2.3.135 Problems 13401 to 13500

Table 2.843: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

13401

25413

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

1.260

13402

8910

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

1.261

13403

17728

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

Series expansion around \(x=0\).

1.261

13404

21696

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

Series expansion around \(x=0\).

1.261

13405

23553

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

1.261

13406

23924

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

1.261

13407

26564

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

1.261

13408

1187

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

1.262

13409

10442

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

1.262

13410

26812

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

Using Laplace transform method.

1.262

13411

3875

\begin{align*} x_{1}^{\prime }&=2 x_{1}+4 x_{2}+8 \sin \left (2 t \right ) \\ x_{2}^{\prime }&=-2 x_{1}-2 x_{2}+8 \cos \left (2 t \right ) \\ \end{align*}

1.263

13412

7425

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

1.263

13413

9412

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

Series expansion around \(x=0\).

1.263

13414

9568

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

1.263

13415

14679

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

1.263

13416

17279

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

1.263

13417

26567

\begin{align*} 4 y^{\prime \prime }+8 y^{\prime }&=x \sin \left (x \right ) \\ \end{align*}

1.263

13418

4597

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

Series expansion around \(x=0\).

1.264

13419

15405

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

1.264

13420

9556

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

Series expansion around \(x=0\).

1.265

13421

14780

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

1.265

13422

24076

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

1.265

13423

27723

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

1.265

13424

563

\begin{align*} x^{\prime \prime }+4 x^{\prime }+13 x&=f \left (t \right ) \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*}

Using Laplace transform method.

1.266

13425

7306

\begin{align*} y^{\prime \prime }-2 y^{\prime }&=9 x \,{\mathrm e}^{-x}-6 x^{2}+4 \,{\mathrm e}^{2 x} \\ \end{align*}

1.266

13426

18217

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

1.266

13427

19851

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

1.266

13428

21295

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

1.266

13429

15815

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

1.267

13430

17197

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

1.267

13431

23301

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

1.267

13432

5643

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

1.268

13433

16517

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

1.268

13434

22888

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

1.268

13435

37

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

1.269

13436

4299

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

1.269

13437

22922

\begin{align*} x^{\prime }+x+2 y&=8 \\ 2 x+y^{\prime }-2 y&=2 \,{\mathrm e}^{-t}-8 \\ \end{align*}

1.269

13438

23984

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

1.269

13439

24824

\begin{align*} 5 {y^{\prime }}^{2}+6 x y^{\prime }-2 y&=0 \\ \end{align*}

1.269

13440

18

\begin{align*} x^{\prime \prime }&=50 \sin \left (5 t \right ) \\ x \left (0\right ) &= 8 \\ x^{\prime }\left (0\right ) &= -10 \\ \end{align*}

1.270

13441

20145

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

Series expansion around \(x=0\).

1.270

13442

26651

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

1.270

13443

8656

\begin{align*} y^{\prime \prime }+2 y^{\prime }+5 y&=25 t -100 \delta \left (t -\pi \right ) \\ y \left (0\right ) &= -2 \\ y^{\prime }\left (0\right ) &= 5 \\ \end{align*}

Using Laplace transform method.

1.271

13444

9784

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

1.271

13445

15304

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

1.271

13446

16418

\begin{align*} y^{\prime \prime }&=y^{\prime } \\ y \left (0\right ) &= 8 \\ y^{\prime }\left (0\right ) &= 5 \\ \end{align*}

1.271

13447

9350

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

1.272

13448

9970

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

Series expansion around \(x=0\).

1.272

13449

12346

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

1.272

13450

14671

\begin{align*} y^{\prime \prime \prime \prime }+10 y^{\prime \prime }+9 y&=\sin \left (2 x \right ) \sin \left (x \right ) \\ \end{align*}

1.272

13451

14689

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

1.272

13452

16382

\begin{align*} x y^{\prime \prime }+4 y^{\prime }&=18 x^{2} \\ \end{align*}

1.272

13453

22227

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

Using Laplace transform method.

1.272

13454

26683

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

1.272

13455

1350

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

1.273

13456

8020

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

1.273

13457

9552

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

Series expansion around \(x=0\).

1.273

13458

13893

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

1.273

13459

17434

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

1.273

13460

21903

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

Series expansion around \(x=0\).

1.273

13461

22202

\begin{align*} 8 x^{2} y^{\prime \prime }+10 x y^{\prime }+\left (x -1\right ) y&=0 \\ \end{align*}

Series expansion around \(x=0\).

1.273

13462

17725

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

Series expansion around \(x=0\).

1.274

13463

20843

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

1.274

13464

21605

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

1.274

13465

860

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

1.275

13466

26725

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

1.275

13467

9429

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

Series expansion around \(x=0\).

1.276

13468

9723

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

1.276

13469

11785

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

1.276

13470

13029

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

1.276

13471

15296

\begin{align*} x^{\prime }&=9 x-3 y-6 t \\ y^{\prime }&=-x+11 y+10 t \\ \end{align*}

1.276

13472

17009

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

1.276

13473

26201

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

1.276

13474

10330

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

1.277

13475

12474

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

1.277

13476

24826

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

1.278

13477

2696

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

Using Laplace transform method.

1.279

13478

4384

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

1.279

13479

5417

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

1.279

13480

15865

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

1.279

13481

18877

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

1.280

13482

23576

\begin{align*} x^{\prime }&=3 x-2 y+2 t^{2} \\ y^{\prime }&=5 x+y-1 \\ \end{align*}

1.280

13483

27404

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

1.280

13484

1614

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

1.281

13485

7225

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

1.281

13486

7540

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

1.281

13487

17352

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

1.281

13488

18326

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

1.281

13489

24772

\begin{align*} 2 y^{\prime }+2 y+w^{\prime }-w&=x +1 \\ y^{\prime }+3 y+w^{\prime }+w&=4 x +14 \\ \end{align*}

1.281

13490

19621

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

Series expansion around \(x=\infty \).

1.282

13491

25094

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

1.282

13492

648

\begin{align*} x_{1}^{\prime }&=-2 x_{1}+9 x_{4} \\ x_{2}^{\prime }&=4 x_{1}+2 x_{2}-10 x_{4} \\ x_{3}^{\prime }&=-x_{3}+8 x_{4} \\ x_{4}^{\prime }&=x_{4} \\ \end{align*}

1.283

13493

1278

\begin{align*} 4 y^{\prime \prime }+9 y&=0 \\ \end{align*}

1.283

13494

10176

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

Series expansion around \(x=0\).

1.283

13495

11730

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

1.283

13496

12366

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

1.283

13497

18257

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

1.283

13498

25294

\begin{align*} y^{\prime }+2 y&=\left \{\begin {array}{cc} 0 & 0\le t <1 \\ -3 & 1\le t \end {array}\right . \\ y \left (0\right ) &= 0 \\ \end{align*}

Using Laplace transform method.

1.283

13499

26629

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

1.283

13500

1348

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

1.284