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‘]]

17.485

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‘]]

14.498

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‘]]

11.281

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‘]]

25.143

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]

36.280

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‘]]

68.718

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‘]]

198.494

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‘]]

24.580

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‘]]

38.056

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‘]]

89.759

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‘]]

14.990

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‘]]

90.015

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‘]]

40.445

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‘]]

26.431

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‘]]

46.876

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‘]]

47.658

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]

68.843

5118

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

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

45.737

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‘]]

48.021

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‘]]

26.991

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‘]]

97.866

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‘]]

96.440

5123

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

[_separable]

11.709

5124

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

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

14.530

5125

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

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

21.833

5126

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

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

11.169

5127

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

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

7.753

5128

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

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

39.667

5129

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

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

22.504

5130

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

[_separable]

12.694

5131

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

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

14.744

5132

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

[_separable]

7.428

5133

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

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

14.790

5134

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

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

11.794

5135

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

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

70.733

5136

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

[_separable]

6.747

5137

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

[_separable]

7.232

5138

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

[_separable]

6.785

5139

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

[_quadrature]

3.069

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‘]]

16.127

5141

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

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

35.362

5142

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

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

30.566

5143

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

[_separable]

7.142

5144

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

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

125.414

5145

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

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

80.546

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‘]]

28.326

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‘]]

38.129

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]

33.029

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‘]]

46.471

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‘]]

42.600

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‘]]

123.256

5152

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

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

96.493

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‘]]

90.189

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‘]]

85.961

5155

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

[_separable]

7.386

5156

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

[_separable]

10.252

5157

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

[_rational, _Bernoulli]

3.927

5158

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

[_separable]

8.499

5159

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

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

7.408

5160

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

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

21.964

5161

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

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

27.068

5162

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

[_rational, _Bernoulli]

25.647

5163

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

[_rational, _Bernoulli]

5.006

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‘]]

9.233

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‘]]

57.220

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‘]]

43.512

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‘]]

45.112

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‘]]

35.006

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‘]]

34.750

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‘]]

33.785

5171

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

[_exact, _rational, _Bernoulli]

5.379

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‘]]

70.752

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‘]]

38.523

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‘]]

8.618

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‘]]

10.345

5176

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

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

31.247

5177

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

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

28.010

5178

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

[_separable]

15.437

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‘]]

37.050

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‘]]

8.244

5181

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

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

75.559

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‘]]

83.664

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‘]]

7.175

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‘]]

55.773

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‘]]

87.181

5186

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

[_separable]

11.648

5187

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

[_separable]

10.626

5188

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

[_separable]

11.641

5189

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

[_rational, _Bernoulli]

4.590

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]

7.431

5191

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

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

78.126

5192

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

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

49.720

5193

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

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

63.033

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]

87.370

5195

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

[_separable]

11.227

5196

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

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

10.845

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]

30.842

5198

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

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

69.137

5199

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

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

8.646

5200

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

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

9.369