2.3.135 Problems 13401 to 13500

Table 2.813: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

13401

16422

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

1.234

13402

23662

\begin{align*} y^{\prime \prime \prime }+8 y&=-12 \,{\mathrm e}^{-2 t} \\ y \left (0\right ) &= -8 \\ y^{\prime }\left (0\right ) &= 24 \\ y^{\prime \prime }\left (0\right ) &= -46 \\ \end{align*}
Using Laplace transform method.

1.234

13403

401

\begin{align*} y^{\prime }&=4 y \\ \end{align*}
Series expansion around \(x=0\).

1.235

13404

9276

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

1.235

13405

10205

\begin{align*} 2 x^{2} y^{\prime \prime }+y^{\prime } x +\left (x -5\right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

1.235

13406

11304

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

1.235

13407

6129

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

1.236

13408

8307

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

1.236

13409

7204

\begin{align*} u^{\prime \prime }+\frac {4 u^{\prime }}{x}-a^{2} u&=0 \\ \end{align*}

1.237

13410

13756

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

1.237

13411

16922

\begin{align*} y^{\prime \prime } x +4 y^{\prime }+\frac {12 y}{\left (2+x \right )^{2}}&=0 \\ \end{align*}
Series expansion around \(x=0\).

1.237

13412

18999

\begin{align*} x_{1}^{\prime }&=-5 x_{1}+x_{2}-4 x_{3}-x_{4} \\ x_{2}^{\prime }&=-3 x_{2} \\ x_{3}^{\prime }&=x_{1}-x_{2}+x_{4} \\ x_{4}^{\prime }&=2 x_{1}-x_{2}+2 x_{3}-2 x_{4} \\ \end{align*}

1.237

13413

21226

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

1.237

13414

23618

\begin{align*} x^{\prime }&=7 x+4 y-4 z \\ y^{\prime }&=4 x-8 y-z \\ z^{\prime }&=-4 x-y-8 z \\ \end{align*}

1.237

13415

13676

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

1.238

13416

22724

\begin{align*} y^{\prime \prime \prime }+4 y^{\prime \prime }-6 y^{\prime }-12 y&=\sinh \left (x \right )^{4} \\ \end{align*}

1.238

13417

23937

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

1.238

13418

15144

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

1.239

13419

16675

\begin{align*} y^{\prime \prime }+9 y&=25 x \cos \left (2 x \right )+3 \sin \left (3 x \right ) \\ \end{align*}

1.239

13420

130

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

1.240

13421

6026

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

1.240

13422

12314

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

1.240

13423

20655

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

1.240

13424

25518

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

1.240

13425

2214

\begin{align*} y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+14 y^{\prime \prime }-20 y^{\prime }+25 y&={\mathrm e}^{x} \left (\left (2+6 x \right ) \cos \left (2 x \right )+3 \sin \left (2 x \right )\right ) \\ \end{align*}

1.241

13426

23585

\begin{align*} x^{\prime }&=3 x-2 y+2 t^{2} \\ y^{\prime }&=5 x+y-1 \\ \end{align*}
With initial conditions
\begin{align*} x \left (0\right ) &= {\frac {534}{2197}} \\ y \left (0\right ) &= {\frac {567}{2197}} \\ \end{align*}

1.241

13427

2705

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

1.242

13428

14318

\begin{align*} x^{\prime \prime }+\frac {x^{\prime }}{100}+4 x&=\cos \left (2 t \right ) \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*}

1.242

13429

14730

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

1.242

13430

9957

\begin{align*} 2 y^{\prime \prime } x +y^{\prime }+y&=0 \\ \end{align*}
Series expansion around \(x=0\).

1.243

13431

3220

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

1.244

13432

14195

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

1.244

13433

14127

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

1.245

13434

18282

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

1.245

13435

22357

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

1.245

13436

22879

\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +6 y&=0 \\ y \left (\frac {1}{2}\right ) &= 10 \\ \end{align*}
Series expansion around \(x={\frac {1}{2}}\).

1.245

13437

23484

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

1.245

13438

23700

\begin{align*} \left (x^{2}+2\right ) y^{\prime \prime }-3 y^{\prime }+\left (x -1\right ) y&=0 \\ y \left (1\right ) &= -20 \\ y^{\prime }\left (1\right ) &= -2 \\ \end{align*}
Series expansion around \(x=1\).

