2.3.276 Problems 27501 to 27600

Table 2.1125: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

27501

11619

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

139.227

27502

13621

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

139.290

27503

6209

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

139.304

27504

13518

\begin{align*} y y^{\prime }-y&=-\frac {12 x}{49}+\frac {6 A \left (-3 \sqrt {x}+23 A +\frac {12 A^{2}}{\sqrt {x}}\right )}{49} \\ \end{align*}

139.533

27505

13528

\begin{align*} y y^{\prime }-y&=-\frac {x}{4}+\frac {6 A \left (\sqrt {x}+8 A +\frac {5 A^{2}}{\sqrt {x}}\right )}{49} \\ \end{align*}

139.636

27506

2535

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

139.743

27507

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*}

140.270

27508

12655

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

140.492

27509

13593

\begin{align*} y y^{\prime }+\frac {a \left (33 x +2\right ) y}{30 x^{{6}/{5}}}&=-\frac {a^{2} \left (x -1\right ) \left (9 x -4\right )}{30 x^{{7}/{5}}} \\ \end{align*}

140.775

27510

5461

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

140.987

27511

13580

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

141.103

27512

19118

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

141.269

27513

6318

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

141.396

27514

6112

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

141.556

27515

13879

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

141.715

27516

5986

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

141.732

27517

13815

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

141.829

27518

18732

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

142.413

27519

19783

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

142.660

27520

21982

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

142.749

27521

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*}

142.835

27522

6210

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

143.367

27523

13598

\begin{align*} y y^{\prime }-\frac {a \left (x +4\right ) y}{5 x^{{8}/{5}}}&=\frac {a^{2} \left (x -1\right ) \left (7+3 x \right )}{5 x^{{3}/{5}}} \\ \end{align*}

143.569

27524

18341

\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*}

143.861

27525

6836

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

143.994

27526

11701

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

144.307

27527

13581

\begin{align*} y y^{\prime }+\frac {a \left (7 x -12\right ) y}{10 x^{{7}/{5}}}&=-\frac {a^{2} \left (x -1\right ) \left (x -16\right )}{10 x^{{9}/{5}}} \\ \end{align*}

145.724

27528

13599

\begin{align*} y y^{\prime }-\frac {a \left (x +4\right ) y}{5 x^{{8}/{5}}}&=\frac {a^{2} \left (x -1\right ) \left (7+3 x \right )}{5 x^{{11}/{5}}} \\ \end{align*}

145.727

27529

13848

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

145.832

27530

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*}

145.987

27531

22392

\begin{align*} y^{\prime }&=\frac {2 x +5 y}{2 x -y} \\ \end{align*}

146.321

27532

13819

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

146.365

27533

22088

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

146.366

27534

13919

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

146.770

27535

13579

\begin{align*} y y^{\prime }+\frac {a \left (13 x -18\right ) y}{15 x^{{7}/{5}}}&=-\frac {4 a^{2} \left (x -1\right ) \left (-6+x \right )}{15 x^{{9}/{5}}} \\ \end{align*}

147.414

27536

13582

\begin{align*} y y^{\prime }+\frac {3 a \left (13 x -8\right ) y}{20 x^{{7}/{5}}}&=-\frac {a^{2} \left (x -1\right ) \left (27 x -32\right )}{20 x^{{9}/{5}}} \\ \end{align*}

147.806

27537

13636

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

147.957

27538

13814

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

148.217

27539

12577

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

148.247

27540

13572

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

148.565

27541

13888

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

148.688

27542

6089

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

149.148

27543

12525

\begin{align*} x \left (x +2\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*}

149.288

27544

12588

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

149.927

27545

6294

\begin{align*} \left (\operatorname {a2} +\operatorname {b2} \,x^{k}\right ) y+x \left (\operatorname {a1} +\operatorname {b1} \,x^{k}\right ) y^{\prime }+x^{2} \left (\operatorname {a0} +\operatorname {b0} \,x^{k}\right ) y^{\prime \prime }&=0 \\ \end{align*}

150.319

27546

13628

\begin{align*} \left (A x y+A k y+B \,x^{2}+B k x \right ) y^{\prime }&=c y^{2}+d x y+k \left (d -B \right ) y \\ \end{align*}

150.506

27547

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*}

151.059

27548

13627

\begin{align*} \left (A x y+B \,x^{2}+k x \right ) y^{\prime }&=A y^{2}+c x y+d \,x^{2}+\left (-A \beta +k \right ) y-c \beta x -k \beta \\ \end{align*}

151.098

27549

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*}

151.260

27550

13111

\begin{align*} x^{\prime }&=a x+g y+\beta z \\ y^{\prime }&=g x+b y+\alpha z \\ z^{\prime }&=\beta x+\alpha y+c z \\ \end{align*}

151.467

27551

13596

\begin{align*} y y^{\prime }-\frac {2 a \left (3 x +2\right ) y}{5 x^{{8}/{5}}}&=\frac {a^{2} \left (x -1\right ) \left (8 x +1\right )}{5 x^{{11}/{5}}} \\ \end{align*}

151.667

27552

27425

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

151.775

27553

6262

\begin{align*} \left (\operatorname {c2} \,x^{2}+\operatorname {b2} x +\operatorname {a2} \right ) y+\operatorname {a1} x \left (-x^{2}+1\right ) y^{\prime }+\left (-x^{2}+1\right )^{2} y^{\prime \prime }&=0 \\ \end{align*}

152.096

27554

18347

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

152.345

27555

6081

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

152.966

27556

20468

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

153.132

27557

13602

\begin{align*} y y^{\prime }-\frac {3 a y}{x^{{7}/{4}}}&=\frac {a^{2} \left (x -1\right ) \left (x -9\right )}{4 x^{{5}/{2}}} \\ \end{align*}

