2.3.105 Problems 10401 to 10500

Table 2.741: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

10401

17591

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

0.543

10402

21897

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

0.543

10403

21942

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

0.543

10404

25803

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

0.543

10405

1405

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

0.544

10406

2468

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

0.544

10407

4013

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

0.544

10408

5609

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

0.544

10409

9526

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

0.544

10410

11718

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

0.544

10411

18327

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

0.544

10412

25413

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

0.544

10413

386

\begin{align*} x^{\prime \prime }+25 x&=90 \cos \left (4 t \right ) \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 90 \\ \end{align*}

0.545

10414

618

\begin{align*} x_{1}^{\prime }&=x_{1}+2 x_{2}+x_{3} \\ x_{2}^{\prime }&=6 x_{1}-x_{2} \\ x_{3}^{\prime }&=-x_{1}-2 x_{2}-x_{3} \\ \end{align*}
With initial conditions
\begin{align*} x_{1} \left (0\right ) &= 1 \\ x_{2} \left (0\right ) &= 2 \\ x_{3} \left (0\right ) &= 3 \\ \end{align*}

0.545

10415

4126

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

0.545

10416

6508

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

0.545

10417

8899

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

0.545

10418

20641

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

0.545

10419

20807

\begin{align*} x^{\prime }-7 x+y&=0 \\ y^{\prime }-2 x-5 y&=0 \\ \end{align*}

0.545

10420

21857

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

0.545

10421

24432

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

0.545

10422

358

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

0.546

10423

1401

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

0.546

10424

1808

\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&=14 x^{{3}/{2}} {\mathrm e}^{x} \\ \end{align*}

0.546

10425

1994

\begin{align*} 8 x^{2} \left (-x^{2}+2\right ) y^{\prime \prime }+2 x \left (-21 x^{2}+10\right ) y^{\prime }-\left (35 x^{2}+2\right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.546

10426

2287

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

0.546

10427

2805

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

0.546

10428

3607

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

0.546

10429

3732

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

0.546

10430

3897

\begin{align*} x_{1}^{\prime }&=-3 x_{1}-x_{2} \\ x_{2}^{\prime }&=4 x_{1}-7 x_{2} \\ x_{3}^{\prime }&=6 x_{1}+6 x_{2}+4 x_{3} \\ \end{align*}

0.546

10431

4012

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

0.546

10432

6142

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

0.546

10433

6540

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

0.546

10434

9793

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

0.546

10435

14649

\begin{align*} y^{\prime \prime }-10 y^{\prime }+29 y&=8 \,{\mathrm e}^{5 x} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 8 \\ \end{align*}

0.546

10436

15266

\begin{align*} x^{\prime }&=\frac {5 x}{4}+\frac {3 y}{4} \\ y^{\prime }&=\frac {x}{2}-\frac {3 y}{2} \\ \end{align*}

0.546

10437

15466

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

0.546

10438

16409

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

0.546

10439

17495

\begin{align*} y^{\prime \prime }-12 y^{\prime }+37 y&={\mathrm e}^{6 t} \sec \left (t \right ) \\ \end{align*}

0.546

10440

18416

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

0.546

10441

22940

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

0.546

10442

23516

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

0.546

10443

25557

\begin{align*} y^{\prime \prime }+k y&={\mathrm e}^{i \omega t} \\ \end{align*}

0.546

10444

1427

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

0.547

10445

3279

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

0.547

10446

3915

\begin{align*} x_{1}^{\prime }&=9 x_{1}-2 x_{2}+9 t \\ x_{2}^{\prime }&=5 x_{1}-2 x_{2} \\ \end{align*}

0.547

10447

4163

\begin{align*} 9 y^{\prime \prime }-6 y^{\prime }+y&=\left (4 x^{2}+24 x +18\right ) {\mathrm e}^{x} \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= 4 \\ \end{align*}

0.547

10448

5442

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

0.547

10449

6354

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

0.547

10450

8219

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

0.547

10451

8393

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

0.547

10452

9263

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

0.547

10453

18269

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

0.547

10454

21642

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

0.547

10455

21656

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

0.547

10456

22863

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

0.547

10457

23744

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

0.547

10458

12517

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

0.548

10459

21133

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

0.548

10460

21777

\begin{align*} x^{\prime }&=2 x-7 y \\ y^{\prime }&=3 x-8 y \\ \end{align*}

0.548

10461

21800

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

0.548

10462

21917

\begin{align*} y^{\prime \prime \prime \prime }-4 y^{\prime \prime }&=0 \\ y \left (0\right ) &= 5 \\ y^{\prime }\left (0\right ) &= 2 \\ y^{\prime \prime }\left (0\right ) &= 8 \\ y^{\prime \prime \prime }\left (0\right ) &= 0 \\ \end{align*}
Using Laplace transform method.

0.548

10463

23536

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

0.548

10464

25582

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

0.548

10465

372

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

0.549

10466

1390

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

0.549

10467

1494

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

0.549

10468

1845

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

0.549

10469

2632

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

0.549

10470

3841

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

0.549

10471

5505

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

0.549

10472

9699

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

0.549

10473

9812

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

0.549

10474

13881

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

0.549

10475

14045

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

0.549

10476

14647

\begin{align*} 9 y+6 y^{\prime }+y^{\prime \prime }&=27 \,{\mathrm e}^{-6 x} \\ y \left (0\right ) &= -2 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

0.549

10477

14859

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

0.549

10478

15549

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

0.549

10479

15746

\(\left [\begin {array}{cccc} 1 & 3 & 5 & 7 \\ 2 & 6 & 10 & 14 \\ 3 & 9 & 15 & 21 \\ 6 & 18 & 30 & 42 \end {array}\right ]\)

N/A

N/A

N/A

0.549

10480

17721

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

0.549

10481

20542

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

0.549

10482

22735

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

0.549

10483

1432

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

0.550

10484

2766

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

0.550

10485

6272

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

0.550

10486

7575

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

0.550

10487

7896

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

0.550

10488

10194

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

0.550

10489

14302

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

0.550

10490

15238

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

0.550

10491

16677

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

0.550

10492

17826

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

0.550

10493

18272

\begin{align*} y^{\prime \prime }-4 y^{\prime }+5 y&=2 \,{\mathrm e}^{x} x^{2} \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 3 \\ \end{align*}

0.550

10494

18979

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

0.550

10495

19551

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

0.550

10496

21213

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

0.550

10497

21938

\begin{align*} y^{\prime \prime }+4 y^{\prime }+13 y&=0 \\ \end{align*}

0.550

10498

22719

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

0.550

10499

1033

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

0.551

10500

5710

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

0.551