2.3.85 Problems 8401 to 8500

Table 2.701: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

8401

4505

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

0.421

8402

6495

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

0.421

8403

7840

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

0.421

8404

8493

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

0.421

8405

9506

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

0.421

8406

10887

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

0.421

8407

14606

\begin{align*} y^{\prime \prime }-4 y^{\prime }+29 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 5 \\ \end{align*}

0.421

8408

14608

\begin{align*} y^{\prime \prime }+6 y^{\prime }+13 y&=0 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*}

0.421

8409

14879

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

0.421

8410

16000

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

0.421

8411

17757

\begin{align*} y^{\prime \prime }+7 y^{\prime }+12 y&=3 t^{2} {\mathrm e}^{-4 t} \\ \end{align*}

0.421

8412

18116

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

0.421

8413

18869

\begin{align*} y^{\prime \prime }-5 y^{\prime }+6 y&=g \left (t \right ) \\ \end{align*}

0.421

8414

19744

\begin{align*} \sqrt {1+v^{\prime }}&=\frac {{\mathrm e}^{u}}{2} \\ \end{align*}

0.421

8415

20119

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

0.421

8416

20506

\begin{align*} x^{3} y^{\prime \prime \prime }+6 x^{2} y^{\prime \prime }+8 y^{\prime } x +2 y&=x^{2}+3 x -4 \\ \end{align*}

0.421

8417

22162

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

0.421

8418

22937

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

0.421

8419

468

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

0.422

8420

2401

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

0.422

8421

7581

\begin{align*} y^{\prime \prime }+25 y&=\cos \left (\omega t \right ) \\ \end{align*}

0.422

8422

9832

\begin{align*} y^{\prime \prime }-9 y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.422

8423

14265

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

0.422

8424

14374

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

0.422

8425

16442

\begin{align*} y^{\prime \prime }&=2 y^{\prime }-5 y+30 \,{\mathrm e}^{3 x} \\ \end{align*}

0.422

8426

16621

\begin{align*} y^{\prime \prime }-6 y^{\prime }+9 y&={\mathrm e}^{2 x} \sin \left (x \right ) \\ \end{align*}

0.422

8427

16655

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

0.422

8428

16844

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

0.422

8429

17606

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

0.422

8430

20360

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

0.422

8431

21121

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

0.422

8432

25364

\begin{align*} y_{1}^{\prime }&=5 y_{1}-2 y_{2} \\ y_{2}^{\prime }&=4 y_{1}-y_{2} \\ \end{align*}
With initial conditions
\begin{align*} y_{1} \left (0\right ) &= 0 \\ y_{2} \left (0\right ) &= 1 \\ \end{align*}

0.422

8433

5809

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

0.423

8434

7090

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

0.423

8435

12528

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

0.423

8436

15450

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

0.423

8437

16078

\begin{align*} y^{\prime \prime }+6 y^{\prime }+8 y&={\mathrm e}^{-t} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

0.423

8438

17116

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

0.423

8439

19580

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

0.423

8440

21136

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

0.423

8441

24752

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

0.423

8442

24768

\begin{align*} y^{\prime }-2 y-v^{\prime }-v&=6 \,{\mathrm e}^{3 x} \\ 2 y^{\prime }-3 y+v^{\prime }-3 v&=6 \,{\mathrm e}^{3 x} \\ \end{align*}

0.423

8443

480

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

0.424

8444

967

\begin{align*} x_{1}^{\prime }&=3 x_{1}+4 x_{2} \\ x_{2}^{\prime }&=3 x_{1}+2 x_{2} \\ \end{align*}
With initial conditions
\begin{align*} x_{1} \left (0\right ) &= 1 \\ x_{2} \left (0\right ) &= 1 \\ \end{align*}

0.424

8445

2659

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

0.424

8446

9804

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

0.424

8447

10942

\begin{align*} \left (2 x^{2}+4 x +5\right ) y^{\prime \prime }-20 \left (x +1\right ) y^{\prime }+60 y&=0 \\ \end{align*}

0.424

8448

12534

\begin{align*} \left (2 x^{2}+6 x +4\right ) y^{\prime \prime }+\left (10 x^{2}+21 x +8\right ) y^{\prime }+\left (12 x^{2}+17 x +8\right ) y&=0 \\ \end{align*}

