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

23600

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

1.471

10402

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*}

1.471

10403

27692

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

1.471

10404

10074

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

1.472

10405

21115

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

1.472

10406

11378

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

1.473

10407

14556

\begin{align*} y^{\prime \prime }+5 y^{\prime }+6 y&={\mathrm e}^{x} \\ y \left (0\right ) &= 5 \\ y^{\prime }\left (0\right ) &= 7 \\ \end{align*}

1.473

10408

22206

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

Series expansion around \(x=0\).

1.473

10409

8853

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

1.474

10410

12926

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

1.474

10411

15325

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

Using Laplace transform method.

1.474

10412

16621

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

1.474

10413

16779

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

Using Laplace transform method.

1.474

10414

18840

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

1.474

10415

20790

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

1.474

10416

21649

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

Series expansion around \(x=0\).

1.474

10417

24019

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

1.474

10418

24544

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

1.474

10419

25575

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

1.474

10420

16766

\begin{align*} y^{\prime \prime }-5 y^{\prime }+6 y&=t^{2} {\mathrm e}^{4 t} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*}

Using Laplace transform method.

1.475

10421

3399

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

Series expansion around \(x=0\).

1.476

10422

6040

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

1.476

10423

16045

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

1.476

10424

20387

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

1.476

10425

24632

\begin{align*} y^{\prime \prime }-9 y&=-72 x \,{\mathrm e}^{-3 x} \\ \end{align*}

1.476

10426

1610

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

1.477

10427

5660

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

1.477

10428

16768

\begin{align*} y^{\prime \prime }-4 y^{\prime }+13 y&={\mathrm e}^{2 t} \sin \left (3 t \right ) \\ y \left (0\right ) &= 4 \\ y^{\prime }\left (0\right ) &= 3 \\ \end{align*}

Using Laplace transform method.

1.477

10429

21601

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

1.477

10430

22100

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

1.477

10431

23479

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

1.477

10432

26099

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

1.477

10433

6219

\begin{align*} \left (6-9 x \right ) y-\left (4-5 x \right ) x y^{\prime }+\left (1-x \right ) x^{2} y^{\prime \prime }&=0 \\ \end{align*}

1.478

10434

14979

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

Series expansion around \(x=0\).

1.478

10435

15092

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

1.478

10436

16008

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

With initial conditions

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

1.478

10437

19010

\begin{align*} x_{1}^{\prime }&=\frac {4 x_{1}}{3}+\frac {4 x_{2}}{3}-\frac {11 x_{3}}{3} \\ x_{2}^{\prime }&=-\frac {16 x_{1}}{3}-\frac {x_{2}}{3}+\frac {14 x_{3}}{3} \\ x_{3}^{\prime }&=3 x_{1}-2 x_{2}-2 x_{3} \\ \end{align*}

1.478

10438

19437

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

1.478

10439

20086

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

1.478

10440

24033

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

1.478

10441

12475

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

1.479

10442

13756

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

1.479

10443

18154

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

1.479

10444

18206

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

1.479

10445

5580

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

1.480

10446

10514

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

1.480

10447

22269

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

With initial conditions

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

1.480

10448

649

\begin{align*} x_{1}^{\prime }&=2 x_{1} \\ x_{2}^{\prime }&=-21 x_{1}-5 x_{2}-27 x_{3}-9 x_{4} \\ x_{3}^{\prime }&=5 x_{3} \\ x_{4}^{\prime }&=-21 x_{3}-2 x_{4} \\ \end{align*}

1.481

10449

5623

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

1.481

10450

9268

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

1.481

10451

21194

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

1.481

10452

21752

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

1.481

10453

16773

\begin{align*} y^{\prime \prime }+9 y&=27 t^{3} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

Using Laplace transform method.

1.483

10454

21270

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

Series expansion around \(t=0\).

1.483

10455

21648

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

Series expansion around \(x=0\).

1.483

10456

24696

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

1.483

10457

316

\begin{align*} x^{2} y^{\prime \prime }+7 y^{\prime } x +25 y&=0 \\ \end{align*}

1.484

10458

5725

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

1.484

10459

6587

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

1.484

10460

9403

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

Series expansion around \(x=0\).

1.484

10461

15684

\begin{align*} y^{\prime \prime \prime \prime }+4 y^{\prime \prime }&=24 x^{2}-6 x +14+32 \cos \left (2 x \right ) \\ \end{align*}

1.484

10462

16127

\begin{align*} y^{\prime \prime }+9 y&=\cos \left (t \right ) \\ \end{align*}

1.484

10463

20111

\begin{align*} y+3 y^{\prime } x +9 x^{2} y^{\prime \prime }+6 x^{3} y^{\prime \prime \prime }+x^{4} y^{\prime \prime \prime \prime }&=\left (1+\ln \left (x \right )\right )^{2} \\ \end{align*}

1.484

10464

23536

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

1.484

10465

11819

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

1.485

10466

17158

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

1.485

10467

17664

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

1.485

10468

5526

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

1.486

10469

9513

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

Series expansion around \(x=0\).

1.486

10470

5862

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

1.487

10471

9665

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

1.487

10472

11327

\begin{align*} y^{\prime }+a y^{2}-b \,x^{2 \nu }-c \,x^{\nu -1}&=0 \\ \end{align*}

1.487

10473

12609

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

1.487

10474

19200

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

1.487

10475

19600

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

Series expansion around \(x=0\).

1.487

10476

25272

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

1.487

10477

8577

\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +30 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= {\frac {15}{8}} \\ \end{align*}

Series expansion around \(x=0\).

1.488

10478

25229

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

1.488

10479

7674

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

1.489

10480

18294

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

1.489

10481

23599

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

1.489

10482

2059

\begin{align*} 4 x^{2} \left (x^{2}+3 x +1\right ) y^{\prime \prime }+8 x^{2} \left (2 x +3\right ) y^{\prime }+\left (9 x^{2}+3 x +1\right ) y&=0 \\ \end{align*}

Series expansion around \(x=0\).

1.490

10483

16669

\begin{align*} y^{\left (5\right )}+18 y^{\prime \prime \prime }+81 y^{\prime }&=x^{2} {\mathrm e}^{3 x} \sin \left (3 x \right ) \\ \end{align*}

1.490

10484

18393

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

1.490

10485

18872

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

1.490

10486

21278

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

1.490

10487

9609

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

Using Laplace transform method.

1.491

10488

14203

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

1.491

10489

21494

\begin{align*} y^{\prime \prime }-6 y^{\prime }+9 y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}

1.491

10490

24932

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

1.491

10491

5751

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

1.492

10492

7660

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

Series expansion around \(x=0\).

1.492

10493

16743

\begin{align*} y^{\prime \prime }-12 y^{\prime }+36 y&=3 x \,{\mathrm e}^{6 x}-2 \,{\mathrm e}^{6 x} \\ \end{align*}

1.492

10494

21753

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

1.492

10495

25106

\begin{align*} y^{\prime \prime }+10 y^{\prime }+25 y&=0 \\ \end{align*}

1.492

10496

26941

\begin{align*} y^{\prime \prime }+3 y^{\prime }+18 y&=0 \\ \end{align*}

1.492

10497

9832

\begin{align*} y^{\prime \prime }-9 y&=0 \\ \end{align*}

Series expansion around \(x=0\).

1.493

10498

14960

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

1.493

10499

16786

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

Using Laplace transform method.

1.493

10500

19779

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

1.493