2.3.256 Problems 25501 to 25600

Table 2.1043: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

25501

21324

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

134.207

25502

196

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

134.437

25503

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*}

134.566

25504

21461

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

134.750

25505

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*}

134.908

25506

3579

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

135.153

25507

11794

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

135.281

25508

6802

\begin{align*} y^{\prime } y^{\prime \prime }&=a x {y^{\prime }}^{5}+3 {y^{\prime \prime }}^{2} \\ \end{align*}

135.398

25509

4744

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

135.833

25510

3004

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

135.862

25511

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*}

136.362

25512

9789

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

136.540

25513

5590

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

136.802

25514

20597

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

137.031

25515

12523

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

137.047

25516

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*}

137.419

25517

20575

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

137.838

25518

25492

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

138.339

25519

13539

\begin{align*} y y^{\prime }-y&=-\frac {12 x}{49}+\frac {A \left (5 \sqrt {x}+262 A +\frac {65 A^{2}}{\sqrt {x}}\right )}{49} \\ \end{align*}

138.899

25520

7125

\begin{align*} r^{\prime \prime }&=-\frac {k}{r^{2}} \\ \end{align*}

139.143

25521

13923

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

139.171

25522

13498

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

140.005

25523

6112

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

140.238

25524

10071

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

140.263

25525

683

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

141.079

25526

6889

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

141.253

25527

47

\begin{align*} y^{\prime }&=64^{{1}/{3}} \left (y x \right )^{{1}/{3}} \\ \end{align*}

141.918

25528

16388

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

142.580

25529

13913

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

142.587

25530

17995

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

142.752

25531

2909

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

144.240

25532

6229

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

144.258

25533

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

144.792

25534

14074

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

144.895

25535

2587

\begin{align*} y^{\prime \prime }+4 y^{\prime }+4 y&=t^{{5}/{2}} {\mathrm e}^{-2 t} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

145.310

25536

7547

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

145.401

25537

5379

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

146.064

25538

6230

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

146.133

25539

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*}

146.654

25540

4975

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

147.148

25541

11748

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

147.262

25542

12590

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

148.143

25543

17322

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

148.625

25544

8156

\begin{align*} R^{\prime \prime }&=-\frac {k}{R^{2}} \\ \end{align*}

149.448

25545

2881

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

149.622

25546

5259

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

149.832

25547

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*}

150.948

25548

5654

\begin{align*} 2 x^{3} {y^{\prime }}^{3}+6 x^{2} y {y^{\prime }}^{2}-\left (1-6 y x \right ) y y^{\prime }+2 y^{3}&=0 \\ \end{align*}

152.138

25549

8821

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

152.183

25550

15330

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

152.501

25551

19157

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

153.122

25552

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*}

153.499

25553

12631

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

153.638

25554

6215

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

153.735

25555

12654

\begin{align*} y^{\prime \prime }&=\frac {\left (7 a \,x^{2}+5\right ) y^{\prime }}{x \left (a \,x^{2}+1\right )}-\frac {\left (15 a \,x^{2}+5\right ) y}{x^{2} \left (a \,x^{2}+1\right )} \\ \end{align*}

154.372

25556

3247

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

154.849

25557

7966

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

154.943

25558

13545

\begin{align*} y y^{\prime }-y&=-\frac {12 x}{49}+\frac {2 A \left (\sqrt {x}+166 A +\frac {55 A^{2}}{\sqrt {x}}\right )}{49} \\ \end{align*}

155.015

25559

23279

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

155.437

25560

5513

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

155.714

25561

12583

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

155.753

25562

16407

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

155.812

25563

6113

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

155.986

25564

12619

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

156.346

25565

23300

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

156.558

25566

7552

\begin{align*} 4 x y^{3}-9 y^{2}+4 x y^{2}+\left (3 y^{2} x^{2}-6 y x +2 x^{2} y\right ) y^{\prime }&=0 \\ \end{align*}

157.172

25567

18021

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

157.243

25568

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*}

157.656

25569

7778

\begin{align*} x^{\prime \prime }+2 x^{\prime }+2 x&=85 \sin \left (3 t \right ) \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= -20 \\ \end{align*}

157.699

25570

6202

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

159.234

25571

13316

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

159.361

25572

12574

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

159.931

25573

886

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

160.027

25574

7542

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

160.573

25575

11687

\begin{align*} {y^{\prime }}^{2}-3 x y^{{2}/{3}} y^{\prime }+9 y^{{5}/{3}}&=0 \\ \end{align*}

160.696

25576

6233

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

160.751

25577

6264

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

160.933

25578

16099

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

161.198

25579

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*}

162.081

25580

2890

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

163.286

25581

13889

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

164.038

25582

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*}

165.232

25583

6118

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

165.549

25584

13866

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

165.705

25585

6177

\begin{align*} -9 y-3 \left (1-3 x \right ) y^{\prime }+\left (1-3 x \right )^{2} y^{\prime \prime }&=0 \\ \end{align*}

165.799

25586

18850

\begin{align*} y^{\prime \prime }+y&=\left \{\begin {array}{cc} A t & 0\le t \le \pi \\ A \left (2 \pi -t \right ) & \pi <t \le 2 \pi \\ 0 & 2 \pi <t \end {array}\right . \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

166.548

25587

20660

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

166.705

25588

11296

\begin{align*} y^{\prime \prime }&=-\frac {\left (5 x^{2}+27\right ) y}{36 \left (x^{2}-1\right )^{2}} \\ \end{align*}

166.796

25589

20450

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

166.862

25590

888

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

166.879

25591

13914

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

166.926

25592

12513

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

167.035

25593

5934

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

167.194

25594

5514

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

168.349

25595

3770

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

168.477

25596

13821

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

169.546

25597

22697

\begin{align*} y^{\prime \prime }+y&=\left \{\begin {array}{cc} x & 0\le x \le \pi \\ 0 & \pi <x \end {array}\right . \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

170.473

25598

13822

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

170.788

25599

6216

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

170.911

25600

13607

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

170.944