2.3.105 Problems 10401 to 10500

Table 2.783: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

10401

6304

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

0.784

10402

14789

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

With initial conditions

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

0.784

10403

15048

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

0.784

10404

19254

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

0.784

10405

20530

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

0.784

10406

20564

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

0.784

10407

27406

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

0.784

10408

643

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

0.785

10409

2666

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

Series expansion around \(t=0\).

0.785

10410

5800

\begin{align*} 12 y-7 y^{\prime }+y^{\prime \prime }&=x \\ \end{align*}

0.785

10411

7171

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

Series expansion around \(x=0\).

0.785

10412

15500

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

0.785

10413

16904

\begin{align*} x^{2} y^{\prime \prime }-\left (2 x^{2}+5 x \right ) y^{\prime }+\left (9+4 x \right ) y&=0 \\ \end{align*}

Series expansion around \(x=0\).

0.785

10414

18959

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

Using Laplace transform method.

0.785

10415

19887

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

0.785

10416

20790

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

0.785

10417

2785

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

With initial conditions

\begin{align*} x_{1} \left (0\right ) &= 0 \\ x_{2} \left (0\right ) &= 0 \\ x_{3} \left (0\right ) &= 0 \\ \end{align*}

0.786

10418

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*}

0.786

10419

5387

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

0.786

10420

8018

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

0.786

10421

9720

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

0.786

10422

10018

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

0.786

10423

14299

\begin{align*} x^{\prime \prime }+x^{\prime }+x&=5 \sin \left (7 t \right ) \\ \end{align*}

0.786

10424

15778

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

0.786

10425

15833

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

0.786

10426

16874

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

Series expansion around \(x=0\).

0.786

10427

18904

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

Using Laplace transform method.

0.786

10428

18907

\begin{align*} y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+6 y^{\prime \prime }-4 y^{\prime }+y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ y^{\prime \prime }\left (0\right ) &= 0 \\ y^{\prime \prime \prime }\left (0\right ) &= 1 \\ \end{align*}

Using Laplace transform method.

0.786

10429

22179

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

Series expansion around \(x=0\).

0.786

10430

640

\begin{align*} x_{1}^{\prime }&=5 x_{1}+x_{2}+3 x_{3} \\ x_{2}^{\prime }&=x_{1}+7 x_{2}+x_{3} \\ x_{3}^{\prime }&=3 x_{1}+x_{2}+5 x_{3} \\ \end{align*}

0.787

10431

2047

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

Series expansion around \(x=0\).

0.787

10432

3858

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

0.787

10433

9631

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

Using Laplace transform method.

0.787

10434

13777

\begin{align*} x^{2} y^{\prime \prime }-\left (a \,x^{3}+\frac {5}{16}\right ) y&=0 \\ \end{align*}

0.787

10435

14331

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

0.787

10436

17508

\begin{align*} y^{\prime \prime }-10 y^{\prime }+25 y&={\mathrm e}^{5 t} \ln \left (2 t \right ) \\ \end{align*}

0.787

10437

20875

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

0.787

10438

22764

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

0.787

10439

25575

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

0.787

10440

5570

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

0.788

10441

12672

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

0.788

10442

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*}

0.788

10443

18868

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

0.788

10444

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*}

0.789

10445

2264

\begin{align*} y_{1}^{\prime }&=6 y_{1}-5 y_{2}+3 y_{3} \\ y_{2}^{\prime }&=2 y_{1}-y_{2}+3 y_{3} \\ y_{3}^{\prime }&=2 y_{1}+y_{2}+y_{3} \\ \end{align*}

0.789

10446

2273

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

With initial conditions

\begin{align*} y_{1} \left (0\right ) &= -2 \\ y_{2} \left (0\right ) &= 1 \\ y_{3} \left (0\right ) &= 3 \\ \end{align*}

0.789

10447

2664

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

Series expansion around \(t=0\).

