2.3.3 first order ode poly

Table 2.401: first order ode poly

#

ODE

CAS classification

Solved?

105

\[ {}\left (x +y\right ) y^{\prime } = x -y \]

[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

108

\[ {}\left (x -y\right ) y^{\prime } = x +y \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

135

\[ {}2 x +3 y+\left (3 x +2 y\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

136

\[ {}4 x -y+\left (6 y-x \right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

163

\[ {}y^{\prime } = \frac {x -y-1}{x +y+3} \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

164

\[ {}y^{\prime } = \frac {2 y-x +7}{4 x -3 y-18} \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

212

\[ {}y^{\prime } = \frac {x +3 y}{y-3 x} \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

729

\[ {}\left (x +y\right ) y^{\prime } = x -y \]

[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

732

\[ {}\left (x -y\right ) y^{\prime } = x +y \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

759

\[ {}2 x +3 y+\left (3 x +2 y\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

760

\[ {}4 x -y+\left (6 y-x \right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

804

\[ {}y^{\prime } = \frac {x +3 y}{y-3 x} \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

1160

\[ {}y^{\prime } = \frac {4 y-3 x}{2 x -y} \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

1161

\[ {}y^{\prime } = -\frac {4 x +3 y}{2 x +y} \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

1162

\[ {}y^{\prime } = \frac {x +3 y}{x -y} \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

1194

\[ {}2 x +4 y+\left (2 x -2 y\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

1197

\[ {}y^{\prime } = \frac {-a x -b y}{b x +c y} \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

1198

\[ {}y^{\prime } = \frac {-a x +b y}{b x -c y} \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

1205

\[ {}2 x -y+\left (-x +2 y\right ) y^{\prime } = 0 \]
i.c.

[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

1231

\[ {}x +y+\left (x +2 y\right ) y^{\prime } = 0 \]
i.c.

[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

1246

\[ {}y^{\prime } = \frac {x +y}{x -y} \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

1615

\[ {}y^{\prime } = \frac {2 x +3 y}{x -4 y} \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

1655

\[ {}y^{\prime } = \frac {x +y}{x -y} \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

1658

\[ {}y^{\prime } = \frac {x +2 y}{2 x +y} \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

1666

\[ {}y^{\prime } = \frac {-6 x +y-3}{2 x -y-1} \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

1667

\[ {}y^{\prime } = \frac {2 x +y+1}{x +2 y-4} \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

1668

\[ {}y^{\prime } = \frac {-x +3 y-14}{x +y-2} \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

1685

\[ {}4 x +7 y+\left (3 x +4 y\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

1687

\[ {}2 x +y+\left (2 y+2 x \right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

1702

\[ {}7 x +4 y+\left (4 x +3 y\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

2333

\[ {}y^{\prime } = \frac {y+t}{t -y} \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

2335

\[ {}y^{\prime } = \frac {t +y+1}{t -y+3} \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

2336

\[ {}1+t -2 y+\left (4 t -3 y-6\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

2337

\[ {}t +2 y+3+\left (2 t +4 y-1\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

2505

\[ {}y^{\prime } = \frac {y+t}{t -y} \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

2507

\[ {}y^{\prime } = \frac {t +y+1}{t -y+3} \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

2508

\[ {}1+t -2 y+\left (4 t -3 y-6\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

2509

\[ {}t +2 y+3+\left (2 t +4 y-1\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

2872

\[ {}\left (x +y\right ) y^{\prime }+x = y \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

2874

\[ {}y^{\prime } = \frac {2 x -y}{x +4 y} \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

2881

\[ {}x +y+\left (x -y\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

2888

\[ {}y^{\prime } = \frac {x +y}{x -y} \]
i.c.

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

2894

\[ {}x +y-\left (x -y+2\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

2896

\[ {}2 x -y+1+\left (x +y\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

2897

\[ {}x -y+2+\left (x +y-1\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

2898

\[ {}x -y+\left (-x +y+1\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

2899

\[ {}y^{\prime } = \frac {x +y-1}{x -y-1} \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

2900

\[ {}x +y+\left (2 x +2 y-1\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

2901

\[ {}x -y+1+\left (x -y-1\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

2902

\[ {}x +2 y+\left (3 x +6 y+3\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

2903

\[ {}x +2 y+2 = \left (2 x +y-1\right ) y^{\prime } \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

2904

\[ {}3 x -y+1+\left (x -3 y-5\right ) y^{\prime } = 0 \]
i.c.