1.245

13439

220

\begin{align*} y^{\prime \prime }+y^{\prime }-6 y&=0 \\ y \left (0\right ) &= 7 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*}

1.246

13440

5382

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

1.246

13441

7644

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

1.246

13442

10206

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

1.246

13443

19854

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

1.246

13444

23671

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

1.246

13445

8178

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

1.247

13446

12586

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

1.247

13447

904

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

1.248

13448

10087

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

1.248

13449

10208

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

1.248

13450

23681

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

1.248

13451

5663

\begin{align*} 16 y^{2} {y^{\prime }}^{3}+2 y^{\prime } x -y&=0 \\ \end{align*}

1.249

13452

16628

\begin{align*} y^{\prime \prime }+4 y^{\prime }&=20 \\ \end{align*}

1.249

13453

22306

\begin{align*} x^{\prime \prime }&=t^{2}-4 t +8 \\ x \left (0\right ) &= 1 \\ x^{\prime }\left (0\right ) &= -3 \\ \end{align*}

1.249

13454

6504

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

1.250

13455

23661

\begin{align*} y^{\prime \prime \prime }+y&=18 \,{\mathrm e}^{2 t} \\ y \left (0\right ) &= -1 \\ y^{\prime }\left (0\right ) &= 13 \\ y^{\prime \prime }\left (0\right ) &= -1 \\ \end{align*}
Using Laplace transform method.

1.250

13456

861

\begin{align*} x^{2} y^{\prime \prime }+7 y^{\prime } x +25 y&=0 \\ \end{align*}

1.251

13457

3392

\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +\left (x +12\right ) y&=x^{2}+x \\ \end{align*}
Series expansion around \(x=0\).

1.251

13458

12490

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

1.251

13459

12875

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

1.251

13460

21318

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

1.251

13461

6501

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

1.252

13462

7206

\begin{align*} y^{\prime \prime }-a^{2} y&=\frac {6 y}{x^{2}} \\ \end{align*}

1.252

13463

23684

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

1.252

13464

811

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

1.253

13465

14203

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

1.253

13466

22944

\begin{align*} x^{\prime }-3 x-6 y&=9-9 t \\ y^{\prime }+3 x+3 y&=9 t \,{\mathrm e}^{-3 t} \\ \end{align*}

1.253

13467

2628

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

1.254

13468

10373

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

1.254

13469

9859

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

1.255

13470

3131

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

1.256

13471

12852

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

1.256

13472

17794

\begin{align*} x \left (x +1\right ) y^{\prime \prime }+\left (1-2 x \right ) y^{\prime }-10 y&=0 \\ \end{align*}
Series expansion around \(x=0\).

1.256

13473

9413

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

1.257

13474

15801

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

1.257

13475

16416

\begin{align*} y^{\prime \prime } x +4 y^{\prime }&=18 x^{2} \\ y \left (1\right ) &= 8 \\ y^{\prime }\left (1\right ) &= -3 \\ \end{align*}

1.257

13476

22282

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

1.257

13477

24112

\begin{align*} 4 x^{2} y^{\prime \prime }+8 y^{\prime } x +\left (2 x -3\right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

1.257

13478

6764

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

1.258

13479

9916

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

1.258

13480

22910

\begin{align*} x^{\prime }&=x+y+z \\ y^{\prime }&=2 x+5 y+3 z \\ z^{\prime }&=3 x+9 y+5 z \\ \end{align*}
With initial conditions
\begin{align*} x \left (0\right ) &= -2 \\ y \left (0\right ) &= -1 \\ z \left (0\right ) &= 3 \\ \end{align*}

1.258

13481

24902

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

1.258

13482

25446

\begin{align*} z^{\prime }+4 i z&={\mathrm e}^{8 i t} \\ \end{align*}

1.258

13483

1838

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

1.259

13484

12865

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

1.259

13485

18808

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

1.259

13486

18950

\begin{align*} y^{\prime \prime }+\frac {y^{\prime }}{4}+y&=\delta \left (t -1\right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}
Using Laplace transform method.

1.259

13487

20776

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

1.259

13488

3865

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

1.260

13489

5662

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

1.260

13490

9862

\begin{align*} 4 y^{\prime \prime } x +3 y^{\prime }+3 y&=0 \\ \end{align*}
Series expansion around \(x=0\).

1.260

13491

14959

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

1.260

13492

20498

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

1.260

13493

25211

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

1.260

13494

26076

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

1.260

13495

3325

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

1.261

13496

231

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

1.262

13497

6598

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

1.262

13498

7374

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

1.262

13499

10357

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

1.262

13500

17207

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

1.262