2.3.115 Problems 11401 to 11500

Table 2.803: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

11401

24797

\begin{align*} {y^{\prime }}^{2}+4 x^{5} y^{\prime }-12 x^{4} y&=0 \\ \end{align*}

0.900

11402

2589

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

0.901

11403

3379

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

Series expansion around \(x=0\).

0.901

11404

7958

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

0.901

11405

8961

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

0.901

11406

14919

\begin{align*} z^{\prime \prime }-4 z^{\prime }+13 z&=0 \\ z \left (0\right ) &= 7 \\ z^{\prime }\left (0\right ) &= 42 \\ \end{align*}

0.901

11407

16393

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

0.901

11408

16879

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

Series expansion around \(x=0\).

0.901

11409

17603

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

0.901

11410

17776

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

0.901

11411

22273

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

With initial conditions

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

0.901

11412

23547

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

0.901

11413

23749

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

Series expansion around \(x=0\).

0.901

11414

26562

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

0.901

11415

502

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

Series expansion around \(x=0\).

0.902

11416

2736

\begin{align*} x_{1}^{\prime }&=x_{1}-x_{2} \\ x_{2}^{\prime }&=x_{1}+2 x_{2}+x_{3} \\ x_{3}^{\prime }&=x_{1}+10 x_{2}+2 x_{3} \\ \end{align*}

With initial conditions

\begin{align*} x_{1} \left (0\right ) &= -1 \\ x_{2} \left (0\right ) &= -4 \\ x_{3} \left (0\right ) &= 13 \\ \end{align*}

0.902

11417

8204

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

0.902

11418

9449

\begin{align*} y^{\prime \prime }+3 y^{\prime }-2 y&=-6 \,{\mathrm e}^{\pi -t} \\ y \left (\pi \right ) &= 1 \\ y^{\prime }\left (\pi \right ) &= 4 \\ \end{align*}

Using Laplace transform method.

0.902

11419

16383

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

0.902

11420

18223

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

0.902

11421

18666

\begin{align*} x^{\prime }&=2 x-\frac {5 y}{2} \\ y^{\prime }&=\frac {9 x}{5}-y \\ \end{align*}

0.902

11422

19485

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

0.902

11423

22726

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

0.902

11424

27187

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

0.902

11425

12

\begin{align*} x^{\prime \prime }&=-20 \\ x \left (0\right ) &= 5 \\ x^{\prime }\left (0\right ) &= -15 \\ \end{align*}

0.903

11426

17791

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

Series expansion around \(x=0\).

0.903

11427

18909

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

Using Laplace transform method.

0.903

11428

21544

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

0.903

11429

11706

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

0.904

11430

12685

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

0.904

11431

18916

\begin{align*} y_{1}^{\prime }&=-4 y_{1}-y_{2}+2 \,{\mathrm e}^{t} \\ y_{2}^{\prime }&=y_{1}-2 y_{2}+\sin \left (2 t \right ) \\ \end{align*}

With initial conditions

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

0.904

11432

20897

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

Series expansion around \(x=0\).

0.904

11433

25347

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

Series expansion around \(t=0\).

0.904

11434

26923

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

0.904

11435

27182

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

With initial conditions

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

0.904

11436

11

\begin{align*} x^{\prime \prime }&=50 \\ x \left (0\right ) &= 20 \\ x^{\prime }\left (0\right ) &= 10 \\ \end{align*}

0.905

11437

2442

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

Series expansion around \(t=0\).

0.905

11438

3363

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

Series expansion around \(x=0\).

0.905

11439

7172

\begin{align*} \left (4 x^{3}-14 x^{2}-2 x \right ) y^{\prime \prime }-\left (6 x^{2}-7 x +1\right ) y^{\prime }+\left (6 x -1\right ) y&=0 \\ \end{align*}

Series expansion around \(x=0\).

