2.3.156 Problems 15501 to 15600

Table 2.885: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

15501

22909

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

With initial conditions

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

3.379

15502

16416

\begin{align*} y^{\prime \prime } x +4 y^{\prime }&=18 x^{2} \\ y \left (1\right ) &= 8 \\ y^{\prime }\left (1\right ) &= -3 \\ \end{align*}

3.381

15503

17955

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

3.381

15504

19016

\begin{align*} x_{1}^{\prime }&=-3 x_{1}-4 x_{2}+5 x_{3}+9 x_{4} \\ x_{2}^{\prime }&=-2 x_{1}-5 x_{2}+4 x_{3}+12 x_{4} \\ x_{3}^{\prime }&=-2 x_{1}-x_{3}+2 x_{4} \\ x_{4}^{\prime }&=-2 x_{2}+2 x_{3}+3 x_{4} \\ \end{align*}

3.381

15505

188

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

3.382

15506

1242

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

3.382

15507

4864

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

3.382

15508

12011

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

3.382

15509

25127

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

3.382

15510

7902

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

3.383

15511

19702

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

3.383

15512

25059

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

Using Laplace transform method.

3.384

15513

9872

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

Series expansion around \(x=0\).

3.385

15514

12441

\begin{align*} x^{2} y^{\prime \prime }-2 y^{\prime } x -4 y-x \sin \left (x \right )-\left (a \,x^{2}+12 a +4\right ) \cos \left (x \right )&=0 \\ \end{align*}

3.385

15515

26065

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

3.385

15516

22491

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

3.386

15517

27689

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

3.387

15518

4924

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

3.388

15519

13933

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

3.388

15520

18355

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

3.388

15521

2836

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

3.390

15522

5918

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

3.390

15523

1667

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

3.392

15524

12979

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

3.392

15525

17472

\begin{align*} y^{\prime \prime }+4 y&=\left \{\begin {array}{cc} 0 & 0\le t <\pi \\ 10 & \pi \le t <2 \pi \\ 0 & 2 \pi \le t \end {array}\right . \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*}

3.392

15526

18743

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

3.393

15527

714

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

3.394

15528

3028

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

3.394

15529

4116

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

3.394

15530

5940

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

3.394

15531

9944

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

Series expansion around \(x=0\).

3.394

15532

12443

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

3.394

15533

21792

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

3.394

15534

26598

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

3.395

15535

4867

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

3.397

15536

9919

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

Series expansion around \(x=0\).

3.398

15537

18532

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

3.399

15538

9809

\begin{align*} 9 {y^{\prime }}^{2}+3 x y^{4} y^{\prime }+y^{5}&=0 \\ \end{align*}

3.400

15539

13274

\begin{align*} x^{n +1} y^{\prime }&=x^{2 n} a y^{2}+b \,x^{n} y+c \,x^{m}+d \\ \end{align*}

3.400

15540

8394

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

3.401

15541

9640

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

Using Laplace transform method.

3.401

15542

21489

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

3.401

15543

25633

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

Using Laplace transform method.

3.401

15544

2977

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

3.402

15545

27718

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

3.402

15546

12147

\begin{align*} y^{\prime }&=-\frac {2 x}{3}+1+y^{2}+\frac {2 x^{2} y}{3}+\frac {x^{4}}{9}+y^{3}+y^{2} x^{2}+\frac {x^{4} y}{3}+\frac {x^{6}}{27} \\ \end{align*}

3.403

15547

26595

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

3.403

15548

124

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

3.404

15549

9812

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

3.404

15550

18584

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

3.404

15551

5740

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

3.405

15552

9643

\begin{align*} y^{\prime \prime }+16 y&=\delta \left (t -2 \pi \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

Using Laplace transform method.

3.405

15553

13889

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

3.406

15554

2306

\begin{align*} \sqrt {t^{2}+1}\, y \,{\mathrm e}^{-t}+y^{\prime }&=0 \\ \end{align*}

3.408

15555

7571

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

3.408

15556

11517

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

3.408

15557

27175

\begin{align*} x_{1}^{\prime }&=x_{1}+x_{2}+6 \,{\mathrm e}^{3 t} \\ x_{2}^{\prime }&=x_{1}+x_{2}+4 \\ \end{align*}

3.408

15558

10178

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

Series expansion around \(x=2\).

3.409

15559

19340

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

3.410

15560

3430

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

3.412

15561

19345

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

3.412

15562

4302

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

3.413

15563

5907

\begin{align*} \left (\operatorname {b2} x +\operatorname {b1} \right ) y+a y^{\prime }+y^{\prime \prime } x&=0 \\ \end{align*}

3.413

15564

24691

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

3.414

15565

15088

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

3.415

15566

23081

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

3.417

15567

11406

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

3.418

15568

12354

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

3.418

15569

25192

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

3.418

15570

5838

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

3.420

15571

10378

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

3.421

15572

20608

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

3.422

15573

5424

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

3.423

15574

26758

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

3.423

15575

27190

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

3.423

15576

21171

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

3.424

15577

26025

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

Series expansion around \(x=0\).

3.424

15578

22725

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

3.425

15579

27156

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

3.425

15580

12341

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

3.426

15581

5917

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

3.427

15582

24044

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

3.427

15583

25638

\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=1 \\ y \left (0\right ) &= 4 \\ y^{\prime }\left (0\right ) &= 5 \\ \end{align*}

Using Laplace transform method.

3.427

15584

17242

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

3.428

15585

11410

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

3.430

15586

21295

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

3.430

15587

2317

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

3.431

15588

23524

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

3.431

15589

24582

\begin{align*} y^{\prime \prime }-y^{\prime }&=42 \,{\mathrm e}^{4 x} \\ \end{align*}

3.431

15590

17143

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

3.432

15591

20498

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

3.433

15592

22797

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

3.433

15593

776

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

3.434

15594

11780

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

3.434

15595

27172

\begin{align*} x_{1}^{\prime }&=x_{1}-3 x_{2}+t \,{\mathrm e}^{-2 t} \\ x_{2}^{\prime }&=3 x_{1}-5 x_{2}+t \,{\mathrm e}^{-2 t} \\ x_{3}^{\prime }&=4 x_{1}+7 x_{2}-2 x_{3}+t^{2} {\mathrm e}^{-2 t} \\ \end{align*}

With initial conditions

\begin{align*} x_{1} \left (0\right ) &= 6 \\ x_{2} \left (0\right ) &= 2 \\ x_{3} \left (0\right ) &= 3 \\ \end{align*}

3.434

15596

3567

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

3.435

15597

12953

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

3.435

15598

17245

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

3.435

15599

11857

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

3.437

15600

7976

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

3.438