2.2.52 Problems 5101 to 5200

Table 2.121: Main lookup table. Sorted sequentially by problem number.

#

ODE

CAS classification

Solved?

Maple

Mma

Sympy

time(sec)

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‘]]

15.502

5102

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

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

12.902

5103

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

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

10.119

5104

\begin{align*} \left (5+3 x -4 y\right ) y^{\prime }&=2+7 x -3 y \\ \end{align*}

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

21.046

5105

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

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

38.305

5106

\begin{align*} \left (11-11 x -4 y\right ) y^{\prime }&=62-8 x -25 y \\ \end{align*}

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

74.473

5107

\begin{align*} \left (6+3 x +5 y\right ) y^{\prime }&=2+x +7 y \\ \end{align*}

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

204.677

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‘]]

26.450

5109

\begin{align*} \left (x +4 x^{3}+5 y\right ) y^{\prime }+7 x^{3}+3 x^{2} y+4 y&=0 \\ \end{align*}

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

25.069

5110

\begin{align*} \left (5-x +6 y\right ) y^{\prime }&=3-x +4 y \\ \end{align*}

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

94.049

5111

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

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

14.224

5112

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

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

108.256

5113

\begin{align*} \left (1+x +9 y\right ) y^{\prime }+1+x +5 y&=0 \\ \end{align*}

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

43.203

5114

\begin{align*} \left (8+5 x -12 y\right ) y^{\prime }&=3+2 x -5 y \\ \end{align*}

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

27.978

5115

\begin{align*} \left (140+7 x -16 y\right ) y^{\prime }+25+8 x +y&=0 \\ \end{align*}

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

44.991

5116

\begin{align*} \left (3+9 x +21 y\right ) y^{\prime }&=45+7 x -5 y \\ \end{align*}

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

52.671

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]

65.160

5118

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

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

41.410

5119

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

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

42.630

5120

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

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

29.468

5121

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

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

115.208

5122

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

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

104.655

5123

\begin{align*} y y^{\prime } x +1+y^{2}&=0 \\ \end{align*}

[_separable]

10.572

5124

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

[[_homogeneous, ‘class D‘], _rational, _Bernoulli]

14.170

5125

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

[[_homogeneous, ‘class A‘], _rational, _Bernoulli]

16.707

5126

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

[[_homogeneous, ‘class D‘], _rational, _Bernoulli]

10.911

5127

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

[[_homogeneous, ‘class D‘], _Bernoulli]

7.470

5128

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

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

41.595

5129

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

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

17.757

5130

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

[_separable]

11.967

5131

\begin{align*} y y^{\prime } x&=a \,x^{n}+b y^{2} \\ \end{align*}

[[_homogeneous, ‘class G‘], _rational, _Bernoulli]

14.175

5132

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

[_separable]

7.302

5133

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

[[_homogeneous, ‘class A‘], _dAlembert]

13.724

5134

\begin{align*} y y^{\prime } x +x^{2} {\mathrm e}^{-\frac {2 y}{x}}-y^{2}&=0 \\ \end{align*}

[[_homogeneous, ‘class A‘], _dAlembert]

11.948

5135

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

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

71.666

5136

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

[_separable]

6.582

5137

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

[_separable]

6.694

5138

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

[_separable]

6.421

5139

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

[_quadrature]

2.904

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‘]]

16.308

5141

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

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

37.294

5142

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

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

16.684

5143

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

[_separable]

6.753

5144

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

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

117.463

5145

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

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

35.356

5146

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

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

31.116

5147

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

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

36.546

5148

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

[[_homogeneous, ‘class A‘], _dAlembert]

34.536

5149

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

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

28.648

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‘]]

41.093

5151

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

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

150.793

5152

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

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

90.165

5153

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

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

85.139

5154

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

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

84.351

5155

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

[_separable]

7.149

5156

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

[_separable]

9.988

5157

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

[_rational, _Bernoulli]

5.628

5158

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

[_separable]

8.222

5159

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

[[_homogeneous, ‘class G‘], _rational, _Bernoulli]

8.481

5160

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

[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli]

17.089

5161

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

[[_homogeneous, ‘class A‘], _rational, _Bernoulli]

20.491

5162

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

[_rational, _Bernoulli]

20.778

5163

\begin{align*} 2 y y^{\prime } x +x^{2} \left (a \,x^{3}+1\right )&=6 y^{2} \\ \end{align*}

[_rational, _Bernoulli]

4.931

5164

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

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

8.313

5165

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

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

79.026

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‘]]

53.087

5167

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

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

42.972

5168

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

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

39.153

5169

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

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

38.914

5170

\begin{align*} 2 x \left (2 x^{2}+y\right ) y^{\prime }+\left (12 x^{2}+y\right ) y&=0 \\ \end{align*}

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

35.512

5171

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

[_exact, _rational, _Bernoulli]

5.089

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‘]]

73.695

5173

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

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

39.142

5174

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

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

8.268

5175

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

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

9.890

5176

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

[[_homogeneous, ‘class A‘], _rational, _Bernoulli]

34.188

5177

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

[[_homogeneous, ‘class A‘], _rational, _Bernoulli]

30.822

5178

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

[_separable]

14.782

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‘]]

38.937

5180

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

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

7.895

5181

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

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

61.339

5182

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

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

84.475

5183

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

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

6.788

5184

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

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

53.092

5185

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

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

85.954

5186

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

[_separable]

10.986

5187

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

[_separable]

10.155

5188

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

[_separable]

12.399

5189

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

[_rational, _Bernoulli]

4.368

5190

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

[[_homogeneous, ‘class D‘], _rational, _Bernoulli]

7.208

5191

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

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

80.197

5192

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

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

47.974

5193

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

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

63.021

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]

111.226

5195

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

[_separable]

10.586

5196

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

[[_homogeneous, ‘class G‘], _rational, _Bernoulli]

10.387

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]

25.398

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‘]]

69.082

5199

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

[[_homogeneous, ‘class G‘], _exact, _rational, _Bernoulli]

8.313

5200

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

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

8.839