Not to be confused with my First order homogeneous type C. These are ode’s called First order homogeneous type C but in the sense define by Maple in here which requires different algorithm. I have note how to solve such ode’s at end of this Number of problems in this table is 175
Column notations: A is ODE degree. B is Program Number of solutions generated. C is CAS Number of solutions generated.
|
# |
ODE |
A |
B |
C |
CAS classification |
Solved? |
Verified? |
time (sec) |
|
\[ {}y y^{\prime } = -1+x \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
4.47 |
|
|
\[ {}y y^{\prime } = -1+x \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
2.789 |
|
|
\[ {}\left (1+x \right ) y^{\prime } = 4 y \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.167 |
|
|
\[ {}2 y+\left (1+x \right ) y^{\prime } = 3+3 x \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.444 |
|
|
\[ {}y^{\prime } = \frac {1-2 x}{y} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
6.71 |
|
|
\[ {}y^{\prime } = \frac {2 x}{1+2 y} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
6.693 |
|
|
\[ {}3+2 x +\left (2 y-2\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
2.759 |
|
|
\[ {}x y^{\prime }-2 y = -1 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.029 |
|
|
\[ {}\frac {y^{\prime }}{\left (y+1\right )^{2}}-\frac {1}{x \left (y+1\right )} = -\frac {3}{x^{2}} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, _Riccati] |
✓ |
✓ |
2.29 |
|
|
\[ {}y^{\prime } = \frac {2 x}{1+2 y} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
4.329 |
|
|
\[ {}y^{\prime } = \frac {t +y+1}{t -y+3} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.988 |
|
|
\[ {}1+t -2 y+\left (4 t -3 y-6\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
4.902 |
|
|
\[ {}\left (1+x \right ) y^{\prime }-1+y = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.157 |
|
|
\[ {}x +y-\left (x -y+2\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.943 |
|
|
\[ {}x +\left (x -2 y+2\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
✓ |
5.287 |
|
|
\[ {}2 x -y+1+\left (x +y\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
4.047 |
|
|
\[ {}x -y+2+\left (x +y-1\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.987 |
|
|
\[ {}y^{\prime } = \frac {x +y-1}{x -y-1} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
3.024 |
|
|
\[ {}x +2 y+2 = \left (2 x +y-1\right ) y^{\prime } \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
5.508 |
|
|
\[ {}3 x -y+1+\left (x -3 y-5\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
6.16 |
|
|
\[ {}2 x +3 y+2+\left (y-x \right ) y^{\prime } = 0 \] |
1 |
1 |
0 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
10.464 |
|
|
\[ {}3 x -y+2+\left (x +2 y+1\right ) y^{\prime } = 0 \] |
1 |
1 |
0 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
9.152 |
|
|
\[ {}3 x +2 y+3-\left (x +2 y-1\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
13.745 |
|
|
\[ {}2 x +y+\left (4 x -2 y+1\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
42.992 |
|
|
\[ {}x y^{\prime } = 5 y+x +1 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
2.558 |
|
|
\[ {}\left (1-x \right ) y^{\prime }-y-1 = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.467 |
|
|
\[ {}x -2 y+1+\left (y-2\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
3.158 |
|
|
\[ {}x +y+\left (2 x +3 y-1\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
5.397 |
|
|
\[ {}x +\left (2 x +3 y+2\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
✓ |
5.302 |
|
|
\[ {}y^{\prime } = \frac {2 y}{t +1} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.977 |
|
|
\[ {}\left (5 x +y-7\right ) y^{\prime } = 3+3 x +3 y \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.904 |
|
|
\[ {}y-\left (-2+x \right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.615 |
|
|
\[ {}x^{\prime }+\frac {2 x}{4-t} = 5 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.122 |
|
|
\[ {}y^{\prime } = \frac {x +2 y-1}{2 x -y+3} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.549 |
|
|
\[ {}5 x +2 y+1+\left (2 x +y+1\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.762 |
|
|
\[ {}x -2 y-3+\left (2 x +y-1\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.013 |
|
|
\[ {}6 x +4 y+1+\left (4 x +2 y+2\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
5.622 |
|
|
\[ {}3 x -y-6+\left (x +y+2\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
4.014 |
|
|
\[ {}x^{2} y^{\prime } = x \left (y-1\right )+\left (y-1\right )^{2} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, _Riccati] |
✓ |
✓ |
1.263 |
|
|
\[ {}3 y-2 x +\left (-2+3 x \right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.383 |
|
|
\[ {}y^{\prime } = \frac {3 x -y+1}{3 y-x +5} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.987 |
|
|
\[ {}3 y-7 x +7+\left (7 y-3 x +3\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
3.057 |
|
|
\[ {}\left (1-x \right ) y^{\prime } = y \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.188 |
