2.4.26 first order ode abel second kind case 3

Table 2.1101: first order ode abel second kind case 3 [152]

#

ODE

CAS classification

Solved

Maple

Mma

Sympy

time(sec)

108

\begin{align*} \left (x -y\right ) y^{\prime }&=x +y \\ \end{align*}

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

3.206

732

\begin{align*} \left (x -y\right ) y^{\prime }&=x +y \\ \end{align*}

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

3.745

1160

\begin{align*} y^{\prime }&=\frac {4 y-3 x}{2 x -y} \\ \end{align*}

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

5.248

1161

\begin{align*} y^{\prime }&=-\frac {4 x +3 y}{2 x +y} \\ \end{align*}

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

15.332

1194

\begin{align*} 2 x +4 y+\left (2 x -2 y\right ) y^{\prime }&=0 \\ \end{align*}

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

8.624

1198

\begin{align*} y^{\prime }&=\frac {-a x +b y}{b x -c y} \\ \end{align*}

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

5.073

1246

\begin{align*} y^{\prime }&=\frac {x +y}{x -y} \\ \end{align*}

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

3.743

1248

\begin{align*} y^{\prime }&=\frac {-3 x^{2} y-y^{2}}{2 x^{3}+3 y x} \\ y \left (1\right ) &= -2 \\ \end{align*}

[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]

4.156

1615

\begin{align*} y^{\prime }&=\frac {2 x +3 y}{x -4 y} \\ \end{align*}

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

6.944

1655

\begin{align*} y^{\prime }&=\frac {x +y}{x -y} \\ \end{align*}

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

3.522

1658

\begin{align*} y^{\prime }&=\frac {x +2 y}{2 x +y} \\ \end{align*}

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

5.493

1659

\begin{align*} y^{\prime }&=\frac {y}{y-2 x} \\ \end{align*}

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

4.218

1664

\begin{align*} y^{\prime }&=\frac {2 y^{2}-y x +2 x^{2}}{y x +2 x^{2}} \\ \end{align*}

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

34.039

1666

\begin{align*} y^{\prime }&=\frac {-6 x +y-3}{2 x -y-1} \\ \end{align*}

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

7.190

1685

\begin{align*} 4 x +7 y+\left (3 x +4 y\right ) y^{\prime }&=0 \\ \end{align*}

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

4.460

1687

\begin{align*} 2 x +y+\left (2 y+2 x \right ) y^{\prime }&=0 \\ \end{align*}

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

5.809

2332

\begin{align*} y^{\prime }&=\frac {t +y}{t -y} \\ \end{align*}

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

4.000

2504

\begin{align*} y^{\prime }&=\frac {t +y}{t -y} \\ \end{align*}

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

3.504

2871

\begin{align*} \left (x +y\right ) y^{\prime }+x&=y \\ \end{align*}

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

4.582

2887

\begin{align*} y^{\prime }&=\frac {x +y}{x -y} \\ y \left (1\right ) &= 0 \\ \end{align*}

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

11.019

2889

\begin{align*} \left (3 y x -2 x^{2}\right ) y^{\prime }&=2 y^{2}-y x \\ y \left (1\right ) &= -1 \\ \end{align*}

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

11.307

2895

\begin{align*} 2 x -y+1+\left (x +y\right ) y^{\prime }&=0 \\ \end{align*}

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

12.754

2937

\begin{align*} y x +\left (y+x^{2}\right ) y^{\prime }&=0 \\ \end{align*}

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

4.662

2949

\begin{align*} \left (2 x +3 x^{2} y\right ) y^{\prime }+y+2 x y^{2}&=0 \\ \end{align*}

[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]

4.270

2963

\begin{align*} y+\left (2 x -3 y\right ) y^{\prime }&=0 \\ \end{align*}

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

21.665

3005

\begin{align*} 2 x +y-\left (x -2 y\right ) y^{\prime }&=0 \\ \end{align*}

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

5.042

3018

\begin{align*} y+\left (3 x -2 y\right ) y^{\prime }&=0 \\ \end{align*}

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

22.938

3020

\begin{align*} \left (3 x +4 y\right ) y^{\prime }+2 x +y&=0 \\ \end{align*}

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

4.945

3036

\begin{align*} y \left (3 x^{2}+y\right )-x \left (x^{2}-y\right ) y^{\prime }&=0 \\ \end{align*}

[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]

9.382

3053

\begin{align*} y^{2}+\left (x^{3}-2 y x \right ) y^{\prime }&=0 \\ y \left (2\right ) &= 1 \\ \end{align*}

[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]

