2.3.271 Problems 27001 to 27100

Table 2.1115: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

27001

26149

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

131.587

27002

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*}

131.956

27003

27384

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

132.020

27004

13530

\begin{align*} y y^{\prime }-y&=-\frac {3 x}{16}+\frac {3 A}{x^{{1}/{3}}}-\frac {12 A^{2}}{x^{{5}/{3}}} \\ \end{align*}

132.089

27005

22559

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

132.098

27006

24394

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

132.109

27007

24340

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

132.256

27008

18553

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

132.326

27009

27271

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

132.446

27010

21392

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

132.489

27011

11771

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

132.653

27012

21367

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

132.792

27013

9059

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

132.848

27014

13295

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

133.017

27015

21813

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

133.017

27016

24409

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

133.039

27017

15820

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

133.190

27018

13408

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

133.269

27019

26912

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

133.385

27020

8225

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

133.510

27021

13374

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

133.521

27022

5151

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

133.621

27023

24381

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

133.822

27024

27281

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

133.984

27025

24179

\begin{align*} y \left (x^{2}+y^{2}\right )+x \left (3 x^{2}-5 y^{2}\right ) y^{\prime }&=0 \\ y \left (2\right ) &= 1 \\ \end{align*}

134.261

27026

14841

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

134.351

27027

8695

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

134.401

27028

19398

\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*}

134.595

27029

20296

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

134.767

27030

27501

\begin{align*} y^{3} {y^{\prime }}^{3}&=27 x \left (y^{2}-2 x^{2}\right ) \\ \end{align*}

134.802

27031

10313

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

135.042

27032

13287

\begin{align*} y^{\prime }&=y^{2}+a \,{\mathrm e}^{2 \lambda x} \left ({\mathrm e}^{\lambda x}+b \right )^{n}-\frac {\lambda ^{2}}{4} \\ \end{align*}

135.160

27033

5194

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

135.344

27034

17076

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

135.388

27035

21453

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

135.401

27036

26437

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

135.444

27037

22466

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

135.548

27038

27359

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

135.621

27039

27334

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

135.664

27040

15357

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

135.716

27041

19092

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

135.825

27042

27432

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

135.825

27043

12620

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

135.832

27044

6470

\begin{align*} 2 y y^{\prime \prime }&=8 y^{3}+{y^{\prime }}^{2} \\ \end{align*}

135.931

27045

26606

\begin{align*} 5 y+2 y^{\prime }+y^{\prime \prime }&=4 \cos \left (2 x \right )+\sin \left (2 x \right ) \\ y \left (-\infty \right ) &= y_{0} \\ \end{align*}

135.973

27046

13514

\begin{align*} y y^{\prime }-y&=-\frac {9 x}{100}+\frac {A}{x^{{5}/{3}}} \\ \end{align*}

136.084

27047

6145

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

136.085

27048

9015

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

136.237

27049

13390

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

136.383

27050

16257

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

136.642

27051

12626

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

136.730

27052

13256

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

136.812

27053

21387

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

136.889

27054

14896

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

137.207

27055

15032

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

137.351

27056

12588

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

137.424

27057

22386

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

137.812

27058

26891

\begin{align*} 4 y^{4}-1+12 x y^{3} y^{\prime }&=0 \\ y \left (1\right ) &= 2 \\ \end{align*}

138.052

27059

3018

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

138.223

27060

13536

\begin{align*} y y^{\prime }-y&=\frac {63 x}{4}+\frac {A}{x^{{5}/{3}}} \\ \end{align*}

138.228

27061

26897

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

138.254

27062

8256

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

138.284

27063

11619

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

138.307

27064

26867

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

138.428

27065

7868

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

138.459

27066

7032

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

138.685

27067

13540

\begin{align*} y y^{\prime }-y&=-\frac {12 x}{49}+A \sqrt {x} \\ \end{align*}

138.699

27068

9019

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

138.961

27069

18732

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

138.981

27070

27412

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

139.490

27071

22770

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

139.569

27072

10316

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

140.072

27073

5250

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

140.224

27074

12566

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

140.289

27075

26397

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

140.303

27076

20952

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

140.325

27077

13617

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

140.395

27078

27214

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

140.874

27079

12604

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

140.984

27080

12525

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

141.239

27081

27476

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

141.304

27082

27280

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

141.356

27083

11798

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

141.386

27084

22009

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

141.427

27085

13633

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

142.018

27086

13253

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

142.235

27087

26907

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

142.313

27088

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*}

142.329

27089

13820

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

142.534

27090

13504

\begin{align*} y y^{\prime }-y&=-\frac {2 x}{9}+6 A^{2} \left (1+\frac {2 A}{\sqrt {x}}\right ) \\ \end{align*}

142.803

27091

23965

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

142.880

27092

27275

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

143.135

27093

27333

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

143.173

27094

27290

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

143.251

27095

13559

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

143.617

27096

9685

\begin{align*} x^{\prime }&=\frac {9 x}{10}+\frac {21 y}{10}+\frac {16 z}{5} \\ y^{\prime }&=\frac {7 x}{10}+\frac {13 y}{2}+\frac {21 z}{5} \\ z^{\prime }&=\frac {11 x}{10}+\frac {17 y}{10}+\frac {17 z}{5} \\ \end{align*}

143.674

27097

25870

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

143.725

27098

27499

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

144.432

27099

25666

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

144.434

27100

5306

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

144.448