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

14284

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

0.843

12402

17774

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

0.843

12403

19639

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

0.843

12404

21332

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

0.843

12405

1977

\begin{align*} 2 x^{2} \left (x^{2}+2\right ) y^{\prime \prime }-x \left (-7 x^{2}+12\right ) y^{\prime }+\left (3 x^{2}+7\right ) y&=0 \\ \end{align*}

Series expansion around \(x=0\).

0.844

12406

9039

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

0.844

12407

7188

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

Series expansion around \(x=0\).

0.845

12408

7622

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

Series expansion around \(x=0\).

0.845

12409

22696

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

0.845

12410

23986

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

0.845

12411

25222

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

0.845

12412

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*}

0.845

12413

26618

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

0.845

12414

26627

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

0.845

12415

22

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

0.846

12416

1750

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

0.846

12417

2190

\begin{align*} y^{\prime \prime \prime \prime }-5 y^{\prime \prime \prime }+13 y^{\prime \prime }-19 y^{\prime }+10 y&={\mathrm e}^{x} \left (\left (7+8 x \right ) \cos \left (2 x \right )+\left (8-4 x \right ) \sin \left (2 x \right )\right ) \\ \end{align*}

0.846

12418

2400

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

0.846

12419

4023

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

Series expansion around \(x=0\).

0.846

12420

6512

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

0.846

12421

10529

\begin{align*} \left (3 x^{2}+x +1\right ) y^{\prime \prime }+\left (2+15 x \right ) y^{\prime }+12 y&=0 \\ \end{align*}

0.846

12422

17591

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

0.846

12423

27151

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

With initial conditions

\begin{align*} x_{1} \left (0\right ) &= 1 \\ x_{2} \left (0\right ) &= 5 \\ x_{3} \left (0\right ) &= 1 \\ \end{align*}

0.846

12424

9890

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

Series expansion around \(x=0\).

0.847

12425

15175

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

0.847

12426

23828

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

0.847

12427

3848

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

0.848

12428

17503

\begin{align*} y^{\prime \prime }+6 y^{\prime }+9 y&=\frac {{\mathrm e}^{-3 t}}{t} \\ \end{align*}

0.848

12429

25274

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

0.848

12430

25434

\begin{align*} y^{\prime }-a \left (t \right ) y&=\delta \left (t \right ) \\ \end{align*}

0.848

12431

27103

\(\left [\begin {array}{cccc} 5 & 1 & 0 & 9 \\ 0 & 1 & 0 & 9 \\ 0 & 0 & 0 & 9 \\ 0 & 0 & 0 & 0 \end {array}\right ]\)

N/A

N/A

N/A

0.848

12432

1357

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

0.849

12433

1963

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

Series expansion around \(x=0\).

0.849

12434

6254

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

0.849

12435

12370

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

0.849

12436

12944

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

0.849

12437

14304

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

0.849

12438

16039

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

0.849

12439

20532

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

0.849

12440

20808

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

0.849

12441

23545

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

0.849

12442

25319

\begin{align*} y^{\prime \prime }-6 y^{\prime }+9 y&=\delta \left (t -3\right ) \\ y \left (0\right ) &= -1 \\ y^{\prime }\left (0\right ) &= -3 \\ \end{align*}

Using Laplace transform method.

0.849

12443

27166

\begin{align*} x_{1}^{\prime }&=7 x_{1}-x_{2}+2 \,{\mathrm e}^{6 t} \\ x_{2}^{\prime }&=x_{1}+5 x_{2}+6 t \,{\mathrm e}^{6 t} \\ \end{align*}

0.849

12444

27186

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

0.849

12445

1988

\begin{align*} 4 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+4 x \left (6 x^{2}+1\right ) y^{\prime }-\left (-25 x^{2}+1\right ) y&=0 \\ \end{align*}

Series expansion around \(x=0\).

0.850

12446

6249

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

0.850

12447

7773

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

0.850

12448

20362

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

0.850

12449

21167

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

0.850

12450

2636

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

0.851

12451

18009

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

0.851

12452

21934

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

0.851

12453

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*}

0.852

12454

2630

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

0.852

12455

9404

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

Series expansion around \(x=0\).