|
|
\[ {}\left (x +y-1\right ) y^{\prime } = x -y+1 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.594 |
|
|
\[ {}y^{\prime } = \frac {x +y+4}{x -y-6} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.974 |
|
|
\[ {}1+y+\left (1-x \right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.994 |
|
|
\[ {}2 x +3 y+1+\left (2 y-3 x +5\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
3.294 |
|
|
\[ {}y^{\prime } = \frac {2 x +y-1}{x -y-2} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
3.213 |
|
|
\[ {}y+2 = \left (-4+2 x +y\right ) y^{\prime } \] |
1 |
1 |
2 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
3.103 |
|
|
\[ {}y^{\prime } = \frac {y+2}{1+x} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.021 |
|
|
\[ {}\left (1-2 x \right ) y^{\prime } = 16+32 x -6 y \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.954 |
|
|
\[ {}x^{2} y^{\prime } = \left (1+2 x -y\right )^{2} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, _Riccati] |
✓ |
✓ |
1.639 |
|
|
\[ {}\left (y+1\right ) y^{\prime } = x +y \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
6.916 |
|
|
\[ {}\left (1+x +y\right ) y^{\prime }+1+4 x +3 y = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.18 |
|
|
\[ {}\left (3-x -y\right ) y^{\prime } = 1+x -3 y \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.21 |
|
|
\[ {}\left (3-x +y\right ) y^{\prime } = 11-4 x +3 y \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.207 |
|
|
\[ {}\left (4+2 x -y\right ) y^{\prime }+5+x -2 y = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.676 |
|
|
\[ {}\left (5-2 x -y\right ) y^{\prime }+4-x -2 y = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.998 |
|
|
\[ {}\left (1-3 x +y\right ) y^{\prime } = 2 x -2 y \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
3.745 |
|
|
\[ {}\left (2-3 x +y\right ) y^{\prime }+5-2 x -3 y = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.981 |
|
|
\[ {}\left (6-4 x -y\right ) y^{\prime } = 2 x -y \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.574 |
|
|
\[ {}\left (1+5 x -y\right ) y^{\prime }+5+x -5 y = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.514 |
|
|
\[ {}\left (1+x -2 y\right ) y^{\prime } = 1+2 x -y \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.033 |
|
|
\[ {}\left (x +2 y+1\right ) y^{\prime }+7+x -4 y = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.697 |
|
|
\[ {}\left (3+2 x -2 y\right ) y^{\prime } = 1+6 x -2 y \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.346 |
|
|
\[ {}\left (19+9 x +2 y\right ) y^{\prime }+18-2 x -6 y = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.625 |
|
|
\[ {}\left (x -3 y\right ) y^{\prime }+4+3 x -y = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.618 |
|
|
\[ {}\left (5+3 x -4 y\right ) y^{\prime } = 2+7 x -3 y \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.467 |
|
|
\[ {}4 \left (1-x -y\right ) y^{\prime }+2-x = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
✓ |
1.184 |
|
|
\[ {}\left (11-11 x -4 y\right ) y^{\prime } = 62-8 x -25 y \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.689 |
|
|
\[ {}\left (6+3 x +5 y\right ) y^{\prime } = 2+x +7 y \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
3.254 |
|
|
\[ {}\left (5-x +6 y\right ) y^{\prime } = 3-x +4 y \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.732 |
|
|
\[ {}3 y-7 x +7+\left (7 y-3 x +3\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.565 |
|
|
\[ {}\left (1+x +9 y\right ) y^{\prime }+1+x +5 y = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.249 |
|
|
\[ {}\left (8+5 x -12 y\right ) y^{\prime } = 3+2 x -5 y \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
3.115 |
|
|
\[ {}\left (140+7 x -16 y\right ) y^{\prime }+25+8 x +y = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.699 |
|
|
\[ {}\left (3+9 x +21 y\right ) y^{\prime } = 45+7 x -5 y \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.666 |
|
|
\[ {}\left (1-3 x -y\right )^{2} y^{\prime } = \left (-2 y+1\right ) \left (3-6 x -4 y\right ) \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational] |
✓ |
✓ |
3.851 |
|
|
\[ {}\left (1-3 x +2 y\right )^{2} y^{\prime } = \left (4+2 x -3 y\right )^{2} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational] |
✓ |
✓ |
5.158 |
|
|
\[ {}y^{\prime } = \frac {x +y-3}{x -y-1} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.603 |
|
|
\[ {}2 x -y+1+\left (2 y-1\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
3.587 |
|
|
\[ {}3 y-7 x +7+\left (7 y-3 x +3\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
3.013 |
|
|
\[ {}x +2 y-4-\left (2 x -4 y\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.886 |
|
|
\[ {}x +y-1-\left (x -y-1\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.878 |
|
|
\[ {}7 y-3+\left (2 x +1\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.137 |
|
|
\[ {}x +2 y+\left (y-1\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.835 |