153.186

27558

13601

\begin{align*} y y^{\prime }+\frac {a \left (-6+x \right ) y}{5 x^{{7}/{5}}}&=\frac {2 a^{2} \left (x -1\right ) \left (x +4\right )}{5 x^{{9}/{5}}} \\ \end{align*}

153.290

27559

13597

\begin{align*} y y^{\prime }-\frac {6 a \left (1+4 x \right ) y}{5 x^{{7}/{5}}}&=\frac {a^{2} \left (x -1\right ) \left (27 x +8\right )}{5 x^{{9}/{5}}} \\ \end{align*}

153.632

27560

6265

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

154.233

27561

13521

\begin{align*} y y^{\prime }-y&=-\frac {12 x}{49}+\frac {4 A \left (-10 \sqrt {x}+27 A +\frac {10 A^{2}}{\sqrt {x}}\right )}{49} \\ \end{align*}

154.270

27562

6173

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

154.917

27563

13529

\begin{align*} y y^{\prime }-y&=-\frac {6 x}{25}+\frac {6 A \left (2 \sqrt {x}+7 A +\frac {4 A^{2}}{\sqrt {x}}\right )}{25} \\ \end{align*}

155.432

27564

21809

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

155.518

27565

12576

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

156.048

27566

13531

\begin{align*} y y^{\prime }-y&=\frac {9 x}{32}+\frac {15 \sqrt {b^{2}+x^{2}}}{32}+\frac {3 b^{2}}{64 \sqrt {b^{2}+x^{2}}} \\ \end{align*}

156.392

27567

13833

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

156.667

27568

11467

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

156.880

27569

13512

\begin{align*} y y^{\prime }-y&=\frac {3 x}{8}+\frac {3 \sqrt {a^{2}+x^{2}}}{8}-\frac {a^{2}}{16 \sqrt {a^{2}+x^{2}}} \\ \end{align*}

157.621

27570

5606

\begin{align*} 9 \left (-x^{2}+1\right ) y^{4} {y^{\prime }}^{2}+6 x y^{5} y^{\prime }+4 x^{2}&=0 \\ \end{align*}

158.332

27571

15330

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

158.413

27572

6113

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

158.892

27573

4986

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

158.929

27574

13538

\begin{align*} y y^{\prime }-y&=2 x +2 A \left (-10 \sqrt {x}+19 A +\frac {30 A^{2}}{\sqrt {x}}\right ) \\ \end{align*}

159.896

27575

6207

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

160.302

27576

13526

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

160.362

27577

6338

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

161.638

27578

11833

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

162.135

27579

13546

\begin{align*} y y^{\prime }-y&=-\frac {4 x}{25}+\frac {A \left (7 \sqrt {x}+49 A +\frac {6 A^{2}}{\sqrt {x}}\right )}{50} \\ \end{align*}

162.208

27580

13515

\begin{align*} y y^{\prime }-y&=-\frac {12 x}{49}+\frac {2 A \left (5 \sqrt {x}+34 A +\frac {15 A^{2}}{\sqrt {x}}\right )}{49} \\ \end{align*}

162.286

27581

20476

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

162.364

27582

13823

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

163.569

27583

13537

\begin{align*} y y^{\prime }-y&=2 x +2 A \left (10 \sqrt {x}+31 A +\frac {30 A^{2}}{\sqrt {x}}\right ) \\ \end{align*}

163.618

27584

11475

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

163.671

27585

13509

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

164.078

27586

6221

\begin{align*} \left (\operatorname {b2} x +\operatorname {a2} \right ) y+x \left (\operatorname {b1} x +\operatorname {a1} \right ) y^{\prime }+x^{2} \left (1-x \right ) y^{\prime \prime }&=0 \\ \end{align*}

164.695

27587

25492

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

166.520

27588

5368

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

167.477

27589

12661

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

167.505

27590

18021

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

167.531

27591

6222

\begin{align*} \left (\operatorname {b2} x +\operatorname {a2} \right ) y+x \left (\operatorname {b1} x +\operatorname {a1} \right ) y^{\prime }+x^{2} \left (\operatorname {a0} +x \right ) y^{\prime \prime }&=0 \\ \end{align*}

167.682

27592

6214

\begin{align*} \operatorname {a2} x y+\left (\operatorname {b1} \,x^{2}+\operatorname {a1} \right ) y^{\prime }+x \left (x^{2}+\operatorname {a0} \right ) y^{\prime \prime }&=0 \\ \end{align*}

167.971

27593

13516

\begin{align*} y y^{\prime }-y&=-\frac {12 x}{49}+\frac {A \left (25 \sqrt {x}+41 A +\frac {10 A^{2}}{\sqrt {x}}\right )}{98} \\ \end{align*}

168.394

27594

20430

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

168.915

27595

12561

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

169.073

27596

13588

\begin{align*} y y^{\prime }+\frac {a \left (39 x -4\right ) y}{42 x^{{9}/{7}}}&=-\frac {a^{2} \left (x -1\right ) \left (9 x -1\right )}{42 x^{{11}/{7}}} \\ \end{align*}

169.372

27597

6180

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

169.470

27598

13584

\begin{align*} y y^{\prime }-\frac {a \left (4 x +3\right ) y}{14 x^{{8}/{7}}}&=-\frac {a^{2} \left (x -1\right ) \left (16 x +5\right )}{14 x^{{9}/{7}}} \\ \end{align*}

170.075

27599

12886

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

170.341

27600

10372

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

170.677