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

2905

\[ {}6 x -3 y+6+\left (2 x -y+5\right ) y^{\prime } = 0 \]
i.c.

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

2907

\[ {}x +y+4 = \left (2 x +2 y-1\right ) y^{\prime } \]
i.c.

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

2908

\[ {}2 x +3 y-1+\left (2 x +3 y+2\right ) y^{\prime } = 0 \]
i.c.

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

2909

\[ {}3 x -y+2+\left (x +2 y+1\right ) y^{\prime } = 0 \]
i.c.

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

2911

\[ {}x -2 y+3+\left (1-x +2 y\right ) y^{\prime } = 0 \]
i.c.

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

2913

\[ {}2 x +y+\left (4 x -2 y+1\right ) y^{\prime } = 0 \]
i.c.

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

2914

\[ {}x +y+\left (x -2 y\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

2915

\[ {}3 x +y+\left (x +3 y\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

2916

\[ {}a_{1} x +b_{1} y+c_{1} +\left (b_{1} x +b_{2} y+c_{2} \right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

3006

\[ {}2 x +y-\left (x -2 y\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

3012

\[ {}x -3 y = \left (3 y-x +2\right ) y^{\prime } \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

3021

\[ {}\left (3 x +4 y\right ) y^{\prime }+2 x +y = 0 \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

3025

\[ {}x +y+\left (2 x +3 y-1\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

3053

\[ {}x -2 y+3 = \left (x -2 y+1\right ) y^{\prime } \]
i.c.

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

3467

\[ {}\left (y-x \right ) y^{\prime }+2 x +3 y = 0 \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

3469

\[ {}y^{\prime } = -\frac {x +y}{3 x +3 y-4} \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

3479

\[ {}\left (5 x +y-7\right ) y^{\prime } = 3 x +3 y+3 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

3651

\[ {}y^{\prime } = \frac {-2 x +4 y}{x +y} \]
i.c.

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

3652

\[ {}y^{\prime } = \frac {2 x -y}{x +4 y} \]
i.c.

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

3655

\[ {}y^{\prime } = \frac {x +a y}{a x -y} \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

3656

\[ {}y^{\prime } = \frac {x +\frac {y}{2}}{\frac {x}{2}-y} \]
i.c.

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

3677

\[ {}y^{\prime } = \frac {x +2 y-1}{2 x -y+3} \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

4081

\[ {}5 x +2 y+1+\left (2 x +y+1\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

4082

\[ {}3 x -y+1-\left (6 x -2 y-3\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

4083

\[ {}x -2 y-3+\left (2 x +y-1\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

4084

\[ {}6 x +4 y+1+\left (4 x +2 y+2\right ) y^{\prime } = 0 \]
i.c.

[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

4085

\[ {}3 x -y-6+\left (x +y+2\right ) y^{\prime } = 0 \]
i.c.

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

4086

\[ {}2 x +3 y+1+\left (4 x +6 y+1\right ) y^{\prime } = 0 \]
i.c.

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

4112

\[ {}y^{\prime } = \frac {2 x -y}{2 x +y} \]
i.c.

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

4113

\[ {}y^{\prime } = \frac {3 x -y+1}{3 y-x +5} \]
i.c.

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

4114

\[ {}3 y-7 x +7+\left (7 y-3 x +3\right ) y^{\prime } = 0 \]
i.c.

