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 by inspection (trials over selected candidates). This is tried only when the three known methods to find integrating factor fail. Number of problems in this table is 105
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) |
|
\[ {}\left (x -y\right ) y^{\prime } = x +y \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.955 |
|
|
\[ {}x \left (x +y\right ) y^{\prime } = y \left (x -y\right ) \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
1.985 |
|
|
\[ {}x^{2} y^{\prime } = x y+y^{2} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.517 |
|
|
\[ {}x y+y^{2}-x^{2} y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.591 |
|
|
\[ {}x^{2} y^{\prime } = x y+3 y^{2} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.075 |
|
|
\[ {}y^{\prime } = \frac {x +y}{x -y} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.519 |
|
|
\[ {}y^{\prime } = \frac {x y+y^{2}}{x^{2}} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.893 |
|
|
\[ {}y^{\prime } = \frac {x +y}{x -y} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.582 |
|
|
\[ {}y^{\prime } = \frac {2 y+x}{y+2 x} \] |
1 |
1 |
3 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
3.706 |
|
|
\[ {}y^{\prime } = \frac {t +y}{t -y} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.089 |
|
|
\[ {}\left (x +y\right ) y^{\prime }+x = y \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.139 |
|
|
\[ {}\left (x y-x^{2}\right ) y^{\prime }-y^{2} = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
2.395 |
|
|
\[ {}y^{\prime } = \frac {x +y}{x -y} \] |
1 |
0 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
3.561 |
|
|
\[ {}\left (3 x y-2 x^{2}\right ) y^{\prime } = 2 y^{2}-x y \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
6.517 |
|
|
\[ {}\left (x^{2}+y^{2}+x \right ) y^{\prime } = y \] |
1 |
1 |
1 |
[_rational] |
✓ |
✓ |
2.014 |
|
|
\[ {}x^{2} y^{\prime }+y^{2} = x y \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.638 |
|
|
\[ {}2 x +y-\left (x -2 y\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.431 |
|
|
\[ {}x y-y^{2}-x^{2} y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
2.412 |
|
|
\[ {}x y^{\prime }+y \ln \left (x \right ) = y \ln \left (y\right ) \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
2.011 |
|
|
\[ {}2 x \left (y+2 x \right ) y^{\prime } = y \left (4 x -y\right ) \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
1.148 |
|
|
\[ {}x y^{\prime } = x^{5}+x^{3} y^{2}+y \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘], _rational, _Riccati] |
✓ |
✓ |
1.711 |
|
|
\[ {}\left (x +y\right ) y^{\prime } = y-x \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.237 |
|
|
\[ {}\left (x y-x^{2}\right ) y^{\prime } = y^{2} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
1.762 |
|
|
\[ {}x y^{\prime } = y \left (1+\ln \left (y\right )-\ln \left (x \right )\right ) \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
3.218 |
|
|
\[ {}x^{2}+y+y^{2}-x y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘], _rational, _Riccati] |
✓ |
✓ |
1.753 |
|
|
\[ {}x y^{\prime } = x^{2}+y \left (y+1\right ) \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘], _rational, _Riccati] |
✓ |
✓ |
1.05 |
|
|
\[ {}x y^{\prime } = y+\left (x^{2}-y^{2}\right ) f \left (x \right ) \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘], _Riccati] |
✓ |
✓ |
1.607 |
|
|
\[ {}x y^{\prime }+\left (1-\ln \left (x \right )-\ln \left (y\right )\right ) y = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
1.304 |
|
|
\[ {}x^{2} y^{\prime } = \left (a y+x \right ) y \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
0.651 |
|
|
\[ {}\left (x +y\right ) y^{\prime }+x -y = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
0.908 |
|
|
\[ {}\left (y+2 x \right ) y^{\prime }+x -2 y = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
0.872 |
|
|
\[ {}\left (2 y+x \right ) y^{\prime }+2 x -y = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
0.891 |
|
|
\[ {}\left (x +4 y\right ) y^{\prime }+4 x -y = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
0.891 |
|
|
\[ {}\left (x a +b y\right ) y^{\prime } = b x +a y \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.796 |
|
|
\[ {}x \left (x -y\right ) y^{\prime }+y^{2} = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
0.925 |
|
|
\[ {}\left (x^{2}+y^{2}+x \right ) y^{\prime } = y \] |
1 |
1 |
1 |
[_rational] |
✓ |
✓ |
0.873 |
|
|
\[ {}x \left (x +6 y^{2}\right ) y^{\prime }+x y-3 y^{3} = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
