
✓ |
1.676 |
|
|
\[ {}x -x y+\left (y+x^{2}\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
4.663 |
|
|
\[ {}x^{2} y^{\prime } = x^{2} y^{2}+x y+1 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
✓ |
0.944 |
|
|
\[ {}x \sin \left (x \right ) y^{\prime }+\left (\sin \left (x \right )-x \cos \left (x \right )\right ) y = \sin \left (x \right ) \cos \left (x \right )-x \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
5.52 |
|
|
\[ {}y-x y^{2} \ln \left (x \right )+x y^{\prime } = 0 \] |
1 |
1 |
1 |
[_Bernoulli] |
✓ |
✓ |
0.984 |
|
|
\[ {}y^{\prime } = \frac {1}{2 x -y^{2}} \] |
1 |
1 |
1 |
[[_1st_order, _with_exponential_symmetries]] |
✓ |
✓ |
0.829 |
|
|
\[ {}x y y^{\prime }-y^{2} = x^{4} \] |
1 |
1 |
2 |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
0.998 |
|
|
\[ {}\left (2 x -1\right ) y^{\prime }-2 y = \frac {1-4 x}{x^{2}} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.589 |
|
|
\[ {}x y^{2} y^{\prime }-y^{3} = \frac {x^{4}}{3} \] |
1 |
1 |
3 |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
1.174 |
|
|
\[ {}x^{2}+y^{2}-x y y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.013 |
|
|
\[ {}y+x y^{2}-x y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
0.939 |
|
|
\[ {}x^{2}+y^{2}+2 x +2 y y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
1.345 |
|
|
\[ {}\left (x -2 x y-y^{2}\right ) y^{\prime }+y^{2} = 0 \] |
1 |
1 |
1 |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
1.728 |
|
|
\[ {}y \cos \left (x \right )+\left (2 y-\sin \left (x \right )\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.917 |
|
|
\[ {}x -y^{2}+2 x y y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
0.971 |
|
|
\[ {}x y^{\prime }+y = y^{2} \ln \left (x \right ) \] |
1 |
1 |
1 |
[_Bernoulli] |
✓ |
✓ |
1.35 |
|
|
\[ {}y^{\prime } = \sqrt {\frac {9 y^{2}-6 y+2}{x^{2}-2 x +5}} \] |
1 |
1 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
2.1 |
|
|
|
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