2.3.232 Problems 23101 to 23200

Table 2.995: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

23101

11532

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

8.383

23102

20983

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

8.400

23103

4709

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

8.402

23104

13222

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

8.403

23105

4855

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

8.408

23106

12230

\begin{align*} y^{\prime }&=-\frac {a x}{2}+1+y^{2}+\frac {a \,x^{2} y}{2}+b x y+\frac {a^{2} x^{4}}{16}+\frac {a \,x^{3} b}{4}+\frac {b^{2} x^{2}}{4}+y^{3}+\frac {3 a \,x^{2} y^{2}}{4}+\frac {3 b x y^{2}}{2}+\frac {3 a^{2} x^{4} y}{16}+\frac {3 y a \,x^{3} b}{4}+\frac {3 b^{2} x^{2} y}{4}+\frac {a^{3} x^{6}}{64}+\frac {3 a^{2} x^{5} b}{32}+\frac {3 a \,x^{4} b^{2}}{16}+\frac {b^{3} x^{3}}{8} \\ \end{align*}

8.408

23107

17970

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

8.410

23108

11870

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

8.437

23109

19665

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

8.438

23110

19180

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

8.439

23111

12854

\begin{align*} y^{\prime \prime }&=\frac {f \left (\frac {y}{\sqrt {x}}\right )}{x^{{3}/{2}}} \\ \end{align*}

8.440

23112

1199

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

8.441

23113

7873

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

8.441

23114

4078

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

8.448

23115

19274

\begin{align*} v^{\prime }&=g -\frac {k v^{2}}{m} \\ \end{align*}

8.451

23116

11415

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

8.456

23117

13321

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

8.477

23118

24181

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

8.479

23119

21604

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

8.480

23120

7715

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

8.490

23121

12266

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

8.497

23122

13591

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

8.503

23123

11574

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

8.508

23124

21671

\begin{align*} x^{2} y^{\prime \prime }+{\mathrm e}^{x} y^{\prime } x +\left (x^{3}-1\right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

8.515

23125

5059

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

8.522

23126

6359

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

8.531

23127

24147

\begin{align*} \left (2 a^{2}-r^{2}\right ) r^{\prime }&=r^{3} \sin \left (\theta \right ) \\ r \left (0\right ) &= a \\ \end{align*}

8.532

23128

13273

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

8.533

23129

12267

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

8.538

23130

5327

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

8.541

23131

17289

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

8.552

23132

9166

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

8.556

23133

19729

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

8.558

23134

24299

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

8.558

23135

806

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

8.562

23136

13356

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

8.562

23137

15640

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

8.567

23138

18726

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

8.579

23139

3035

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

8.580

23140

18731

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

8.585

23141

21412

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

8.585

23142

14021

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

8.586

23143

17214

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

8.587

23144

5319

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

8.595

23145

5304

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

8.596

23146

12161

\begin{align*} y^{\prime }&=\frac {-18 y x -6 x^{3}-18 x +27 y^{3}+27 y^{2} x^{2}+9 x^{4} y+x^{6}}{27 y+9 x^{2}+27} \\ \end{align*}

8.611

23147

5094

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

8.619

23148

19327

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

8.619

23149

1194

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

8.624

23150

9179

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

8.626

23151

11646

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

8.626

23152

12461

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

8.627

23153

12247

\begin{align*} y^{\prime }&=-\frac {x \left (-513-432 x -576 x^{5}-594 x^{2} y-1134 x^{2}-972 x^{4} y^{2}-378 y+864 x^{5} y^{2}-864 x^{4}-216 x^{4} y-456 x^{6}+288 x^{7} y-144 x^{7}+720 x^{3} y-96 x^{8}-1296 y^{2} x^{2}-216 y^{3}-288 x^{6} y-216 x^{6} y^{3}-288 y x^{8}-756 x^{3}+432 x^{3} y^{2}-540 y^{2}-648 x^{2} y^{3}+1008 x^{5} y+64 x^{9}-648 y^{3} x^{4}-216 x^{6} y^{2}+432 y^{2} x^{7}\right )}{216 \left (x^{2}+1\right )^{4}} \\ \end{align*}

8.628

23154

19283

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

8.634

23155

24384

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

8.634

23156

11571

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

8.636

23157

4237

\begin{align*} x y^{\prime } y&=\sqrt {y^{2}-9} \\ y \left ({\mathrm e}^{4}\right ) &= 5 \\ \end{align*}

8.641

23158

17034

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

8.667

23159

5233

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

8.687

23160

3435

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

8.697

23161

12042

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

8.704

23162

2854

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

8.708

23163

20306

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

8.708

23164

5025

\begin{align*} y^{\prime } \sqrt {a_{4} x^{4}+a_{3} x^{3}+a_{2} x^{2}+a_{1} x +a_{0}}&=\sqrt {b_{0} +b_{1} y+b_{2} y^{2}} \\ \end{align*}

8.710

23165

24896

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

8.710

23166

21409

\begin{align*} 2 y-8 x^{2}+y^{\prime } x&=0 \\ \end{align*}

8.724

23167

21413

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

8.724

23168

11900

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

8.726

23169

11580

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

8.729

23170

13624

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

8.730

23171

23944

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

8.732

23172

21057

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

8.734

23173

24163

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

8.738

23174

13971

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

8.740

23175

528

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

8.754

23176

13226

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

8.760

23177

7030

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

8.763

23178

12265

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

8.763

23179

4417

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

8.766

23180

1622

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

8.767

23181

23147

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

8.767

23182

13986

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

8.772

23183

7392

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

8.778

23184

3677

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

8.796

23185

21348

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

8.797

23186

7714

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

8.801

23187

11869

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

8.806

23188

18349

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

8.809

23189

1608

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

8.823

23190

2858

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

8.823

23191

21458

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

8.828

23192

12216

\begin{align*} y^{\prime }&=-\frac {x}{4}+1+y^{2}+\frac {7 x^{2} y}{16}-\frac {y x}{2}+\frac {5 x^{4}}{128}-\frac {5 x^{3}}{64}+\frac {x^{2}}{16}+y^{3}+\frac {3 y^{2} x^{2}}{8}-\frac {3 x y^{2}}{4}+\frac {3 x^{4} y}{64}-\frac {3 x^{3} y}{16}+\frac {x^{6}}{512}-\frac {3 x^{5}}{256} \\ \end{align*}

8.829

23193

15638

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

8.830

23194

23149

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

8.831

23195

20405

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

8.832

23196

19710

\begin{align*} v^{\prime }+\frac {2 v}{u}&=3 \\ \end{align*}

8.835

23197

11962

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

8.836

23198

21463

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

8.840

23199

12157

\begin{align*} y^{\prime }&=\frac {-2 y x +2 x^{3}-2 x -y^{3}+3 y^{2} x^{2}-3 x^{4} y+x^{6}}{-y+x^{2}-1} \\ \end{align*}

8.842

23200

7032

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

8.843