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

4239

\[ {}\left (x +y-1\right ) y^{\prime } = x -y+1 \]

[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

4248

\[ {}y^{\prime } = \frac {x +y+4}{x -y-6} \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

4249

\[ {}y^{\prime } = \frac {x +y+4}{x +y-6} \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

4267

\[ {}\left (x +y\right ) y^{\prime } = y-x \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

4276

\[ {}2 x +3 y+1+\left (2 y-3 x +5\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

4285

\[ {}6 x +4 y+3+\left (3 x +2 y+2\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

4321

\[ {}\left (3+2 x +4 y\right ) y^{\prime } = x +2 y+1 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

4322

\[ {}y^{\prime } = \frac {2 x +y-1}{x -y-2} \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

5034

\[ {}\left (x +y\right ) y^{\prime }+x -y = 0 \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

5035

\[ {}\left (x +y\right ) y^{\prime } = x -y \]

[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

5040

\[ {}\left (x +y+1\right ) y^{\prime }+1+4 x +3 y = 0 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

5041

\[ {}\left (x +y+2\right ) y^{\prime } = 1-x -y \]

[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

5042

\[ {}\left (3-x -y\right ) y^{\prime } = 1+x -3 y \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

5043

\[ {}\left (3-x +y\right ) y^{\prime } = 11-4 x +3 y \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

5044

\[ {}\left (2 x +y\right ) y^{\prime }+x -2 y = 0 \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

5045

\[ {}\left (2 x -y+2\right ) y^{\prime }+3+6 x -3 y = 0 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

5047

\[ {}\left (4+2 x -y\right ) y^{\prime }+5+x -2 y = 0 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

5048

\[ {}\left (5-2 x -y\right ) y^{\prime }+4-x -2 y = 0 \]

[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

5049

\[ {}\left (1-3 x +y\right ) y^{\prime } = 2 x -2 y \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

5050

\[ {}\left (2-3 x +y\right ) y^{\prime }+5-2 x -3 y = 0 \]

[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

5051

\[ {}\left (4 x -y\right ) y^{\prime }+2 x -5 y = 0 \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

5052

\[ {}\left (6-4 x -y\right ) y^{\prime } = 2 x -y \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

5053

\[ {}\left (1+5 x -y\right ) y^{\prime }+5+x -5 y = 0 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

5054

\[ {}\left (a +b x +y\right ) y^{\prime }+a -b x -y = 0 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

5061

\[ {}\left (x +2 y\right ) y^{\prime }+2 x -y = 0 \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

5062

\[ {}\left (x -2 y\right ) y^{\prime }+2 x +y = 0 \]

[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

5063

\[ {}\left (x -2 y+1\right ) y^{\prime } = 1+2 x -y \]

[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

5064

\[ {}\left (x +2 y+1\right ) y^{\prime }+1-x -2 y = 0 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

5065

\[ {}\left (x +2 y+1\right ) y^{\prime }+7+x -4 y = 0 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

5067

\[ {}\left (3+2 x -2 y\right ) y^{\prime } = 1+6 x -2 y \]

[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

5068

\[ {}\left (1-4 x -2 y\right ) y^{\prime }+2 x +y = 0 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

5069

\[ {}\left (6 x -2 y\right ) y^{\prime } = 2+3 x -y \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

5070

\[ {}\left (19+9 x +2 y\right ) y^{\prime }+18-2 x -6 y = 0 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

5076

\[ {}\left (x -3 y\right ) y^{\prime }+4+3 x -y = 0 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

5077

\[ {}\left (4-x -3 y\right ) y^{\prime }+3-x -3 y = 0 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

5078

\[ {}\left (2 x +3 y+2\right ) y^{\prime } = 1-2 x -3 y \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

5079

\[ {}\left (5-2 x -3 y\right ) y^{\prime }+1-2 x -3 y = 0 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

5080

\[ {}\left (1+9 x -3 y\right ) y^{\prime }+2+3 x -y = 0 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

5081

\[ {}\left (x +4 y\right ) y^{\prime }+4 x -y = 0 \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

5082

\[ {}\left (3+2 x +4 y\right ) y^{\prime } = x +2 y+1 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

5083

\[ {}\left (5+2 x -4 y\right ) y^{\prime } = x -2 y+3 \]

[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

5084

\[ {}\left (5+3 x -4 y\right ) y^{\prime } = 2+7 x -3 y \]

[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

5086

\[ {}\left (11-11 x -4 y\right ) y^{\prime } = 62-8 x -25 y \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