12.815

3466

\begin{align*} \left (y-x \right ) y^{\prime }+2 x +3 y&=0 \\ \end{align*}

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

6.307

3654

\begin{align*} y^{\prime }&=\frac {x +a y}{a x -y} \\ \end{align*}

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

6.136

3655

\begin{align*} y^{\prime }&=\frac {x +\frac {y}{2}}{\frac {x}{2}-y} \\ y \left (1\right ) &= 1 \\ \end{align*}

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

10.549

4079

\begin{align*} 4 x y^{2}+6 y+\left (5 x^{2} y+8 x \right ) y^{\prime }&=0 \\ \end{align*}

[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]

4.304

4111

\begin{align*} y^{\prime }&=\frac {2 x -y}{2 x +y} \\ y \left (2\right ) &= 2 \\ \end{align*}

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

26.700

4266

\begin{align*} \left (x +y\right ) y^{\prime }&=y-x \\ \end{align*}

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

3.899

4277

\begin{align*} y^{2}&=\left (x^{3}-y x \right ) y^{\prime } \\ \end{align*}

[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]

3.885

5054

\begin{align*} \left (x +y\right ) y^{\prime }+x -y&=0 \\ \end{align*}

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

4.312

5064

\begin{align*} \left (2 x +y\right ) y^{\prime }+x -2 y&=0 \\ \end{align*}

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

4.261

5081

\begin{align*} \left (x +2 y\right ) y^{\prime }+2 x -y&=0 \\ \end{align*}

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

3.556

5096

\begin{align*} \left (x -3 y\right ) y^{\prime }+4+3 x -y&=0 \\ \end{align*}

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

32.937

5101

\begin{align*} \left (x +4 y\right ) y^{\prime }+4 x -y&=0 \\ \end{align*}

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

4.782

5108

\begin{align*} \left (7 x +5 y\right ) y^{\prime }+10 x +8 y&=0 \\ \end{align*}

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

3.705

5117

\begin{align*} \left (a x +b y\right ) y^{\prime }+x&=0 \\ \end{align*}

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

31.006

5118

\begin{align*} \left (a x +b y\right ) y^{\prime }+y&=0 \\ \end{align*}

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

5.223

5120

\begin{align*} \left (a x +b y\right ) y^{\prime }&=b x +a y \\ \end{align*}

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

5.464

5140

\begin{align*} \left (2+3 x -y x \right ) y^{\prime }+y&=0 \\ \end{align*}

[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class B‘]]

1.289

5146

\begin{align*} x \left (x +y\right ) y^{\prime }&=y^{2}+x^{2} \\ \end{align*}

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

4.710

5150

\begin{align*} x \left (2 x +y\right ) y^{\prime }&=x^{2}+y x -y^{2} \\ \end{align*}

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

9.906

5166

\begin{align*} x \left (x +2 y\right ) y^{\prime }+y \left (2 x -y\right )&=0 \\ \end{align*}

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

27.512

5172

\begin{align*} x \left (2 x +3 y\right ) y^{\prime }&=y^{2} \\ \end{align*}

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

31.144

5179

\begin{align*} x \left (x -a y\right ) y^{\prime }&=y \left (y-a x \right ) \\ \end{align*}

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

6.300

5194

\begin{align*} x^{2} \left (x -2 y\right ) y^{\prime }&=2 x^{3}-4 x y^{2}+y^{3} \\ \end{align*}

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

42.043

5197

\begin{align*} x^{2} \left (4 x -3 y\right ) y^{\prime }&=\left (6 x^{2}-3 y x +2 y^{2}\right ) y \\ \end{align*}

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

8.040

5198

\begin{align*} \left (1-x^{3} y\right ) y^{\prime }&=y^{2} x^{2} \\ \end{align*}

[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]

4.005

5201

\begin{align*} x \left (3+2 x^{2} y\right ) y^{\prime }+\left (4+3 x^{2} y\right ) y&=0 \\ \end{align*}

[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]

12.228

6834

\begin{align*} \left (7 x +5 y\right ) y^{\prime }+10 x +8 y&=0 \\ \end{align*}

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

5.846

6858

\begin{align*} \left (7 x +5 y\right ) y^{\prime }+10 x +8 y&=0 \\ \end{align*}

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

5.813

6897

\begin{align*} x +y-\left (x -y\right ) y^{\prime }&=0 \\ \end{align*}

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

3.892

6909

\begin{align*} x +2 y-4-\left (2 x -4 y\right ) y^{\prime }&=0 \\ \end{align*}

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

6.517

7485

\begin{align*} 2 y^{2}-6 y x +\left (3 y x -4 x^{2}\right ) y^{\prime }&=0 \\ \end{align*}