|
|
\[ {}3 x -2 y+4-\left (2 x +7 y-1\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
5.572 |
|
|
\[ {}3 x +2 y+3-\left (x +2 y-1\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
3.75 |
|
|
\[ {}y+7+\left (2 x +y+3\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
4.445 |
|
|
\[ {}x +y+2-\left (x -y-4\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.932 |
|
|
\[ {}\left (3 x +2 y+1\right ) y^{\prime }+4 x +3 y+2 = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
5.098 |
|
|
\[ {}\left (x -y\right ) y^{\prime }+1+x +y = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.817 |
|
|
\[ {}x -y-1+\left (4 y+x -1\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.734 |
|
|
\[ {}3 y-7 x +7+\left (7 y-3 x +3\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.688 |
|
|
\[ {}x y^{\prime }+2 y = 3 x -1 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.792 |
|
|
\[ {}1+y-\left (1+x \right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.408 |
|
|
\[ {}1+2 y-\left (4-x \right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.612 |
|
|
\[ {}3 y-7 x +7+\left (7 y-3 x +3\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.744 |
|
|
\[ {}x +y+1-\left (x -y-3\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.921 |
|
|
\[ {}x y^{\prime } = 1-x +2 y \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.968 |
|
|
\[ {}y^{\prime } = \frac {2 \left (y+2\right )^{2}}{\left (1+x +y\right )^{2}} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational] |
✓ |
✓ |
1.73 |
|
|
\[ {}y+2 = \left (-4+2 x +y\right ) y^{\prime } \] |
1 |
1 |
2 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.622 |
|
|
\[ {}\left (y^{\prime }+1\right ) \ln \left (\frac {x +y}{x +3}\right ) = \frac {x +y}{x +3} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _exact, _dAlembert] |
✓ |
✓ |
6.257 |
|
|
\[ {}3+2 x +\left (2 y-2\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
2.096 |
|
|
\[ {}y^{\prime } = \frac {x +y-1}{3+x -y} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.736 |
|
|
\[ {}y^{\prime } = \frac {\left (x +y-1\right )^{2}}{2 \left (2+x \right )^{2}} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, _Riccati] |
✓ |
✓ |
2.06 |
|
|
\[ {}1+y+\left (1-x \right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.761 |
|
|
\[ {}y^{\prime } = \frac {x +y+4}{x -y-6} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
3.154 |
|
|
\[ {}2 x -2 y+\left (y-1\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
3.46 |
|
|
\[ {}y^{\prime } = \frac {x +y-1}{x +4 y+2} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
11.516 |
|
|
\[ {}2 x +3 y-1-4 \left (1+x \right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
2.355 |
|
|
\[ {}2 t +3 x+\left (x+2\right ) x^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.444 |
|
|
\[ {}\left (y+1\right ) y^{\prime }-y-x = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
12.486 |
|
|
\[ {}\left (x +y-1\right ) y^{\prime }-y+2 x +3 = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.851 |
|
|
\[ {}\left (y+2 x -2\right ) y^{\prime }-y+x +1 = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
3.328 |
|
|
\[ {}\left (y-2 x +1\right ) y^{\prime }+y+x = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
3.267 |
|
|
\[ {}\left (2 y+x +7\right ) y^{\prime }-y+2 x +4 = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.214 |
|
|
\[ {}\left (4 y-3 x -5\right ) y^{\prime }-3 y+7 x +2 = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
4.281 |
|
|
\[ {}\left (4 y+11 x -11\right ) y^{\prime }-25 y-8 x +62 = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
3.253 |
|
|
\[ {}\left (12 y-5 x -8\right ) y^{\prime }-5 y+2 x +3 = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
3.935 |
|
|
\[ {}\left (3 x +2\right ) \left (y-2 x -1\right ) y^{\prime }-y^{2}+x y-7 x^{2}-9 x -3 = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
4.573 |
|
|
\[ {}\left (y+3 x -1\right )^{2} y^{\prime }-\left (2 y-1\right ) \left (4 y+6 x -3\right ) = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational] |
✓ |
✓ |
4.532 |
|
|
\[ {}\left (1-3 x +2 y\right )^{2} y^{\prime }-\left (3 y-2 x -4\right )^{2} = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational] |
✓ |
✓ |
4.156 |
|
|
\[ {}y^{\prime } = \frac {-125+300 x -240 x^{2}+64 x^{3}-80 y^{2}+64 x y^{2}+64 y^{3}}{\left (4 x -5\right )^{3}} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, _Abel] |
✓ |
✓ |
8.832 |
|
|
\[ {}6 x -2 y+1+\left (2 y-2 x -3\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
4.003 |
|
|
\[ {}\left (1+x +y\right ) y^{\prime }+1+4 x +3 y = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.957 |
|
|
\[ {}4 x -y+2+\left (x +y+3\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.927 |
|
|
\[ {}\left (4+2 x -y\right ) y^{\prime }+5+x -2 y = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
3.618 |
|
|
\[ {}x^{\prime } = \frac {2 x}{t +1} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.369 |