5087

\[ {}\left (6+3 x +5 y\right ) y^{\prime } = 2+x +7 y \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

5088

\[ {}\left (7 x +5 y\right ) y^{\prime }+10 x +8 y = 0 \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

5090

\[ {}\left (5-x +6 y\right ) y^{\prime } = 3-x +4 y \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

5091

\[ {}3 \left (x +2 y\right ) y^{\prime } = 1-x -2 y \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

5092

\[ {}3 y-7 x +7+\left (7 y-3 x +3\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

5093

\[ {}\left (1+x +9 y\right ) y^{\prime }+1+x +5 y = 0 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

5094

\[ {}\left (8+5 x -12 y\right ) y^{\prime } = 3+2 x -5 y \]

[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

5095

\[ {}\left (140+7 x -16 y\right ) y^{\prime }+25+8 x +y = 0 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

5096

\[ {}\left (3+9 x +21 y\right ) y^{\prime } = 45+7 x -5 y \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

5099

\[ {}\left (a x +b y\right ) y^{\prime }+b x +a y = 0 \]

[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

5100

\[ {}\left (a x +b y\right ) y^{\prime } = b x +a y \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

5565

\[ {}\left (x +y\right )^{2} {y^{\prime }}^{2}-\left (x^{2}-x y-2 y^{2}\right ) y^{\prime }-\left (x -y\right ) y = 0 \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

5570

\[ {}\left (x^{2}-4 y^{2}\right ) {y^{\prime }}^{2}+6 x y y^{\prime }-4 x^{2}+y^{2} = 0 \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

5637

\[ {}\left (x +2 y\right ) {y^{\prime }}^{3}+3 \left (x +y\right ) {y^{\prime }}^{2}+\left (2 x +y\right ) y^{\prime } = 0 \]

[_quadrature]

5690

\[ {}y^{\prime } = \frac {x +y-3}{x -y-1} \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

5691

\[ {}y^{\prime } = \frac {2 x +y-1}{4 x +2 y+5} \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

5709

\[ {}\left (7 x +5 y\right ) y^{\prime }+10 x +8 y = 0 \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

5711

\[ {}3 y-7 x +7+\left (7 y-3 x +3\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

5734

\[ {}\left (7 x +5 y\right ) y^{\prime }+10 x +8 y = 0 \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

5773

\[ {}x +y-\left (x -y\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

5785

\[ {}x +2 y-4-\left (2 x -4 y\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

5786

\[ {}3 x +2 y+1-\left (3 x +2 y-1\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

5788

\[ {}x +y-1+\left (2 x +2 y-3\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

5789

\[ {}x +y-1-\left (x -y-1\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

5790

\[ {}x +y+\left (2 x +2 y-1\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

5792

\[ {}x +2 y+\left (3 x +6 y+3\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

5794

\[ {}3 x -2 y+4-\left (2 x +7 y-1\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

5796

\[ {}3 x +2 y+3-\left (x +2 y-1\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

5798

\[ {}x +y+2-\left (x -y-4\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

5873

\[ {}\left (3 x +2 y+1\right ) y^{\prime }+4 x +3 y+2 = 0 \]

[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

6123

\[ {}\left (x -y\right ) y^{\prime }+x +y+1 = 0 \]

[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

6224

\[ {}\left (2 x +y\right ) y^{\prime }-x +2 y = 0 \]

[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

6435

\[ {}\left (-x +2 y\right ) y^{\prime } = 2 x +y \]

[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

6438

\[ {}y-3 x +\left (3 x +4 y\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

6445

\[ {}\left (3 x +3 y-4\right ) y^{\prime } = -x -y \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

6447

\[ {}x -y-1+\left (4 y+x -1\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

6448

\[ {}3 y-7 x +7+\left (7 y-3 x +3\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

6469

\[ {}y^{\prime } = \frac {x -2 y+1}{2 x -4 y} \]
i.c.

