2.3.272 Problems 27101 to 27200

Table 2.1117: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

27101

12024

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

76.715

27102

13986

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

76.793

27103

13401

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

76.852

27104

6573

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

76.861

27105

4389

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

76.907

27106

13517

\begin{align*} y y^{\prime }-y&=-\frac {2 x}{9}+\frac {A}{\sqrt {x}} \\ \end{align*}

76.910

27107

19154

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

76.959

27108

18557

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

77.033

27109

13846

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

77.125

27110

14546

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

77.136

27111

25884

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

77.147

27112

23141

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

77.502

27113

8708

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

77.598

27114

20744

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

77.649

27115

13978

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

77.725

27116

19139

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

77.798

27117

13220

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

77.811

27118

13564

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

77.891

27119

17275

\begin{align*} 2 t^{2}-7 y t +5 y^{2}+t y y^{\prime }&=0 \\ \end{align*}

77.904

27120

11817

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

77.909

27121

13577

\begin{align*} y y^{\prime }+\frac {a \left (6 x -1\right ) y}{2 x}&=-\frac {a^{2} \left (x -1\right ) \left (4 x -1\right )}{2 x} \\ \end{align*}

77.925

27122

19717

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

78.055

27123

13364

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

78.070

27124

5191

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

78.126

27125

19901

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

78.357

27126

6448

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

78.464

27127

12088

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

78.584

27128

25760

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

78.826

27129

12597

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

78.961

27130

19215

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

79.006

27131

10312

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

79.026

27132

13399

\begin{align*} \left (a \tan \left (\lambda x \right )+b \right ) y^{\prime }&=y^{2}+k \tan \left (\mu x \right ) y-d^{2}+k d \tan \left (\mu x \right ) \\ \end{align*}

79.035

27133

16325

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

79.165

27134

11806

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

79.302

27135

21429

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

79.336

27136

27445

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

79.418

27137

1720

\begin{align*} 12 x^{3} y+24 x^{2} y^{2}+\left (9 x^{4}+32 x^{3} y+4 y\right ) y^{\prime }&=0 \\ \end{align*}

79.457

27138

6088

\begin{align*} \left (\operatorname {c0} \,x^{2}+\operatorname {b0} x +\operatorname {a0} \right ) y+a x y^{\prime }+\left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\ \end{align*}

79.511

27139

20619

\begin{align*} 4 x^{2} y^{\prime \prime }+4 x^{5} y^{\prime }+\left (x^{3}+6 x^{2}+4\right ) y&=0 \\ \end{align*}

79.628

27140

13591

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

79.772

27141

2943

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

79.918

27142

12072

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

79.925

27143

15360

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

80.047

27144

18719

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

80.112

27145

26673

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

80.342

27146

11907

\begin{align*} y^{\prime }&=\frac {x^{{5}/{3}}}{y+x^{{4}/{3}}} \\ \end{align*}

80.438

27147

5145

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

80.546

27148

10411

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

80.707

27149

26053

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

80.839

27150

13578

\begin{align*} y y^{\prime }-\frac {a \left (1+\frac {2 b}{x^{2}}\right ) y}{2}&=\frac {a^{2} \left (3 x +\frac {4 b}{x}\right )}{16} \\ \end{align*}

80.878

27151

27336

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

80.907

27152

17051

\begin{align*} y^{\prime }&=\sqrt {25-y^{2}} \\ y \left (3\right ) &= -6 \\ \end{align*}

81.023

27153

21823

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

81.384

27154

13527

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

81.391

27155

22932

\begin{align*} x^{\prime }-x+2 y-z&=t^{2} \\ y^{\prime }+3 x-y+4 z&={\mathrm e}^{t} \\ z^{\prime }-2 x+y-z&=0 \\ \end{align*}

81.501

27156

17267

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

81.533

27157

22013

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

81.734

27158

25496

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

81.775

27159

25528

\begin{align*} m y^{\prime \prime }+k y&=1 \\ \end{align*}

81.775

27160

12673

\begin{align*} y^{\prime \prime }&=-\frac {\left (a p \,x^{b}+q \right ) y^{\prime }}{x \left (a \,x^{b}-1\right )}-\frac {\left (a r \,x^{b}+s \right ) y}{x^{2} \left (a \,x^{b}-1\right )} \\ \end{align*}

81.789

27161

11674

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

81.808

27162

20100

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

81.977

27163

17919

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

82.389

27164

13469

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

82.390

27165

10154

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

82.399

27166

21462

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

82.543

27167

22386

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

82.610

27168

13617

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

82.632

27169

27147

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

82.655

27170

19817

\begin{align*} \left (6 x -5 y+4\right ) y^{\prime }&=1+2 x -y \\ \end{align*}

82.740

27171

18605

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

83.207

27172

12516

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

83.336

27173

15630

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

83.362

27174

13567

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

83.497

27175

8734

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

83.615

27176

13834

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

83.658

27177

5182

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

83.664

27178

6170

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

83.796

27179

12500

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

84.074

27180

5360

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

84.177

27181

19905

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

84.217

27182

13031

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

84.245

27183

13620

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

84.415

27184

13613

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

84.477

27185

12634

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

84.609

27186

6279

\begin{align*} -\left (4 k^{2}+\left (-4 p^{2}+1\right ) \left (-x^{2}+1\right )\right ) y-8 x \left (-x^{2}+1\right ) y^{\prime }+4 \left (-x^{2}+1\right )^{2} y^{\prime \prime }&=0 \\ \end{align*}

84.694

27187

6258

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

84.813

27188

12090

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

84.898

27189

15585

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

85.439

27190

25886

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

85.551

27191

6260

\begin{align*} \left (\operatorname {a4} \,x^{4}+\operatorname {a2} \,x^{2}+\operatorname {a0} \right ) y-2 x \left (-x^{2}+1\right ) y^{\prime }+\left (-x^{2}+1\right )^{2} y^{\prime \prime }&=0 \\ \end{align*}

85.697

27192

24386

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

85.750

27193

6278

\begin{align*} -\left (4 k^{2}+\left (4 p^{2}+1\right ) \left (-x^{2}+1\right )\right ) y-8 x \left (-x^{2}+1\right ) y^{\prime }+4 \left (-x^{2}+1\right )^{2} y^{\prime \prime }&=0 \\ \end{align*}

85.793

27194

13225

\begin{align*} x^{n +1} y^{\prime }&=x^{2 n} a y^{2}+c \,x^{m}+d \\ \end{align*}

85.931

27195

11909

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

85.950

27196

5154

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

85.961

27197

13433

\begin{align*} y^{\prime }&=\lambda \arccos \left (x \right )^{n} \left (y-a \,x^{m}-b \right )^{2}+a m \,x^{m -1} \\ \end{align*}

86.013

27198

25769

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

86.093

27199

13655

\begin{align*} y^{\prime }&=\frac {y^{3}}{\sqrt {a \,x^{2}+b x +c}}+y^{2} \\ \end{align*}

86.231

27200

21853

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

86.265