2.3.104 Problems 10301 to 10400

Table 2.751: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

10301

16901

\begin{align*} y^{\prime \prime }+\frac {y^{\prime }}{x}+y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.714

10302

19993

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

0.714

10303

20376

\begin{align*} y^{\prime \prime \prime \prime }+10 y^{\prime \prime }+9 y&=96 \sin \left (2 x \right ) \cos \left (x \right ) \\ \end{align*}

0.714

10304

21234

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

0.714

10305

1987

\begin{align*} 9 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+3 x \left (13 x^{2}+3\right ) y^{\prime }-\left (-25 x^{2}+1\right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.715

10306

3238

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

0.715

10307

8808

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

0.715

10308

14412

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

0.715

10309

16099

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

0.715

10310

17509

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

0.715

10311

18927

\begin{align*} y^{\prime \prime }+y&=\operatorname {Heaviside}\left (t -3 \pi \right ) \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}
Using Laplace transform method.

0.715

10312

22214

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

0.715

10313

25422

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

0.715

10314

1996

\begin{align*} 3 x^{2} \left (x +1\right )^{2} y^{\prime \prime }-x \left (-11 x^{2}-10 x +1\right ) y^{\prime }+\left (5 x^{2}+1\right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.716

10315

2614

\begin{align*} t \left (2-t \right ) y^{\prime \prime }-6 \left (t -1\right ) y^{\prime }-4 y&=0 \\ y \left (1\right ) &= 1 \\ y^{\prime }\left (1\right ) &= 0 \\ \end{align*}
Series expansion around \(t=1\).

0.716

10316

7902

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

0.716

10317

24814

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

0.716

10318

2582

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

0.717

10319

12610

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

0.717

10320

17592

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

0.717

10321

19060

\begin{align*} x_{1}^{\prime }&=x_{1}+x_{2} \\ x_{2}^{\prime }&=-14 x_{1}-5 x_{2}+x_{3} \\ x_{3}^{\prime }&=15 x_{1}+5 x_{2}-2 x_{3} \\ \end{align*}
With initial conditions
\begin{align*} x_{1} \left (0\right ) &= 5 \\ x_{2} \left (0\right ) &= 5 \\ x_{3} \left (0\right ) &= -4 \\ \end{align*}

0.717

10322

20126

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

0.717

10323

21225

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

0.717

10324

1385

\begin{align*} x^{2} y^{\prime \prime }+\left (x +1\right ) y^{\prime }+3 y \ln \left (x \right )&=0 \\ y \left (1\right ) &= 2 \\ y^{\prime }\left (1\right ) &= 0 \\ \end{align*}
Series expansion around \(x=1\).

0.718

10325

2619

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

0.718

10326

3332

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

0.718

10327

3841

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

0.718

10328

4459

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

0.718

10329

4577

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

0.718

10330

18415

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

0.718

10331

18979

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

0.718

10332

20649

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

0.718

10333

24468

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

0.718

10334

4044

\begin{align*} x^{2} y^{\prime \prime }+x \left (x^{2}+6\right ) y^{\prime }+6 y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.719

10335

5409

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

0.719

10336

6956

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

0.719

10337

8947

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

0.719

10338

9699

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

0.719

10339

9850

\begin{align*} 2 y^{\prime \prime }+9 y^{\prime } x -36 y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.719

10340

18109

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

0.719

10341

19455

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

0.719

10342

19698

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

0.719

10343

20202

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

0.719

10344

22196

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

0.719

10345

24731

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

0.719

10346

25356

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

0.719

10347

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*}

0.720

10348

2017

\begin{align*} 25 x^{2} y^{\prime \prime }+x \left (15+x \right ) y^{\prime }+\left (x +1\right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.720

10349

3628

\begin{align*} y^{\prime }-2 y&=\left \{\begin {array}{cc} 1 & x \le 1 \\ 0 & 1<x \end {array}\right . \\ y \left (0\right ) &= 3 \\ \end{align*}

0.720

10350

5927

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

0.720

10351

6183

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

0.720

10352

14678

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

0.720

10353

16387

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

0.720

10354

16867

\begin{align*} y^{\prime }+y \ln \left (x \right )&=0 \\ \end{align*}
Series expansion around \(x=1\).

0.720

10355

16916

\begin{align*} y^{\prime \prime }+\frac {y^{\prime }}{x}+y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.720

10356

18232

\begin{align*} y^{\prime \prime }-3 y^{\prime }&=18 x -10 \cos \left (x \right ) \\ \end{align*}

0.720

10357

19226

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

0.720

10358

20455

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

0.720

10359

21667

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

0.720

10360

2022

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

0.721

10361

3252

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

0.721

10362

3691

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

0.721

10363

4180

\begin{align*} y^{\prime \prime }+\frac {2 y^{\prime }}{x}+y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.721

10364

11319

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

0.721

10365

15434

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

0.721

10366

23814

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

0.721

10367

24488

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

0.721

10368

988

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

0.722

10369

7781

\begin{align*} x^{\prime \prime }+5 x^{\prime }+6 x&=\cos \left (t \right ) \\ x \left (0\right ) &= {\frac {1}{10}} \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*}

0.722

10370

8221

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

0.722

10371

14804

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

N/A

N/A

N/A

0.722

10372

21752

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

0.722

10373

23635

\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}
Using Laplace transform method.

0.722

10374

1631

\begin{align*} x^{2} y^{\prime }+2 y&=2 \,{\mathrm e}^{\frac {1}{x}} \sqrt {y} \\ \end{align*}

0.723

10375

1974

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

0.723

10376

3356

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

0.723

10377

3499

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

0.723

10378

6033

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

0.723

10379

8247

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

0.723

10380

9069

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

0.723

10381

9740

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

0.723

10382

18084

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

0.723

10383

20149

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

0.723

10384

20526

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

0.723

10385

25246

\begin{align*} t y^{\prime \prime }+2 y^{\prime }+9 t y&=0 \\ \end{align*}
Using Laplace transform method.

0.723

10386

1632

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

0.724

10387

1753

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

0.724

10388

2021

\begin{align*} x^{2} \left (1-4 x \right ) y^{\prime \prime }+3 \left (1-6 x \right ) x y^{\prime }+\left (1-12 x \right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.724

10389

3352

\begin{align*} x^{2} \left (x +4\right ) y^{\prime \prime }+7 y^{\prime } x -y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.724

10390

6182

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

0.724

10391

11365

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

0.724

10392

12151

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

0.724

10393

12570

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

0.724

10394

15836

\begin{align*} v^{\prime }&=\frac {K -v}{R C} \\ \end{align*}

0.724

10395

16044

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

0.724

10396

18827

\begin{align*} u^{\prime \prime }+w_{0}^{2} u&=\cos \left (w t \right ) \\ \end{align*}

0.724

10397

19108

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

0.724

10398

19254

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

0.724

10399

20945

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

0.724

10400

21682

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

0.724