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

6587

\[ {}x +y+1+\left (2 x +2 y+1\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

6590

\[ {}x +2 y+\left (2 x +3 y\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

6592

\[ {}3 y-7 x +7+\left (7 y-3 x +3\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

6598

\[ {}3 x +2 y+1-\left (3 x +2 y-1\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

6619

\[ {}x +y+1-\left (x -y-3\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

6956

\[ {}\left (y-x \right ) y^{\prime } = x +y \]

[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

7417

\[ {}\left (x +y\right ) y^{\prime }+x -y = 0 \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

7428

\[ {}x +y-\left (x -y\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

7447

\[ {}y^{\prime } = \frac {x +y-2}{y-x -4} \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

7448

\[ {}2 x -4 y+6+\left (x +y-2\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

7449

\[ {}y^{\prime } = \frac {2 y-x +5}{2 x -y-4} \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

7450

\[ {}y^{\prime } = -\frac {4 x +3 y+15}{2 x +y+7} \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

7451

\[ {}y^{\prime } = \frac {x +3 y-5}{x -y-1} \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

7453

\[ {}2 x +y+1-\left (4 x +2 y-3\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

7454

\[ {}x -y-1+\left (y-x +2\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

7455

\[ {}\left (x +4 y\right ) y^{\prime } = 2 x +3 y-5 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

7458

\[ {}y^{\prime } = \frac {x -2 y+5}{y-2 x -4} \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

7459

\[ {}y^{\prime } = \frac {3 x -y+1}{2 x +y+4} \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

7477

\[ {}2 x +4 y+\left (2 x -2 y\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

7506

\[ {}y^{\prime } = \frac {x +y-1}{x -y+3} \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

7510

\[ {}x +y-\left (x -y\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

7564

\[ {}x +y y^{\prime }+y-y^{\prime } x = 0 \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

7739

\[ {}y^{\prime } = \frac {x +y}{x -y} \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

7743

\[ {}y^{\prime } = \frac {x -y+2}{x +y-1} \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

7744

\[ {}y^{\prime } = \frac {2 x +3 y+1}{x -2 y-1} \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

7745

\[ {}y^{\prime } = \frac {x +y+1}{2 x +2 y-1} \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

7876

\[ {}x -y-\left (x +y\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

7881

\[ {}y^{\prime } = \frac {x +y+4}{x -y-6} \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

7882

\[ {}y^{\prime } = \frac {x +y+4}{x +y-6} \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

7884

\[ {}y^{\prime } = \frac {x +y-1}{x +4 y+2} \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

7922

\[ {}y^{\prime } = \frac {x +2 y}{2 x -y} \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

7929

\[ {}y^{\prime } = \frac {x +y}{x -y} \]
i.c.

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

8446

\[ {}\left (4 x -y\right ) {y^{\prime }}^{2}+6 \left (x -y\right ) y^{\prime }+2 x -5 y = 0 \]

[_quadrature]

8450

\[ {}\left (x +y\right )^{2} {y^{\prime }}^{2}+\left (2 y^{2}+x y-x^{2}\right ) y^{\prime }+y \left (y-x \right ) = 0 \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

8701

\[ {}y^{\prime } = \frac {2 x -y}{x +4 y} \]
i.c.

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

10227

\[ {}\left (x +y-1\right ) y^{\prime }-y+2 x +3 = 0 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

10228

\[ {}\left (y+2 x -2\right ) y^{\prime }-y+x +1 = 0 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

10229

\[ {}\left (y-2 x +1\right ) y^{\prime }+y+x = 0 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

10234

\[ {}\left (x +2 y+1\right ) y^{\prime }+1-x -2 y = 0 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

10235

\[ {}\left (2 y+x +7\right ) y^{\prime }-y+2 x +4 = 0 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

10236

\[ {}\left (-x +2 y\right ) y^{\prime }-y-2 x = 0 \]

[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

10237

\[ {}\left (2 y-6 x \right ) y^{\prime }-y+3 x +2 = 0 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

10238

\[ {}\left (3+2 x +4 y\right ) y^{\prime }-2 y-x -1 = 0 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

10239

\[ {}\left (4 y-2 x -3\right ) y^{\prime }+2 y-x -1 = 0 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

10240

\[ {}\left (4 y-3 x -5\right ) y^{\prime }-3 y+7 x +2 = 0 \]