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

7.168

7715

\begin{align*} y-3 x +\left (3 x +4 y\right ) y^{\prime }&=0 \\ \end{align*}

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

8.490

7737

\begin{align*} y^{\prime }&=\frac {y^{2}+2 y x}{x^{2}+2 y x} \\ \end{align*}

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

7.879

8469

\begin{align*} y+\left (2 x +y x -3\right ) y^{\prime }&=0 \\ \end{align*}

[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class B‘]]

1.821

8692

\begin{align*} \left (x +y\right ) y^{\prime }+x -y&=0 \\ \end{align*}

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

5.482

8703

\begin{align*} x +y-\left (x -y\right ) y^{\prime }&=0 \\ \end{align*}

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

5.557

8730

\begin{align*} \left (x +4 y\right ) y^{\prime }&=2 x +3 y-5 \\ \end{align*}

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

7.180

8752

\begin{align*} 2 x +4 y+\left (2 x -2 y\right ) y^{\prime }&=0 \\ \end{align*}

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

7.122

8785

\begin{align*} x +y-\left (x -y\right ) y^{\prime }&=0 \\ \end{align*}

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

4.658

8839

\begin{align*} x +y^{\prime } y+y-y^{\prime } x&=0 \\ \end{align*}

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

4.492

9014

\begin{align*} y^{\prime }&=\frac {x +y}{x -y} \\ \end{align*}

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

3.833

9159

\begin{align*} y^{\prime }&=\frac {x +y-1}{x +4 y+2} \\ \end{align*}

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

24.447

9197

\begin{align*} y^{\prime }&=\frac {x +2 y}{2 x -y} \\ \end{align*}

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

4.072

9204

\begin{align*} y^{\prime }&=\frac {x +y}{x -y} \\ y \left (1\right ) &= 1 \\ \end{align*}

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

12.103

10002

\begin{align*} y^{\prime }&=\frac {-y x -1}{4 x^{3} y-2 x^{2}} \\ \end{align*}

[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]

2.945

11542

\begin{align*} \left (2 y x +4 x^{3}\right ) y^{\prime }+y^{2}+112 x^{2} y&=0 \\ \end{align*}

[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]

7.014

11558

\begin{align*} \left (2 x^{2} y-x^{3}\right ) y^{\prime }+y^{3}-4 x y^{2}+2 x^{3}&=0 \\ \end{align*}

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

54.079

11560

\begin{align*} 2 x \left (x^{3} y+1\right ) y^{\prime }+\left (3 x^{3} y-1\right ) y&=0 \\ \end{align*}

[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]

7.631

13997

\begin{align*} x^{4} y \left (3 y+2 y^{\prime } x \right )+x^{2} \left (4 y+3 y^{\prime } x \right )&=0 \\ \end{align*}

[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]

30.588

14002

\begin{align*} x +y-\left (x -y\right ) y^{\prime }&=0 \\ \end{align*}

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

6.197

14013

\begin{align*} x +y^{\prime } y+y-y^{\prime } x&=0 \\ \end{align*}

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

5.757

14546

\begin{align*} 4 x y^{2}+6 y+\left (5 x^{2} y+8 x \right ) y^{\prime }&=0 \\ \end{align*}

[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]

4.206

15350

\begin{align*} x +y+\left (y-x \right ) y^{\prime }&=0 \\ \end{align*}

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

3.583

15352

\begin{align*} \left (7 x +5 y\right ) y^{\prime }+10 x +8 y&=0 \\ \end{align*}

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

4.177

16325

\begin{align*} \frac {2 y}{x}+\left (4 x^{2} y-3\right ) y^{\prime }&=0 \\ \end{align*}

[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]