0.789

10448

5562

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

0.789

10449

6367

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

0.789

10450

15445

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

With initial conditions

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

0.789

10451

17733

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

0.789

10452

19042

\begin{align*} x_{1}^{\prime }&=2 x_{1}-5 x_{2}-\cos \left (t \right ) \\ x_{2}^{\prime }&=x_{1}-2 x_{2}+\sin \left (t \right ) \\ \end{align*}

0.789

10453

19568

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

0.789

10454

20518

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

0.789

10455

21601

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

0.789

10456

22936

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

0.789

10457

23463

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

0.789

10458

3

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

0.790

10459

1040

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

0.790

10460

1407

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

0.790

10461

4498

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

0.790

10462

9834

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

Series expansion around \(x=0\).

0.790

10463

9835

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

Series expansion around \(x=0\).

0.790

10464

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*}

0.790

10465

24759

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

0.790

10466

190

\begin{align*} 6 x y^{3}+2 y^{4}+\left (9 x^{2} y^{2}+8 x y^{3}\right ) y^{\prime }&=0 \\ \end{align*}

0.791

10467

15321

\begin{align*} y^{\prime \prime }+9 y&=18 t \\ y \left (0\right ) &= 0 \\ y \left (\frac {\pi }{2}\right ) &= 0 \\ \end{align*}

Using Laplace transform method.

0.791

10468

19510

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

0.791

10469

21663

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

Series expansion around \(x=-1\).

0.791

10470

21737

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

0.791

10471

996

\begin{align*} x_{1}^{\prime }&=-20 x_{1}+11 x_{2}+13 x_{3} \\ x_{2}^{\prime }&=12 x_{1}-x_{2}-7 x_{3} \\ x_{3}^{\prime }&=-48 x_{1}+21 x_{2}+31 x_{3} \\ \end{align*}

0.792

10472

1386

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

Series expansion around \(x=0\).

0.792

10473

1975

\begin{align*} 4 x^{2} \left (-x^{2}+1\right ) y^{\prime \prime }+x \left (-19 x^{2}+7\right ) y^{\prime }-\left (14 x^{2}+1\right ) y&=0 \\ \end{align*}

Series expansion around \(x=0\).

0.792

10474

1982

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

Series expansion around \(x=0\).

0.792

10475

3296

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

0.792

10476

4606

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

Series expansion around \(x=0\).

0.792

10477

5398

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

0.792

10478

7040

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

0.792

10479

12281

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

0.792

10480

15721

\begin{align*} y^{\prime \prime }-4 y&=\left \{\begin {array}{cc} x & 0\le x <1 \\ 1 & 1\le x \end {array}\right . \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

Using Laplace transform method.

0.792

10481

15758

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

0.792

10482

16907

\begin{align*} 4 x^{2} y^{\prime \prime }+8 x^{2} y^{\prime }+y&=0 \\ \end{align*}

Series expansion around \(x=0\).

0.792

10483

16918

\begin{align*} x^{2} y^{\prime \prime }-\left (2 x^{2}+5 x \right ) y^{\prime }+9 y&=0 \\ \end{align*}

Series expansion around \(x=0\).

0.792

10484

642

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

0.793

10485

3870

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

0.793

10486

4501

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

0.793

10487

8479

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

Series expansion around \(x=1\).

0.793

10488

8505

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

Series expansion around \(x=0\).

0.793

10489

9701

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

0.793

10490

10170

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

Series expansion around \(x=0\).

0.793

10491

11682

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

0.793

10492

12460

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

0.793

10493

14941

\begin{align*} x^{\prime \prime }+6 x^{\prime }+10 x&={\mathrm e}^{-2 t} \cos \left (t \right ) \\ \end{align*}

0.793

10494

16387

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

0.793

10495

17303

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

0.793

10496

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*}

0.793

10497

20523

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

0.793

10498

22822

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

Series expansion around \(x=0\).

0.793

10499

25422

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

0.793

10500

1192

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

0.794