[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

10241

\[ {}\left (4 y+11 x -11\right ) y^{\prime }-25 y-8 x +62 = 0 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

10242

\[ {}\left (12 y-5 x -8\right ) y^{\prime }-5 y+2 x +3 = 0 \]

[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

10244

\[ {}\left (a y+b x +c \right ) y^{\prime }+\alpha y+\beta x +\gamma = 0 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

12494

\[ {}\left (A y+B x +a \right ) y^{\prime }+B y+k x +b = 0 \]

[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

12495

\[ {}\left (y+a x +b \right ) y^{\prime } = \alpha y+\beta x +\gamma \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

12802

\[ {}6 x -2 y+1+\left (2 y-2 x -3\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

12813

\[ {}\left (x +y+1\right ) y^{\prime }+1+4 x +3 y = 0 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

12814

\[ {}4 x -y+2+\left (x +y+3\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

12815

\[ {}2 x +y-\left (4 x +2 y-1\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

12834

\[ {}x +y-\left (x -y\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

12845

\[ {}x +y y^{\prime }+y-y^{\prime } x = 0 \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

12857

\[ {}\left (4+2 x -y\right ) y^{\prime }+5+x -2 y = 0 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

12868

\[ {}2 x +3 y-1+\left (2 x +3 y-5\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

13272

\[ {}3 x +2 y+\left (2 x +y\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

13308

\[ {}\left (4 x -y\right ) y^{\prime }+2 x -5 y = 0 \]
i.c.

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

13310

\[ {}x +2 y+\left (2 x -y\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

13311

\[ {}3 x -y-\left (x +y\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

13355

\[ {}3 x -5 y+\left (x +y\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

13361

\[ {}y^{\prime } = \frac {2 x -7 y}{3 y-8 x} \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

13370

\[ {}y^{\prime } = \frac {2 x +7 y}{2 x -2 y} \]
i.c.

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

13381

\[ {}5 x +2 y+1+\left (2 x +y+1\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

13382

\[ {}3 x -y+1-\left (6 x -2 y-3\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

13383

\[ {}x -2 y-3+\left (2 x +y-1\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

13384

\[ {}10 x -4 y+12-\left (x +5 y+3\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

13385

\[ {}6 x +4 y+1+\left (4 x +2 y+2\right ) y^{\prime } = 0 \]
i.c.

[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

13386

\[ {}3 x -y-6+\left (x +y+2\right ) y^{\prime } = 0 \]
i.c.

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

13387

\[ {}2 x +3 y+1+\left (4 x +6 y+1\right ) y^{\prime } = 0 \]
i.c.

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

13388

\[ {}\left (x +y+1\right ) y^{\prime }+1+4 x +3 y = 0 \]
i.c.

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

13849

\[ {}12 x +6 y-9+\left (5 x +2 y-3\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

13867

\[ {}y^{\prime } = \frac {2 y-x -4}{2 x -y+5} \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

13872

\[ {}2 x +2 y-1+\left (x +y-2\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

13882

\[ {}y^{\prime } = \frac {3 x -4 y-2}{3 x -4 y-3} \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

13890

\[ {}y^{\prime } = \frac {x +y-3}{-x +y+1} \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

13893

\[ {}\left (3+2 x +4 y\right ) y^{\prime }-2 y-x -1 = 0 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

14175

\[ {}y-x +\left (x +y\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

14177

\[ {}x +y+\left (y-x \right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

14179

\[ {}\left (7 x +5 y\right ) y^{\prime }+10 x +8 y = 0 \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

14184

\[ {}3 y-7 x +7-\left (3 x -7 y-3\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

14185

\[ {}x +2 y+1-\left (3+2 x +4 y\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

14283

\[ {}2 x +2 y-1+\left (x +y-2\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

14371

\[ {}y^{\prime } = \frac {2 x -y}{x +3 y} \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

15119

\[ {}y^{\prime } = \frac {x -y}{x +y} \]
i.c.

