2.3.56 Problems 5501 to 5600

Table 2.685: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

5501

24087

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

Series expansion around \(x=0\).

0.430

5502

26070

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

0.430

5503

1888

\begin{align*} \left (x^{8}+1\right ) y^{\prime \prime }-16 x^{7} y^{\prime }+72 x^{6} y&=0 \\ \end{align*}

Series expansion around \(x=0\).

0.431

5504

6629

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

0.431

5505

7458

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

0.431

5506

7783

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

0.431

5507

7948

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

0.431

5508

9213

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

0.431

5509

10292

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

0.431

5510

15939

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

0.431

5511

15990

\begin{align*} x^{\prime }&=5 x+4 y \\ y^{\prime }&=9 x \\ \end{align*}

0.431

5512

16111

\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=5 \cos \left (t \right ) \\ \end{align*}

0.431

5513

16112

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

0.431

5514

16820

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

Series expansion around \(x=0\).

0.431

5515

17738

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

0.431

5516

18754

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

0.431

5517

19556

\begin{align*} y^{\prime \prime }-2 y^{\prime }-3 y&=6 \,{\mathrm e}^{5 x} \\ \end{align*}

0.431

5518

20166

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

0.431

5519

20928

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

0.431

5520

21290

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

With initial conditions

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

0.431

5521

23848

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

0.431

5522

24775

\begin{align*} {y^{\prime }}^{2} x^{2}-7 x y y^{\prime }+12 y^{2}&=0 \\ \end{align*}

0.431

5523

26949

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

0.431

5524

26989

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

0.431

5525

1262

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

0.432

5526

12369

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

0.432

5527

24115

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

Series expansion around \(x=0\).

0.432

5528

25553

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

0.432

5529

864

\begin{align*} x^{\prime \prime }+8 x^{\prime }+16 x&=0 \\ x \left (0\right ) &= 5 \\ x^{\prime }\left (0\right ) &= -10 \\ \end{align*}

0.433

5530

2775

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

With initial conditions

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

0.433

5531

3285

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

0.433

5532

6693

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

0.433

5533

14200

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

0.433

5534

14414

\begin{align*} 12 y-7 y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}

0.433

5535

15986

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

0.433

5536

23072

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

0.433

5537

23586

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

With initial conditions

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

0.433

5538

23841

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

0.433

5539

25632

\begin{align*} y^{\prime \prime }&={\mathrm e}^{a t} \\ y \left (0\right ) &= A \\ y^{\prime }\left (0\right ) &= B \\ \end{align*}

Using Laplace transform method.

0.433

5540

601

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

0.434

5541

1394

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

Series expansion around \(x=1\).

0.434

5542

2774

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

With initial conditions

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

0.434

5543

4516

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

Using Laplace transform method.

0.434

5544

7088

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

0.434

5545

7844

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

Series expansion around \(x=0\).

0.434

5546

9216

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

0.434

5547

10024

\begin{align*} u^{\prime }+u^{2}&=\frac {1}{x^{{4}/{5}}} \\ \end{align*}

0.434

5548

11714

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

0.434

5549

11733

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

0.434

5550

12899

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

0.434

5551

15508

\begin{align*} y^{\prime \prime }-y^{\prime }-6 y&=0 \\ \end{align*}

0.434

5552

15730

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

0.434

5553

16825

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

Series expansion around \(x=0\).

0.434

5554

20465

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

0.434

5555

21906

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

Series expansion around \(x=0\).

0.434

5556

22493

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

0.434

5557

23084

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

0.434

5558

23993

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

0.434

5559

24706

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

0.434

5560

26109

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

0.434

5561

429

\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }+6 x y^{\prime }+4 y&=0 \\ \end{align*}

Series expansion around \(x=0\).

0.435

5562

1291

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

0.435

5563

1634

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

0.435

5564

9222

\begin{align*} 4 y^{\prime \prime }+20 y^{\prime }+25 y&=0 \\ \end{align*}

0.435

5565

14399

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

0.435

5566

14421

\begin{align*} y^{\prime \prime }-2 y^{\prime }-8 y&=0 \\ \end{align*}

0.435

5567

15984

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

0.435

5568

16336

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

0.435

5569

16424

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

0.435

5570

16833

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

Series expansion around \(x=0\).

0.435

5571

18773

\begin{align*} y^{\prime \prime }+2 y^{\prime }+\frac {5 y}{4}&=0 \\ \end{align*}

0.435

5572

20416

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

0.435

5573

20889

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

Series expansion around \(x=0\).

0.435

5574

26675

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

0.435

5575

27070

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

Series expansion around \(x=0\).

0.435

5576

447

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

Series expansion around \(x=-3\).

0.436

5577

9711

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

0.436

5578

10291

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

0.436

5579

10342

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

Using Laplace transform method.

0.436

5580

22109

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

0.436

5581

23679

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

Series expansion around \(x=0\).

0.436

5582

27068

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

Series expansion around \(x=0\).

0.436

5583

446

\begin{align*} \left (4 x^{2}+16 x +17\right ) y^{\prime \prime }&=8 y \\ y \left (-2\right ) &= 1 \\ y^{\prime }\left (-2\right ) &= 0 \\ \end{align*}

Series expansion around \(x=-2\).

0.437

5584

867

\begin{align*} 2 x^{\prime \prime }+16 x^{\prime }+40 x&=0 \\ x \left (0\right ) &= 5 \\ x^{\prime }\left (0\right ) &= 4 \\ \end{align*}

0.437

5585

2225

\begin{align*} x^{4} y^{\prime \prime \prime \prime }-4 x^{3} y^{\prime \prime \prime }+12 x^{2} y^{\prime \prime }-24 x y^{\prime }+24 y&=x^{4} \\ \end{align*}

0.437

5586

2226

\begin{align*} x^{4} y^{\prime \prime \prime \prime }+6 x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }-4 x y^{\prime }+4 y&=12 x^{2} \\ \end{align*}

0.437

5587

3343

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

Series expansion around \(x=0\).

0.437

5588

3819

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

With initial conditions

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

0.437

5589

4591

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

Series expansion around \(x=0\).

0.437

5590

9259

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

0.437

5591

10346

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

Series expansion around \(x=0\).

0.437

5592

16002

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

With initial conditions

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

0.437

5593

16030

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

With initial conditions

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

0.437

5594

16058

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

0.437

5595

16948

\begin{align*} x^{\prime }&=5 x+4 y \\ y^{\prime }&=8 x+y \\ \end{align*}

0.437

5596

23034

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

0.437

5597

23773

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

With initial conditions

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

0.437

5598

26492

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

0.437

5599

26966

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

0.437

5600

26972

\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&=10 \sin \left (x \right ) \\ \end{align*}

0.437