2.3.125 Problems 12401 to 12500

Table 2.823: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

12401

16384

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

1.054

12402

2178

\begin{align*} y^{\prime \prime \prime }-2 y^{\prime \prime }+y^{\prime }-2 y&=-{\mathrm e}^{x} \left (\left (4 x^{2}+5 x +9\right ) \cos \left (2 x \right )-\left (-3 x^{2}-5 x +6\right ) \sin \left (2 x \right )\right ) \\ \end{align*}

1.055

12403

8190

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

1.055

12404

12436

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

1.055

12405

14130

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

1.055

12406

16385

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

1.055

12407

2708

\begin{align*} x^{\prime }&=y+\textit {f\_1} \left (t \right ) \\ y^{\prime }&=-x+f_{2} \left (t \right ) \\ \end{align*}

With initial conditions

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

1.056

12408

3395

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

Series expansion around \(x=0\).

1.056

12409

3397

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

Series expansion around \(x=0\).

1.056

12410

7084

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

1.056

12411

8048

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

1.056

12412

12883

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

1.056

12413

18767

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

1.056

12414

20626

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

1.056

12415

228

\begin{align*} x^{2} y^{\prime \prime }+2 x y^{\prime }-6 y&=0 \\ y \left (2\right ) &= 10 \\ y^{\prime }\left (2\right ) &= 15 \\ \end{align*}

1.057

12416

1268

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

1.057

12417

9740

\begin{align*} 2 x {y^{\prime }}^{3}-6 y {y^{\prime }}^{2}+x^{4}&=0 \\ \end{align*}

1.057

12418

10374

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

1.057

12419

26502

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

1.057

12420

1969

\begin{align*} x^{2} \left (x +2\right ) y^{\prime \prime }+5 x \left (1-x \right ) y^{\prime }-\left (2-8 x \right ) y&=0 \\ \end{align*}

Series expansion around \(x=0\).

1.058

12421

4014

\begin{align*} 6 x^{2} y^{\prime \prime }+x \left (1+18 x \right ) y^{\prime }+\left (1+12 x \right ) y&=0 \\ \end{align*}

Series expansion around \(x=0\).

1.058

12422

4017

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

Series expansion around \(x=0\).

1.058

12423

4484

\begin{align*} y^{\prime \prime }-4 y&=96 x^{2} {\mathrm e}^{2 x}+4 \,{\mathrm e}^{-2 x} \\ \end{align*}

1.058

12424

7685

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

1.058

12425

18760

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

1.058

12426

26215

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

1.058

12427

9517

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

Series expansion around \(x=0\).

1.059

12428

16414

\begin{align*} y^{\prime \prime }+4 y^{\prime }&=9 \,{\mathrm e}^{-3 x} \\ \end{align*}

1.059

12429

16797

\begin{align*} y^{\prime \prime }+9 y&=\operatorname {Heaviside}\left (t -10\right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

Using Laplace transform method.

1.059

12430

22274

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

With initial conditions

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

1.059

12431

8593

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

Series expansion around \(x=0\).

1.060

12432

12926

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

1.060

12433

18854

\begin{align*} y^{\prime \prime }+\frac {y^{\prime }}{8}+4 y&=3 \cos \left (\frac {t}{4}\right ) \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

1.060

12434

22830

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

Series expansion around \(x=1\).

1.060

12435

26197

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

1.060

12436

13884

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

1.061

12437

18988

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

1.061

12438

19858

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

1.061

12439

19888

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

1.061

12440

2448

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

Series expansion around \(t=0\).

1.062

12441

7902

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

1.062

12442

18737

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

1.062

12443

22722

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

1.062

12444

4050

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

Series expansion around \(x=0\).

1.063

12445

8280

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

1.063

12446

12285

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

1.063

12447

15299

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

1.063

12448

17716

\begin{align*} y^{\prime \prime }+\left (\frac {16}{3 x}-1\right ) y^{\prime }-\frac {16 y}{3 x^{2}}&=0 \\ \end{align*}

Series expansion around \(x=0\).

