2.3.104 Problems 10301 to 10400

Table 2.739: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

10301

10646

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

0.536

10302

17500

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

0.536

10303

653

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

0.537

10304

886

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

0.537

10305

3871

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

0.537

10306

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*}

0.537

10307

6487

\begin{align*} 3 y y^{\prime \prime }&=5 {y^{\prime }}^{2} \\ \end{align*}

0.537

10308

8134

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

0.537

10309

10172

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

0.537

10310

13202

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

0.537

10311

16386

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

0.537

10312

20143

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

0.537

10313

2704

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

0.538

10314

8221

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

0.538

10315

10018

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

0.538

10316

14839

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

0.538

10317

16039

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

0.538

10318

16926

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

0.538

10319

18680

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

0.538

10320

18960

\begin{align*} y^{\prime \prime \prime \prime }-16 y&=g \left (t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime \prime }\left (0\right ) &= 0 \\ y^{\prime \prime \prime }\left (0\right ) &= 0 \\ \end{align*}
Using Laplace transform method.

0.538

10321

23574

\begin{align*} x^{\prime }&=5 x-6 y+1 \\ y^{\prime }&=6 x-7 y+1 \\ \end{align*}

0.538

10322

24888

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

0.538

10323

338

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

0.539

10324

643

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

0.539

10325

835

\begin{align*} 4 x^{2} y^{\prime \prime }+8 y^{\prime } x -3 y&=0 \\ \end{align*}

0.539

10326

908

\begin{align*} x^{\prime \prime }+9 x&=10 \cos \left (2 t \right ) \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*}

0.539

10327

1991

\begin{align*} 6 x^{2} \left (2 x^{2}+1\right ) y^{\prime \prime }+x \left (50 x^{2}+1\right ) y^{\prime }+\left (30 x^{2}+1\right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.539

10328

4181

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

0.539

10329

5739

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

0.539

10330

6205

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

0.539

10331

6964

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

0.539

10332

7086

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

0.539

10333

12421

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

0.539

10334

16085

\begin{align*} y^{\prime \prime }+4 y^{\prime }+20 y&={\mathrm e}^{-\frac {t}{2}} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

0.539

10335

16889

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

0.539

10336

17496

\begin{align*} y^{\prime \prime }-8 y^{\prime }+17 y&={\mathrm e}^{4 t} \sec \left (t \right ) \\ \end{align*}

0.539

10337

19835

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

0.539

10338

21746

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

0.539

10339

21793

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

0.539

10340

23579

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

0.539

10341

637

\begin{align*} x_{1}^{\prime }&=4 x_{1}+x_{2}+4 x_{3} \\ x_{2}^{\prime }&=x_{1}+7 x_{2}+x_{3} \\ x_{3}^{\prime }&=4 x_{1}+x_{2}+4 x_{3} \\ \end{align*}

0.540

10342

878

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

0.540

10343

1844

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

0.540

10344

1990

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

0.540

10345

2586

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

0.540

10346

6412

\begin{align*} b +a x y-\left (-12 x^{2}+k \,x^{-1+k}\right ) \left (y^{2}+3 y^{\prime }\right )+2 \left (-4 x^{3}+x^{k}\right ) \left (-y^{3}+y^{\prime } y+y^{\prime \prime }\right )&=0 \\ \end{align*}

0.540

10347

7122

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

0.540

10348

8148

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

0.540

10349

8392

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

0.540

10350

9396

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

0.540

10351

9623

\begin{align*} y+y^{\prime }&=\left \{\begin {array}{cc} 0 & 0\le t <1 \\ 5 & 1\le t \end {array}\right . \\ y \left (0\right ) &= 0 \\ \end{align*}
Using Laplace transform method.

0.540

10352

13104

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

0.540

10353

14981

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

0.540

10354

15662

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

0.540

10355

16626

\begin{align*} y^{\prime \prime }+9 y&=39 x \,{\mathrm e}^{2 x} \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

0.540

10356

16897

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

0.540

10357

21588

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

0.540

10358

9815

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

0.541

10359

14646

\begin{align*} 16 y+8 y^{\prime }+y^{\prime \prime }&=8 \,{\mathrm e}^{-2 x} \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

0.541

10360

15454

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

0.541

10361

19213

\begin{align*} y^{\prime }&=-z \\ z^{\prime }&=y \\ \end{align*}
With initial conditions
\begin{align*} y \left (0\right ) &= 1 \\ z \left (0\right ) &= 0 \\ \end{align*}

0.541

10362

21516

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

0.541

10363

25417

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

0.541

10364

25624

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

0.541

10365

331

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

0.542

10366

638

\begin{align*} x_{1}^{\prime }&=x_{1}+2 x_{2}+2 x_{3} \\ x_{2}^{\prime }&=2 x_{1}+7 x_{2}+x_{3} \\ x_{3}^{\prime }&=2 x_{1}+x_{2}+7 x_{3} \\ \end{align*}

0.542

10367

983

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

0.542

10368

2421

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

0.542

10369

3958

\begin{align*} y^{\prime }+2 y&=\operatorname {Heaviside}\left (t -\pi \right ) \sin \left (2 t \right ) \\ y \left (0\right ) &= 3 \\ \end{align*}
Using Laplace transform method.

0.542

10370

4071

\begin{align*} 4 y^{\prime \prime } x +3 y^{\prime }+3 y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.542

10371

5139

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

0.542

10372

5871

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

0.542

10373

5982

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

0.542

10374

6051

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

0.542

10375

12583

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

0.542

10376

17497

\begin{align*} y^{\prime \prime }-9 y&=\frac {1}{1+{\mathrm e}^{3 t}} \\ \end{align*}

0.542

10377

19567

\begin{align*} 12 y-7 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{2 x} \left (x^{3}-5 x^{2}\right ) \\ \end{align*}

0.542

10378

19642

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

0.542

10379

19661

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

0.542

10380

21115

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

0.542

10381

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*}

0.542

10382

22169

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

0.542

10383

22692

\begin{align*} y^{\prime \prime }+16 y&=5 \sin \left (x \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

0.542

10384

474

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

0.543

10385

475

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

0.543

10386

584

\begin{align*} x^{\prime }&=-y \\ y^{\prime }&=13 x+4 y \\ \end{align*}
With initial conditions
\begin{align*} x \left (0\right ) &= 0 \\ y \left (0\right ) &= 3 \\ \end{align*}

0.543

10387

977

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

0.543

10388

2284

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

0.543

10389

2831

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

0.543

10390

3236

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

0.543

10391

5423

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

0.543

10392

6719

\begin{align*} 10 x^{2} y^{\prime }+8 x^{3} y^{\prime \prime }+x^{2} \left (x^{2}+1\right ) y^{\prime \prime \prime }&=-1+3 x^{2}+2 \ln \left (x \right ) x^{2} \\ \end{align*}

0.543

10393

8897

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

0.543

10394

9702

\begin{align*} x^{\prime }&=4 x+5 y \\ y^{\prime }&=-2 x+6 y \\ \end{align*}

0.543

10395

9726

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

0.543

10396

11739

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

0.543

10397

12973

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

0.543

10398

15247

\begin{align*} 10 Q^{\prime }+100 Q&=\operatorname {Heaviside}\left (-1+t \right )-\operatorname {Heaviside}\left (t -2\right ) \\ Q \left (0\right ) &= 0 \\ \end{align*}
Using Laplace transform method.

0.543

10399

15474

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

0.543

10400

17011

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

0.543