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

15181

\[ {}y^{\prime } = \frac {x +2 y}{x +2 y+3} \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

15182

\[ {}y^{\prime } = \frac {x +2 y}{2 x -y} \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

15850

\[ {}2 x -3 y+\left (2 y-3 x \right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

15955

\[ {}y^{\prime } = \frac {x +y+3}{3 x +3 y+1} \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

15956

\[ {}y^{\prime } = \frac {x -y+2}{2 x -2 y-1} \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

16056

\[ {}1+5 t -y-\left (t +2 y\right ) y^{\prime } = 0 \]
i.c.

[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

16076

\[ {}\frac {9 t}{5}+2 y+\left (2 t +2 y\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

16077

\[ {}2 t +\frac {19 y}{10}+\left (\frac {19 t}{10}+2 y\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

16099

\[ {}y^{\prime } = \frac {t +4 y}{4 t +y} \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

16119

\[ {}1+t -2 y+\left (4 t -3 y-6\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

16120

\[ {}5 t +2 y+1+\left (2 t +y+1\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

16121

\[ {}3 t -y+1-\left (6 t -2 y-3\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

16122

\[ {}2 t +3 y+1+\left (4 t +6 y+1\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

16147

\[ {}y-t +\left (y+t \right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

16166

\[ {}2 x -y-2+\left (-x +2 y\right ) y^{\prime } = 0 \]
i.c.

[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

16689

\[ {}y^{\prime } = \frac {x +y}{x -y} \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

16743

\[ {}4 x -3 y+\left (2 y-3 x \right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

16744

\[ {}y-x +\left (x +y\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

16746

\[ {}3 y-7 x +7-\left (3 x -7 y-3\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

16747

\[ {}x +y-2+\left (x -y+4\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

16748

\[ {}x +y+\left (x -y-2\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

16749

\[ {}2 x +3 y-5+\left (3 x +2 y-5\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

16750

\[ {}8 x +4 y+1+\left (4 x +2 y+1\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

16751

\[ {}x -2 y-1+\left (3 x -6 y+2\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

16752

\[ {}x +y+\left (x +y-1\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

16880

\[ {}x -y+3+\left (3 x +y+1\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

16886

\[ {}x -y+2+\left (x -y+3\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

16895

\[ {}\left (3 x +3 y+a^{2}\right ) y^{\prime } = 4 x +4 y+b^{2} \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

16900

\[ {}\left (5 x -7 y+1\right ) y^{\prime }+x +y-1 = 0 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

16901

\[ {}x +y+1+\left (2 x +2 y-1\right ) y^{\prime } = 0 \]
i.c.

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

17378

\[ {}y^{\prime } = \frac {t -y}{2 t +5 y} \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

17396

\[ {}2 x +4 y+\left (2 x -2 y\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

17399

\[ {}y^{\prime } = -\frac {4 x +2 y}{2 x +3 y} \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

17400

\[ {}y^{\prime } = -\frac {4 x -2 y}{2 x -3 y} \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

17407

\[ {}2 x -y+\left (-x +2 y\right ) y^{\prime } = 0 \]
i.c.

[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

17427

\[ {}y^{\prime } = \frac {4 y-7 x}{5 x -y} \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

17443

\[ {}\left (3 x-y \right ) x^{\prime }+9 y -2 x = 0 \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

17900

\[ {}\left (x +y\right ) y^{\prime } = y-x \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

17902

\[ {}3 y-7 x +7 = \left (3 x -7 y-3\right ) y^{\prime } \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

17903

\[ {}\left (x +2 y+1\right ) y^{\prime } = 3+2 x +4 y \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

18109

\[ {}x -y-\left (x +y\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

18116

\[ {}y^{\prime } = \frac {x +y+4}{x -y-6} \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

18117

\[ {}y^{\prime } = \frac {x +y+4}{x +y-6} \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

18119

\[ {}y^{\prime } = \frac {x +y-1}{x +4 y+2} \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

18158

\[ {}\left (x +y\right ) y^{\prime } = y-x \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

18201

\[ {}2 x +3 y+1+\left (2 y-3 x +5\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

18212

\[ {}6 x +4 y+3+\left (3 x +2 y+2\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

18228

\[ {}y^{\prime } = \frac {x +2 y+2}{-2 x +y} \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

18236

\[ {}y^{\prime } = \frac {-3 x -2 y-1}{2 x +3 y-1} \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