1.339 |
|
|
\[ {}x \left (x^{2}-6 y^{2}\right ) y^{\prime } = 4 \left (x^{2}+3 y^{2}\right ) y \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
3.709 |
|
|
\[ {}x \left (1+x y^{2}\right ) y^{\prime } = \left (2-3 x y^{2}\right ) y \] |
1 |
1 |
2 |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
3.484 |
|
|
\[ {}\left (x \,a^{2}+\left (x^{2}-y^{2}\right ) y\right ) y^{\prime }+x \left (x^{2}-y^{2}\right ) = y a^{2} \] |
1 |
1 |
0 |
[_rational] |
✓ |
✓ |
1.569 |
|
|
\[ {}x \left (x -y^{3}\right ) y^{\prime } = \left (3 x +y^{3}\right ) y \] |
1 |
1 |
3 |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
3.442 |
|
|
\[ {}x \left (x +y+2 y^{3}\right ) y^{\prime } = y \left (x -y\right ) \] |
1 |
1 |
1 |
[_rational] |
✓ |
✓ |
1.237 |
|
|
\[ {}x \left (x -y \tan \left (\frac {y}{x}\right )\right ) y^{\prime }+\left (x +y \tan \left (\frac {y}{x}\right )\right ) y = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
1.917 |
|
|
\[ {}x +y-\left (x -y\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.359 |
|
|
\[ {}y+x \ln \left (\frac {y}{x}\right ) y^{\prime }-2 x y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
3.474 |
|
|
\[ {}x y-y^{2}-x^{2} y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.472 |
|
|
\[ {}x^{2}-y^{2}-y-\left (x^{2}-y^{2}-x \right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
✓ |
2.471 |
|
|
\[ {}y-\left (x^{2}+y^{2}+x \right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_rational] |
✓ |
✓ |
1.223 |
|
|
\[ {}\left (2 x y^{3}+x y+x^{2}\right ) y^{\prime }-x y+y^{2} = 0 \] |
1 |
1 |
1 |
[_rational] |
✓ |
✓ |
1.994 |
|
|
\[ {}x^{2} y^{\prime }+y^{2}-x y = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.135 |
|
|
\[ {}y^{2}-x y+\left (x^{2}+x y\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
1.007 |
|
|
\[ {}y^{\prime } = \frac {2 y^{2}}{x}+\frac {y}{x}-2 x \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘], _rational, _Riccati] |
✓ |
✓ |
1.372 |
|
|
\[ {}x^{2} y^{\prime } = y^{2}-x y y^{\prime } \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
5.341 |
|
|
\[ {}x^{2} y^{\prime }+y^{2} = x y y^{\prime } \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
1.405 |
|
|
\[ {}y \sqrt {x^{2}+y^{2}}-x \left (x +\sqrt {x^{2}+y^{2}}\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _dAlembert] |
✓ |
✓ |
4.592 |
|
|
\[ {}y \left (x -2 y\right )-x^{2} y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.345 |
|
|
\[ {}x^{2} y^{\prime }+y^{2}-x y = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
0.875 |
|
|
\[ {}x +y-\left (x -y\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.274 |
|
|
\[ {}-y+x y^{\prime } = x^{2}+y^{2} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘], _rational, _Riccati] |
✓ |
✓ |
1.256 |
|
|
\[ {}x +y y^{\prime }+y-x y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.022 |
|
|
\[ {}x y^{\prime } = y+x^{2}+y^{2} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘], _rational, _Riccati] |
✓ |
✓ |
1.287 |
|
|
\[ {}y^{\prime } = \frac {y^{2}}{x y-x^{2}} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
1.466 |
|
|
\[ {}y^{\prime } = \frac {2 y+x}{2 x -y} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
3.238 |
|
|
\[ {}y^{\prime } = \frac {x +y}{x -y} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
6.302 |
|
|
\[ {}x^{2} y^{\prime }+y^{2} = x y y^{\prime } \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
1.532 |
|
|
\[ {}x^{2} y^{\prime }-y^{2}-x y = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.117 |
|
|
\[ {}\left (x^{2}+y^{2}+x \right ) y^{\prime }-y = 0 \] |
1 |
1 |
1 |
[_rational] |
✓ |
✓ |
1.581 |
|
|
\[ {}\left (6 x y^{2}+x^{2}\right ) y^{\prime }-y \left (3 y^{2}-x \right ) = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
1.961 |
|
|
\[ {}\left (2 x y^{3}+x y+x^{2}\right ) y^{\prime }-x y+y^{2} = 0 \] |
1 |
1 |
1 |
[_rational] |
✓ |
✓ |
1.961 |
|
|
\[ {}\left (y f \left (x^{2}+y^{2}\right )-x \right ) y^{\prime }+y+x f \left (x^{2}+y^{2}\right ) = 0 \] |
1 |
1 |
1 |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
9.193 |
|
|
\[ {}y^{\prime } = \frac {y-\ln \left (\frac {1+x}{-1+x}\right ) x^{3}+\ln \left (\frac {1+x}{-1+x}\right ) x y^{2}}{x} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘], _Riccati] |
✓ |
✓ |
2.185 |
|
|
\[ {}y^{\prime } = \frac {y+{\mathrm e}^{\frac {1+x}{-1+x}} x^{3}+{\mathrm e}^{\frac {1+x}{-1+x}} x y^{2}}{x} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘], _Riccati] |
✓ |
✓ |
3.069 |
|
|