1.063

12449

18235

\begin{align*} 5 y+2 y^{\prime }+y^{\prime \prime }&=4 \,{\mathrm e}^{-x}+17 \sin \left (2 x \right ) \\ \end{align*}

1.063

12450

18308

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

1.063

12451

21693

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

Series expansion around \(x=\infty \).

1.063

12452

3259

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

1.065

12453

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*}

1.065

12454

4187

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

Series expansion around \(x=0\).

1.065

12455

5957

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

1.065

12456

10371

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

1.065

12457

15332

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

1.065

12458

16010

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

With initial conditions

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

1.065

12459

17101

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

1.065

12460

23104

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

1.065

12461

23470

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

1.065

12462

2603

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

1.066

12463

4571

\begin{align*} x_{1}^{\prime }&=-x_{1}+8 x_{2}+9 t \\ x_{2}^{\prime }&=x_{1}+x_{2}+3 \,{\mathrm e}^{-t} \\ \end{align*}

1.066

12464

15655

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

1.066

12465

5592

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

1.067

12466

18390

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

1.067

12467

24141

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

1.067

12468

22941

\begin{align*} x^{\prime }+3 x+4 y&=8 \,{\mathrm e}^{t} \\ -x+y^{\prime }-y&=0 \\ \end{align*}

1.068

12469

2007

\begin{align*} 9 x^{2} y^{\prime \prime }+3 x \left (-2 x^{2}+3 x +5\right ) y^{\prime }+\left (-14 x^{2}+12 x +1\right ) y&=0 \\ \end{align*}

Series expansion around \(x=0\).

1.069

12470

4045

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

Series expansion around \(x=0\).

1.069

12471

9678

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

1.069

12472

13298

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

1.069

12473

19985

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

1.069

12474

20651

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

1.069

12475

22224

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

Series expansion around \(x=0\).

1.069

12476

25571

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

1.069

12477

26855

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

1.069

12478

5718

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

1.070

12479

11736

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

1.070

12480

13017

\begin{align*} \left (4 y^{3}-a y-b \right ) y^{\prime \prime }-\left (6 y^{2}-\frac {a}{2}\right ) {y^{\prime }}^{2}&=0 \\ \end{align*}

1.070

12481

23923

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

1.070

12482

27225

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

1.070

12483

6505

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

1.071

12484

8613

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

Series expansion around \(x=0\).

1.071

12485

16396

\begin{align*} y^{\prime \prime }+4 y^{\prime }&=9 \,{\mathrm e}^{-3 x} \\ \end{align*}

1.071

12486

17727

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

Series expansion around \(x=0\).

1.071

12487

70

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

1.072

12488

4181

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

Series expansion around \(x=0\).

1.072

12489

7139

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

1.072

12490

9480

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

1.072

12491

20599

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

1.072

12492

21750

\begin{align*} x^{\prime }&=7 x-y+6 z \\ y^{\prime }&=-10 x+4 y-12 z \\ z^{\prime }&=-2 x+y-z \\ \end{align*}

1.072

12493

23544

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

1.072

12494

24915

\begin{align*} y^{\prime }&=3 y+12 \\ \end{align*}

1.072

12495

4053

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

Series expansion around \(x=0\).

1.073

12496

4464

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

1.073

12497

7946

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

1.073

12498

9518

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

Series expansion around \(x=0\).

1.073

12499

11303

\begin{align*} y^{\prime }-\frac {1}{\sqrt {\operatorname {a4} \,x^{4}+\operatorname {a3} \,x^{3}+\operatorname {a2} \,x^{2}+\operatorname {a1} x +\operatorname {a0}}}&=0 \\ \end{align*}

1.073

12500

17718

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

Series expansion around \(x=0\).

1.073