18547

\[ {}2 a x +b y+\left (2 c y+b x +e \right ) y^{\prime } = g \]

[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

18575

\[ {}y^{\prime } = 1+\frac {2 y}{x -y} \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

18647

\[ {}\left (3 x +2 y-7\right ) y^{\prime } = 2 x -3 y+6 \]

[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

18648

\[ {}\left (6 x -5 y+4\right ) y^{\prime } = 2 x -y+1 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

18649

\[ {}\left (5 x -2 y+7\right ) y^{\prime } = x -3 y+2 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

18650

\[ {}\left (x -3 y+4\right ) y^{\prime } = 5 x -7 y \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

18651

\[ {}\left (x -3 y+4\right ) y^{\prime } = 2 x -6 y+7 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

18652

\[ {}\left (5 x -2 y+7\right ) y^{\prime } = 10 x -4 y+6 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

18653

\[ {}\left (2 x -2 y+5\right ) y^{\prime } = x -y+3 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

18654

\[ {}\left (6 x -4 y+1\right ) y^{\prime } = 3 x -2 y+1 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

18734

\[ {}\left (3 x +4 y\right ) y^{\prime }+y-2 x = 0 \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

18735

\[ {}3 y-7 x +7+\left (7 y-3 x +3\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

18736

\[ {}\left (y-3 x +3\right ) y^{\prime } = 2 y-x -4 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

18740

\[ {}2 a x +b y+g +\left (2 c y+b x +e \right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

18773

\[ {}2 x -y+1+\left (2 y-x -1\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

18781

\[ {}x +y y^{\prime } = m \left (-y+y^{\prime } x \right ) \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

18791

\[ {}\left (x +y\right ) y^{\prime }+x -y = 0 \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

18795

\[ {}3 y+2 x +4-\left (4 x +6 y+5\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

18803

\[ {}\left (x +2 y\right ) {y^{\prime }}^{3}+3 \left (x +y\right ) {y^{\prime }}^{2}+\left (2 x +y\right ) y^{\prime } = 0 \]

[_quadrature]

19050

\[ {}y-x +\left (x +y\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

19056

\[ {}x +y y^{\prime } = m \left (-y+y^{\prime } x \right ) \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

19073

\[ {}\left (x +y-1\right ) y^{\prime } = x +y+1 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

19074

\[ {}\left (2 x +2 y+1\right ) y^{\prime } = x +y+1 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

19075

\[ {}2 x +3 y-1+\left (2 x +3 y-5\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

19080

\[ {}\left (2 x -2 y+5\right ) y^{\prime }-x +y-3 = 0 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

19081

\[ {}x +y+1-\left (2 x +2 y+1\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

19087

\[ {}\left (6 x -5 y+4\right ) y^{\prime }+y-2 x -1 = 0 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

19088

\[ {}\left (x -3 y+4\right ) y^{\prime }+7 y-5 x = 0 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

19089

\[ {}\left (3+2 x +4 y\right ) y^{\prime } = x +2 y+1 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

19093

\[ {}y^{\prime } = \frac {2 x -y+1}{x +2 y-3} \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

19094

\[ {}\left (x -y\right ) y^{\prime } = x +y+1 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

19095

\[ {}x -y-2-\left (2 x -2 y-3\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

19137

\[ {}x +y y^{\prime } = m \left (-y+y^{\prime } x \right ) \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

19146

\[ {}\left (2 x +2 y+3\right ) y^{\prime } = x +y+1 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

19158

\[ {}y^{\prime }+\frac {a x +b y+c}{b x +f y+e} = 0 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

19265

\[ {}y-y^{\prime } x = x +y y^{\prime } \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

19516

\[ {}y^{\prime } = \frac {6 x -2 y-7}{2 x +3 y-6} \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

19517

\[ {}2 x +y+1+\left (4 x +2 y-1\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

19547

\[ {}\left (x +2 y\right ) {y^{\prime }}^{3}+3 \left (x +y\right ) {y^{\prime }}^{2}+\left (2 x +y\right ) y^{\prime } = 0 \]

[_quadrature]