\[ {}y^{\prime } = \frac {\left (x^{3}+3 y^{2}\right ) y}{\left (x +6 y^{2}\right ) x} \] |
1 |
1 |
1 |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
1.286 |
|
|
\[ {}y^{\prime } = \frac {y \left (x -y\right )}{x \left (x -y^{3}\right )} \] |
1 |
1 |
3 |
[_rational] |
✓ |
✓ |
0.972 |
|
|
\[ {}y^{\prime } = \frac {y \left (x +y\right )}{x \left (x +y^{3}\right )} \] |
1 |
1 |
3 |
[_rational] |
✓ |
✓ |
1.083 |
|
|
\[ {}y^{\prime } = \frac {\left (x^{2}+3 y^{2}\right ) y}{\left (x +6 y^{2}\right ) x} \] |
1 |
1 |
1 |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
1.331 |
|
|
\[ {}y^{\prime } = \frac {\left (x^{4}+x^{3}+x +3 y^{2}\right ) y}{\left (x +6 y^{2}\right ) x} \] |
1 |
1 |
1 |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
1.605 |
|
|
\[ {}y^{\prime } = \frac {y \left (x +y\right )}{x \left (x +y+y^{3}+y^{4}\right )} \] |
1 |
1 |
1 |
[_rational] |
✓ |
✓ |
2.342 |
|
|
\[ {}y^{\prime } = \frac {y \left (x -y\right )}{x \left (x -y-y^{3}-y^{4}\right )} \] |
1 |
1 |
1 |
[_rational] |
✓ |
✓ |
2.397 |
|
|
\[ {}y^{\prime } = \frac {-30 x^{3} y+12 x^{6}+70 x^{\frac {7}{2}}-30 x^{3}-25 y \sqrt {x}+50 x -25 \sqrt {x}-25}{5 \left (-5 y+2 x^{3}+10 \sqrt {x}-5\right ) x} \] |
1 |
1 |
2 |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
5.822 |
|
|
\[ {}y^{\prime } = -\left (-\frac {\ln \left (y\right )}{x}+\frac {\cos \left (x \right ) \ln \left (y\right )}{\sin \left (x \right )}-\textit {\_F1} \left (x \right )\right ) y \] |
1 |
1 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
9.809 |
|
|
\[ {}y^{\prime } = -\left (-\frac {\ln \left (y\right )}{x}+\frac {\ln \left (y\right )}{x \ln \left (x \right )}-\textit {\_F1} \left (x \right )\right ) y \] |
1 |
1 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
3.809 |
|
|
\[ {}y^{\prime } = -\frac {\left (-\frac {\ln \left (y\right )^{2}}{2 x}-\textit {\_F1} \left (x \right )\right ) y}{\ln \left (y\right )} \] |
1 |
1 |
2 |
[NONE] |
✓ |
✓ |
3.614 |
|
|
\[ {}x^{2} y^{\prime }+y^{2}-x y = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
0.946 |
|
|
\[ {}x^{2} y^{\prime }+y^{2}-x y = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
0.939 |
|
|
\[ {}x +y-\left (x -y\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.5 |
|
|
\[ {}-y+x y^{\prime } = x^{2}+y^{2} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘], _rational, _Riccati] |
✓ |
✓ |
1.434 |
|
|
\[ {}x +y y^{\prime }+y-x y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.106 |
|
|
\[ {}x y^{2} \left (3 y+x y^{\prime }\right )-2 y+x y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
3.125 |
|
|
\[ {}y+x \left (x^{2}+y^{2}\right )^{2}+\left (y \left (x^{2}+y^{2}\right )^{2}-x \right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
✓ |
1.89 |
|
|
\[ {}x \left (\ln \left (x \right )-\ln \left (y\right )\right ) y^{\prime }-y = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
5.086 |
|
|
\[ {}y \left (x -y\right )-x^{2} y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.256 |
|
|
\[ {}y \left (x -y\right )-x^{2} y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.2 |
|
|
\[ {}x +y+\left (y-x \right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.426 |
|
|
\[ {}x^{2} y^{\prime }-x y = y^{2} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
0.936 |
|
|
\[ {}y^{\prime }-\frac {3 y}{x} = \frac {y^{2}}{x^{2}} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.058 |
|
|
\[ {}y^{\prime } = \frac {2 y+x}{2 x -y} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.306 |
|
|
\[ {}y^{\prime }-\frac {y}{t} = \frac {y^{2}}{t^{2}} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.177 |
|
|
\[ {}y^{\prime } = \frac {4 y+t}{4 t +y} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
3.911 |
|
|
\[ {}y^{2} = \left (t y-4 t^{2}\right ) y^{\prime } \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
1.947 |
|
|
\[ {}t \left (\ln \left (t \right )-\ln \left (y\right )\right ) y^{\prime } = y \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
3.945 |
|
|
\[ {}y^{\prime } = \frac {x +y}{x -y} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.728 |
|
|
\[ {}x y^{\prime } = y \left (\ln \left (y\right )-\ln \left (x \right )\right ) \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
6.031 |
|
|
\[ {}2 x y^{\prime } \left (x -y^{2}\right )+y^{3} = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
2.533 |
|
|
\[ {}y^{3}+2 \left (x^{2}-x y^{2}\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
1.227 |
|
|
|
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