0.852

12456

13155

\(\left [\begin {array}{ccc} 1 & 0 & 0 \\ -6 & 8 & 2 \\ 12 & -15 & -3 \end {array}\right ]\)

N/A

N/A

N/A

0.852

12457

16723

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

0.852

12458

16901

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

Series expansion around \(x=0\).

0.852

12459

20150

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

Series expansion around \(x=0\).

0.852

12460

23510

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

0.852

12461

23741

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

Series expansion around \(x=0\).

0.852

12462

23927

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

0.852

12463

24106

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

Series expansion around \(x=0\).

0.852

12464

26066

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

0.852

12465

26072

\begin{align*} y^{\prime }&=-3 y+z-w \\ z^{\prime }&=5 y-z-7 w \\ w^{\prime }&=-y+z-3 w \\ \end{align*}

0.852

12466

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*}

0.852

12467

1984

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

Series expansion around \(x=0\).

0.853

12468

16942

\begin{align*} x^{\prime }&=8 x+2 y-17 \\ y^{\prime }&=4 x+y-13 \\ \end{align*}

With initial conditions

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

0.853

12469

19370

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

0.853

12470

19568

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

0.853

12471

20401

\begin{align*} 3 {y^{\prime }}^{5}-y y^{\prime }+1&=0 \\ \end{align*}

0.853

12472

20878

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

0.853

12473

22857

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

Series expansion around \(x=0\).

0.853

12474

23627

\begin{align*} x^{\prime }&=-10 x+y+7 z \\ y^{\prime }&=-9 x+4 y+5 z \\ z^{\prime }&=-17 x+y+12 z \\ \end{align*}

With initial conditions

\begin{align*} x \left (0\right ) &= 6 \\ y \left (0\right ) &= 1 \\ z \left (0\right ) &= 10 \\ \end{align*}

0.853

12475

23922

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

0.853

12476

2580

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

0.854

12477

3163

\begin{align*} y^{\prime \prime }+9 y&=\csc \left (x \right ) \sec \left (x \right ) \\ \end{align*}

0.854

12478

20506

\begin{align*} x^{3} y^{\prime \prime \prime }+6 x^{2} y^{\prime \prime }+8 y^{\prime } x +2 y&=x^{2}+3 x -4 \\ \end{align*}

0.854

12479

26038

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

0.854

12480

26974

\begin{align*} y^{\prime \prime }-4 y^{\prime }+13 y&=3 \,{\mathrm e}^{2 x}-5 \,{\mathrm e}^{3 x} \\ \end{align*}

0.854

12481

2249

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

0.855

12482

3383

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

Series expansion around \(x=0\).

0.855

12483

3584

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

0.855

12484

6867

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

0.855

12485

9681

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

0.855

12486

14720

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

0.855

12487

27127

\(\left [\begin {array}{ccc} 2 & -4 & 0 \\ -4 & 0 & 0 \\ 0 & 0 & 0 \end {array}\right ]\)

N/A

N/A

N/A

0.855

12488

27136

\(\left [\begin {array}{ccc} -1 & 0 & 3-i \\ 0 & 1 & 0 \\ 3+i & 0 & 0 \end {array}\right ]\)

N/A

N/A

N/A

0.855

12489

9208

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

0.856

12490

9556

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

Series expansion around \(x=0\).

0.856

12491

12493

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

0.856

12492

18438

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

0.856

12493

1506

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

Using Laplace transform method.

0.857

12494

1959

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

Series expansion around \(x=0\).

0.857

12495

11602

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

0.857

12496

13151

\(\left [\begin {array}{ccc} 5 & 0 & 0 \\ 4 & -4 & -2 \\ -2 & 12 & 6 \end {array}\right ]\)

N/A

N/A

N/A

0.857

12497

16044

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

0.857

12498

23103

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

0.857

12499

25403

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

0.857

12500

2384

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

0.858