5.112

16330

\begin{align*} 4 y x +\left (3 x^{2}+5 y\right ) y^{\prime }&=0 \\ \end{align*}

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

2.833

16355

\begin{align*} y^{\prime }&=\frac {x +2 y}{2 x -y} \\ \end{align*}

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

4.199

17269

\begin{align*} t y-y^{2}+t \left (t -3 y\right ) y^{\prime }&=0 \\ \end{align*}

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

6.921

17272

\begin{align*} y^{\prime }&=\frac {t +4 y}{4 t +y} \\ \end{align*}

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

10.013

17319

\begin{align*} 3 t +\left (t -4 y\right ) y^{\prime }&=0 \\ \end{align*}

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

7.580

17862

\begin{align*} y^{\prime }&=\frac {x +y}{x -y} \\ \end{align*}

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

6.539

18073

\begin{align*} \left (5 x -7 y+1\right ) y^{\prime }+x +y-1&=0 \\ \end{align*}

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

12.612

18551

\begin{align*} y^{\prime }&=\frac {t -y}{2 t +5 y} \\ \end{align*}

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

7.395

18569

\begin{align*} 2 x +4 y+\left (2 x -2 y\right ) y^{\prime }&=0 \\ \end{align*}

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

7.906

18573

\begin{align*} y^{\prime }&=-\frac {4 x -2 y}{2 x -3 y} \\ \end{align*}

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

9.161

18600

\begin{align*} y^{\prime }&=\frac {4 y-7 x}{5 x -y} \\ \end{align*}

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

8.085

18605

\begin{align*} y^{\prime }&=\frac {x +y}{x -y} \\ y \left (5\right ) &= 8 \\ \end{align*}

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

78.362

18616

\begin{align*} \left (3 x-y \right ) x^{\prime }+9 y -2 x&=0 \\ \end{align*}

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

6.722

18626

\begin{align*} x^{\prime }&=\frac {2 x y +x^{2}}{3 y^{2}+2 x y} \\ \end{align*}

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

5.309

19072

\begin{align*} \left (x +y\right ) y^{\prime }&=y-x \\ \end{align*}

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

3.427

19290

\begin{align*} y^{\prime }&=\frac {x +y-1}{x +4 y+2} \\ \end{align*}

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

108.712

19329

\begin{align*} \left (x +y\right ) y^{\prime }&=y-x \\ \end{align*}

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

8.879

19374

\begin{align*} y^{2}&=\left (x^{3}-y x \right ) y^{\prime } \\ \end{align*}

[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]

20.256

19411

\begin{align*} 3 y x +y^{2}+\left (3 y x +x^{2}\right ) y^{\prime }&=0 \\ \end{align*}

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

23.863

19746

\begin{align*} y^{\prime }&=1+\frac {2 y}{x -y} \\ \end{align*}

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

15.741

19810

\begin{align*} x \left (x -2 y\right ) y^{\prime }+x^{2}+2 y^{2}&=0 \\ \end{align*}

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

31.905

19813

\begin{align*} \left (x^{2}+2 y x \right ) y^{\prime }-3 x^{2}+2 y x -y^{2}&=0 \\ \end{align*}

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

49.566

19903

\begin{align*} \left (3 x +4 y\right ) y^{\prime }+y-2 x&=0 \\ \end{align*}

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

91.762

19924

\begin{align*} y^{2}+2 x^{2} y+\left (2 x^{3}-y x \right ) y^{\prime }&=0 \\ \end{align*}

[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]

25.785

19950

\begin{align*} y^{\prime } y+x&=m \left (-y+y^{\prime } x \right ) \\ \end{align*}

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

50.895

19960

\begin{align*} \left (x +y\right ) y^{\prime }+x -y&=0 \\ \end{align*}

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

11.377

19966

\begin{align*} 2 y^{2} x^{2}+y-\left (x^{3} y-3 x \right ) y^{\prime }&=0 \\ \end{align*}

[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]

19.698

20225

\begin{align*} y^{\prime } y+x&=m \left (-y+y^{\prime } x \right ) \\ \end{align*}

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

6.916

20263

\begin{align*} \left (x -y\right ) y^{\prime }&=x +y+1 \\ \end{align*}

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

5.765

20294

\begin{align*} y^{2}+2 x^{2} y+\left (2 x^{3}-y x \right ) y^{\prime }&=0 \\ \end{align*}

[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]

6.102

20295

\begin{align*} 2 y+3 y^{\prime } x +2 x y \left (3 y+4 y^{\prime } x \right )&=0 \\ \end{align*}

[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]

10.228

20306

\begin{align*} y^{\prime } y+x&=m \left (-y+y^{\prime } x \right ) \\ \end{align*}

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

8.708

20313

\begin{align*} 2 y+3 y^{\prime } x +2 x y \left (3 y+4 y^{\prime } x \right )&=0 \\ \end{align*}

[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]

8.084

20434

\begin{align*} y-y^{\prime } x&=y^{\prime } y+x \\ \end{align*}

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

3.656

21365

\begin{align*} x -y+\left (x -4 y\right ) y^{\prime }&=0 \\ \end{align*}

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

39.810

21390

\begin{align*} x +y-\left (x -y\right ) y^{\prime }&=0 \\ \end{align*}

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

39.132

21403

\begin{align*} \left (2+3 x -y x \right ) y^{\prime }+y&=0 \\ \end{align*}

[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class B‘]]