|
|
\[ {}\left (2 u+1\right ) u^{\prime }-t -1 = 0 \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
2.651 |
|
|
\[ {}5 x +2 y+1+\left (2 x +y+1\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
4.466 |
|
|
\[ {}x -2 y-3+\left (2 x +y-1\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.211 |
|
|
\[ {}10 x -4 y+12-\left (x +5 y+3\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
4.471 |
|
|
\[ {}6 x +4 y+1+\left (4 x +2 y+2\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
9.043 |
|
|
\[ {}3 x -y-6+\left (x +y+2\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
5.579 |
|
|
\[ {}\left (1+x +y\right ) y^{\prime }+1+4 x +3 y = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
13.358 |
|
|
\[ {}12 x +6 y-9+\left (5 x +2 y-3\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
5.199 |
|
|
\[ {}y^{\prime } = \frac {2 y-x -4}{2 x -y+5} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
5.189 |
|
|
\[ {}y^{\prime } = \frac {x +y-3}{-x +y+1} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
4.433 |
|
|
\[ {}1+y-\left (1-x \right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.373 |
|
|
\[ {}3 y-7 x +7-\left (3 x -7 y-3\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.181 |
|
|
\[ {}x +2 y+1-\left (2 x -3\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.298 |
|
|
\[ {}y = x y^{\prime }+y^{\prime } \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.766 |
|
|
\[ {}y^{\prime } = \frac {y+1}{t +1} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.167 |
|
|
\[ {}y^{\prime } = \frac {2 y+1}{t} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.311 |
|
|
\[ {}y^{\prime } = \frac {t}{y-2} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
6.28 |
|
|
\[ {}y^{\prime } = -\frac {y}{t +1}+2 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.886 |
|
|
\[ {}y^{\prime } = \frac {\left (t +1\right )^{2}}{\left (y+1\right )^{2}} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
142.759 |
|
|
\[ {}y^{\prime } = \frac {2 y+1}{t} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.338 |
|
|
\[ {}\left (-2+x \right ) y^{\prime } = 3+y \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.36 |
|
|
\[ {}\left (y-2\right ) y^{\prime } = x -3 \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
2.321 |
|
|
\[ {}2 y-6 x +\left (1+x \right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.564 |
|
|
\[ {}y^{\prime } = \frac {y+1}{t +1} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.514 |
|
|
\[ {}y^{\prime } = \frac {y+2}{1+2 t} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.882 |
|
|
\[ {}4 \left (-1+x \right )^{2} y^{\prime }-3 \left (3+y\right )^{2} = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.885 |
|
|
\[ {}y^{\prime } = \frac {3+y}{1+3 x} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.444 |
|
|
\[ {}y^{\prime } = \frac {3 y+1}{x +3} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.701 |
|
|
\[ {}y^{\prime } = -\frac {y-2}{-2+x} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.186 |
|
|
\[ {}1+5 t -y-\left (t +2 y\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
5.456 |
|
|
\[ {}1+t -2 y+\left (4 t -3 y-6\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
4.077 |
|
|
\[ {}5 t +2 y+1+\left (2 t +y+1\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
4.359 |
|
|
\[ {}y = t \left (y^{\prime }+1\right )+2 y^{\prime }+1 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.308 |
|
|
\[ {}2 x -y-2+\left (2 y-x \right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
7.896 |
|
|
\[ {}y^{\prime } = -\frac {y}{t -2} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.637 |
|
|
\[ {}y^{\prime } = \frac {y+1}{x -y} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.871 |
|
|
\[ {}y^{\prime } = \frac {y+1}{-1+x} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.953 |
|
|
\[ {}\left (1+x \right ) y^{\prime } = y-1 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.071 |
|
|
\[ {}x +y-2+\left (1-x \right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.473 |
|
|
\[ {}3 y-7 x +7-\left (3 x -7 y-3\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
4.897 |
|
|
\[ {}x +y-2+\left (-y+4+x \right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
4.743 |
|
|
\[ {}x +y+\left (x -y-2\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
4.56 |
|
|
\[ {}2 x +3 y-5+\left (3 x +2 y-5\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
3.665 |
|
|
\[ {}x -y+3+\left (3 x +y+1\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.276 |
|
|
\[ {}\left (5 x -7 y+1\right ) y^{\prime }+x +y-1 = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.893 |
|
|
\[ {}y^{\prime } = \frac {2 \left (y+2\right )^{2}}{\left (x +y-1\right )^{2}} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational] |
✓ |
✓ |
1.625 |
|
|
|
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|
|
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