0.905

11440

7266

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

0.905

11441

9460

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

0.905

11442

9676

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

0.905

11443

17446

\begin{align*} y^{\prime \prime }-9 y&=54 t \sin \left (2 t \right ) \\ \end{align*}

0.905

11444

21198

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

0.905

11445

22690

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

0.905

11446

26734

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

0.905

11447

9269

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

0.906

11448

9383

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

Series expansion around \(x=0\).

0.906

11449

10041

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

0.906

11450

16905

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

Series expansion around \(x=0\).

0.906

11451

19013

\begin{align*} x_{1}^{\prime }&=\frac {3 x_{1}}{4}+\frac {29 x_{2}}{4}-\frac {11 x_{3}}{2} \\ x_{2}^{\prime }&=-\frac {3 x_{1}}{4}+\frac {3 x_{2}}{4}-\frac {5 x_{3}}{2} \\ x_{3}^{\prime }&=\frac {5 x_{1}}{4}+\frac {11 x_{2}}{4}-\frac {5 x_{3}}{2} \\ \end{align*}

0.906

11452

6875

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

0.907

11453

7141

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

0.907

11454

14730

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

Series expansion around \(x=0\).

0.907

11455

25511

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

0.907

11456

27364

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

0.907

11457

3752

\begin{align*} y^{\prime \prime }-6 y^{\prime }+13 y&=4 \,{\mathrm e}^{3 x} \sec \left (2 x \right )^{2} \\ \end{align*}

0.908

11458

8512

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

Series expansion around \(x=0\).

0.908

11459

9425

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

Series expansion around \(x=0\).

0.908

11460

12911

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

0.908

11461

14942

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

0.908

11462

15459

\begin{align*} x^{\prime }&=-4 x-10 y \\ y^{\prime }&=x-2 y \\ \end{align*}

0.908

11463

16212

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

0.908

11464

5921

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

0.909

11465

10188

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

Series expansion around \(x=0\).

0.909

11466

19488

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

0.909

11467

22812

\begin{align*} y^{\prime \prime }-2 y^{\prime }+y&=12 t \\ y \left (0\right ) &= 4 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}

Using Laplace transform method.

0.909

11468

7910

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

0.910

11469

10083

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

0.910

11470

10190

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

Series expansion around \(x=0\).

0.910

11471

10205

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

Series expansion around \(x=0\).

0.910

11472

17820

\begin{align*} x^{\prime \prime }+\frac {x^{\prime }}{10}+x&=3 \cos \left (2 t \right ) \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*}

0.910

11473

22842

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

Series expansion around \(x=0\).

0.910

11474

23050

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

0.910

11475

24099

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

Series expansion around \(x=0\).

0.910

11476

4060

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

Series expansion around \(x=0\).

0.911

11477

4416

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

0.911

11478

4459

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

0.911

11479

7176

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

Series expansion around \(x=0\).

0.911

11480

14287

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

0.911

11481

14772

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

0.911

11482

14978

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

Series expansion around \(x=0\).

0.911

11483

18640

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

With initial conditions

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

0.911

11484

18834

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

0.911

11485

20463

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

0.911

11486

22270

\begin{align*} x^{\prime }&=y \\ y^{\prime }&=-9 x+6 y+t \\ \end{align*}

0.911

11487

23296

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

0.911

11488

25417

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

0.911

11489

26030

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

Series expansion around \(x=0\).

0.911

11490

3366

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

Series expansion around \(x=0\).

0.912

11491

6935

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

0.912

11492

8262

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

0.912

11493

13109

\begin{align*} x^{\prime }&=-3 x+48 y-28 z \\ y^{\prime }&=-4 x+40 y-22 z \\ z^{\prime }&=-6 x+57 y-31 z \\ \end{align*}

0.912

11494

565

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

Using Laplace transform method.

0.913

11495

2408

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

0.913

11496

4569

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

0.913

11497

12907

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

0.913

11498

14807

\(\left [\begin {array}{ccc} -2 & 5 & 5 \\ -1 & 4 & 5 \\ 3 & -3 & 2 \end {array}\right ]\)

N/A

N/A

N/A

0.913

11499

21143

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

0.913

11500

22809

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

Using Laplace transform method.

0.913