0.424

8449

14610

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

0.424

8450

14731

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

0.424

8451

15003

\begin{align*} x^{\prime }&=x+20 y \\ y^{\prime }&=40 x-19 y \\ \end{align*}

0.424

8452

16346

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

0.424

8453

18679

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

0.424

8454

20361

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

0.424

8455

22186

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

0.424

8456

23473

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

0.424

8457

23939

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

0.424

8458

257

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

0.425

8459

2796

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

0.425

8460

4021

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

0.425

8461

5378

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

0.425

8462

6268

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

0.425

8463

7094

\begin{align*} y^{\prime \prime }-5 y^{\prime }-6 y&={\mathrm e}^{3 x} \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}

0.425

8464

12981

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

0.425

8465

14688

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

0.425

8466

15085

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

0.425

8467

16933

\begin{align*} x^{\prime }&=x+2 y \\ y^{\prime }&=5 x-2 y \\ \end{align*}
With initial conditions
\begin{align*} x \left (0\right ) &= 7 \\ y \left (0\right ) &= -7 \\ \end{align*}

0.425

8468

18234

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

0.425

8469

20940

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

0.425

8470

1893

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

0.426

8471

5630

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

0.426

8472

6393

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

0.426

8473

14215

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

0.426

8474

14611

\begin{align*} 4 y^{\prime \prime }+4 y^{\prime }+37 y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= -4 \\ \end{align*}

0.426

8475

14978

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

0.426

8476

18398

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

0.426

8477

20519

\begin{align*} x^{3} y^{\prime \prime \prime }+6 x^{2} y^{\prime \prime }+8 y^{\prime } x +2 y&=x^{2}+3 x -4 \\ \end{align*}

0.426

8478

23571

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

0.426

8479

24105

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

0.426

8480

326

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

0.427

8481

1314

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

0.427

8482

1444

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

0.427

8483

1892

\begin{align*} \left (2 x^{2}+x +1\right ) y^{\prime \prime }+\left (2+8 x \right ) y^{\prime }+4 y&=0 \\ y \left (0\right ) &= -1 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*}
Series expansion around \(x=0\).

0.427

8484

4498

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

0.427

8485

6430

\begin{align*} y y^{\prime \prime }&={\mathrm e}^{x} y \left (\operatorname {a0} +\operatorname {a1} y^{2}\right )+{\mathrm e}^{2 x} \left (\operatorname {a2} +\operatorname {a3} y^{4}\right )+{y^{\prime }}^{2} \\ \end{align*}

0.427

8486

7292

\begin{align*} y^{\prime \prime }+2 y^{\prime }+17 y&=60 \,{\mathrm e}^{-4 x} \sin \left (5 x \right ) \\ \end{align*}

0.427

8487

7293

\begin{align*} 4 y^{\prime \prime }+4 y^{\prime }+5 y&=40 \,{\mathrm e}^{-\frac {3 x}{2}} \sin \left (2 x \right ) \\ \end{align*}

0.427

8488

10738

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

0.427

8489

14625

\begin{align*} y^{\prime \prime }+2 y^{\prime }+10 y&=5 \,{\mathrm e}^{-2 x} x \\ \end{align*}

0.427

8490

14793

\begin{align*} x^{\prime }&=-2 x+7 y \\ y^{\prime }&=3 x+2 y \\ \end{align*}
With initial conditions
\begin{align*} x \left (0\right ) &= 9 \\ y \left (0\right ) &= -1 \\ \end{align*}

0.427

8491

15994

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

0.427

8492

15998

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

0.427

8493

21591

\begin{align*} y^{\prime \prime }+y^{\prime }-12 y&={\mathrm e}^{x} x^{2} \\ \end{align*}

0.427

8494

25385

\begin{align*} y_{1}^{\prime }&=-2 y_{1}+y_{2} \\ y_{2}^{\prime }&=-4 y_{1}+3 y_{2} \\ \end{align*}
With initial conditions
\begin{align*} y_{1} \left (0\right ) &= 1 \\ y_{2} \left (0\right ) &= -2 \\ \end{align*}

0.427

8495

25763

\begin{align*} y^{\prime \prime }+2 y^{\prime }-3 y&=-12 x +8 \\ y \left (1\right ) &= -2 \\ y^{\prime }\left (1\right ) &= 4 \\ \end{align*}

0.427

8496

25764

\begin{align*} y^{\prime \prime }+2 y^{\prime }-3 y&=-12 x +8 \\ y \left (-1\right ) &= 1 \\ y^{\prime }\left (-1\right ) &= 1 \\ \end{align*}

0.427

8497

1188

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

0.428

8498

1901

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

0.428

8499

1913

\begin{align*} \left (10-2 x \right ) y^{\prime \prime }+\left (x +1\right ) y&=0 \\ y \left (2\right ) &= 2 \\ y^{\prime }\left (2\right ) &= -4 \\ \end{align*}
Series expansion around \(x=2\).

0.428

8500

2583

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

0.428