7.061

21420

\begin{align*} y \left (x +y+1\right )+x \left (x +3 y+2\right ) y^{\prime }&=0 \\ \end{align*}

[_rational, [_Abel, ‘2nd type‘, ‘class B‘]]

12.914

21449

\begin{align*} y^{2}+\left (3 y x -1\right ) y^{\prime }&=0 \\ \end{align*}

[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]

35.495

21811

\begin{align*} a x -b y+\left (b x -a y\right ) y^{\prime }&=0 \\ \end{align*}

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

81.242

21823

\begin{align*} 3 y+2 y^{\prime } x +4 x y^{2}+3 x^{2} y y^{\prime }&=0 \\ \end{align*}

[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]

91.640

21851

\begin{align*} 2 x -y+1+\left (x -2 y-1\right ) y^{\prime }&=0 \\ \end{align*}

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

123.100

22033

\begin{align*} \left (x +y\right ) y^{\prime }+x -y&=0 \\ \end{align*}

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

4.290

22303

\begin{align*} y+\left (2 x -3 y\right ) y^{\prime }&=0 \\ \end{align*}

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

17.885

22343

\begin{align*} y^{\prime }&=\frac {x -2 y}{y-2 x} \\ y \left (1\right ) &= 2 \\ \end{align*}

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

7.465

22392

\begin{align*} y^{\prime }&=\frac {2 x +5 y}{2 x -y} \\ \end{align*}

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

9.132

22413

\begin{align*} y^{\prime }&=\frac {x}{x +y} \\ \end{align*}

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

7.357

22428

\begin{align*} \left (x +y\right ) y^{\prime }+x -y&=0 \\ \end{align*}

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

3.805

22430

\begin{align*} x y^{2}+2 y+\left (3 x^{2} y-4 x \right ) y^{\prime }&=0 \\ \end{align*}

[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]

4.753

22447

\begin{align*} 2 y^{2}+4 x^{2} y+\left (4 y x +3 x^{3}\right ) y^{\prime }&=0 \\ \end{align*}

[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]

12.365

22458

\begin{align*} y^{2}+\left (-x^{3}+y x \right ) y^{\prime }&=0 \\ \end{align*}

[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]

4.143

22580

\begin{align*} y^{\prime }&=\frac {x +3 y}{x -3 y} \\ \end{align*}

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

5.577

23208

\begin{align*} 3 y+\left (7 x -y\right ) y^{\prime }&=0 \\ \end{align*}

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

6.354

23212

\begin{align*} x -y+\left (2 x +y\right ) y^{\prime }&=0 \\ \end{align*}

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

6.322

23862

\begin{align*} y+x y^{2}-\left (x +2 x^{2} y\right ) y^{\prime }&=0 \\ \end{align*}

[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]

6.275

23902

\begin{align*} x y^{2}+\left (3-2 x^{2} y\right ) y^{\prime }&=0 \\ \end{align*}

[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]

5.706

23903

\begin{align*} y+2 x^{3}+\left (2 x -\frac {x^{4}}{y}\right ) y^{\prime }&=0 \\ \end{align*}

[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]

5.607

24150

\begin{align*} \left (2 x +y\right ) y^{\prime }+x -2 y&=0 \\ \end{align*}

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

9.345

24180

\begin{align*} 16 x +15 y+\left (3 x +y\right ) y^{\prime }&=0 \\ y \left (1\right ) &= -3 \\ \end{align*}

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

47.966

24249

\begin{align*} v+\left (2 x +1-v x \right ) v^{\prime }&=0 \\ \end{align*}

[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class B‘]]

1.618

24270

\begin{align*} y^{2}-x \left (2 x +3 y\right ) y^{\prime }&=0 \\ \end{align*}

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

43.328

24321

\begin{align*} y x +\left (x^{2}-3 y\right ) y^{\prime }&=0 \\ \end{align*}

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

7.797

24328

\begin{align*} y+x \left (3 y x -2\right ) y^{\prime }&=0 \\ \end{align*}

[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]

7.511

24367

\begin{align*} y \left (1+2 x -y\right )+x \left (3 x -4 y+3\right ) y^{\prime }&=0 \\ \end{align*}

[_rational, [_Abel, ‘2nd type‘, ‘class B‘]]

2.426

25032

\begin{align*} 3 y-5 t +2 y y^{\prime }-t y^{\prime }&=0 \\ \end{align*}

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

6.857

25037

\begin{align*} a t +b y-\left (c t +d y\right ) y^{\prime }&=0 \\ \end{align*}

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

7.496

25496

\begin{align*} y^{\prime }&=\frac {c t -a y}{A t +b y} \\ \end{align*}

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

47.760