2.3.134 Problems 13301 to 13400

Table 2.841: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

13301

16897

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

Series expansion around \(x=0\).

2.363

13302

22650

\begin{align*} s^{\prime \prime }+16 s^{\prime }+64 s&=0 \\ s \left (0\right ) &= 0 \\ s^{\prime }\left (0\right ) &= -4 \\ \end{align*}

2.363

13303

9383

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

Series expansion around \(x=0\).

2.364

13304

23091

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

2.364

13305

9970

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

Series expansion around \(x=0\).

2.365

13306

21885

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

2.365

13307

23437

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

Series expansion around \(x=0\).

2.365

13308

1355

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

2.366

13309

9518

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

Series expansion around \(x=0\).

2.366

13310

22495

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

2.366

13311

27683

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

2.366

13312

4481

\begin{align*} y^{\prime \prime }-y&=12 \,{\mathrm e}^{x} x^{2}+3 \,{\mathrm e}^{2 x}+10 \cos \left (3 x \right ) \\ \end{align*}

2.368

13313

6418

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

2.368

13314

18876

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

2.368

13315

27094

\(\left [\begin {array}{ccc} 2 & 0 & 0 \\ 1 & 0 & 2 \\ 0 & 0 & 3 \end {array}\right ]\)

N/A

N/A

N/A

2.368

13316

6422

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

2.369

13317

21605

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

2.369

13318

26246

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

2.369

13319

13387

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

2.371

13320

720

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

2.372

13321

8992

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

Series expansion around \(x=0\).

2.372

13322

9039

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

2.372

13323

15858

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

2.372

13324

20651

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

2.372

13325

23681

\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 \(x=0\).

2.372

13326

1240

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

2.373

13327

7204

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

2.373

13328

12342

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

2.373

13329

717

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

2.374

13330

1508

\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=\delta \left (t -5\right )+\operatorname {Heaviside}\left (t -10\right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= {\frac {1}{2}} \\ \end{align*}

Using Laplace transform method.

2.374

13331

10392

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

2.374

13332

14140

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

2.374

13333

8619

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

Series expansion around \(x=0\).

2.375

13334

12684

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

2.375

13335

13903

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

2.375

13336

15887

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

2.375

13337

22782

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

2.375

13338

23509

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

2.375

13339

801

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

2.376

13340

14988

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

With initial conditions

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

2.376

13341

23688

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

Series expansion around \(x=0\).

2.376

13342

6460

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

2.378

13343

25373

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

With initial conditions

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

2.378

13344

6959

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

2.379

13345

8093

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

Series expansion around \(x=0\).

2.379

13346

18249

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

2.379

13347

10081

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

2.380

13348

8556

\begin{align*} 16 x^{2} y^{\prime \prime }+32 y^{\prime } x +\left (x^{4}-12\right ) y&=0 \\ \end{align*}

Series expansion around \(x=0\).

2.381

13349

11636

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

2.381

13350

16414

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

2.381

13351

17638

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

2.381

13352

23694

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

Series expansion around \(x=0\).

2.381

13353

1552

\begin{align*} y^{\prime }+\frac {y}{x}&=\frac {7}{x^{2}}+3 \\ \end{align*}

2.382

13354

2891

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

2.382

13355

9522

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

Series expansion around \(x=0\).

2.382

13356

10122

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

2.382

13357

12531

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

2.382

13358

22172

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

Series expansion around \(x=0\).

2.382

13359

22215

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

Series expansion around \(x=0\).

2.382

13360

1184

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

2.383

13361

17473

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

2.383

13362

26111

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

2.383

13363

22926

\begin{align*} 3 x-y^{\prime }-2 y&=8 t \\ x^{\prime }-2 x+y&=16 \,{\mathrm e}^{-t} \\ \end{align*}

2.384

13364

6496

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

2.385

13365

27752

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

2.385

13366

14745

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

Series expansion around \(x=0\).

2.387

13367

27738

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

2.387

13368

2489

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

2.388

13369

3050

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

2.388

13370

4699

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

2.388

13371

27682

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

2.388

13372

10240

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

2.389

13373

18009

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

2.389

13374

8617

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

Series expansion around \(x=0\).

2.390

13375

4754

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

2.391

13376

10183

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

Series expansion around \(x=0\).

2.391

13377

17528

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

2.391

13378

20144

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

2.391

13379

20844

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

2.391

13380

1229

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

2.392

13381

4887

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

2.392

13382

10455

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

Series expansion around \(x=0\).

2.392

13383

16723

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

2.392

13384

20635

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

2.392

13385

3632

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

2.393

13386

6555

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

2.393

13387

16844

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

Series expansion around \(x=0\).

2.393

13388

23616

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

2.393

13389

8087

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

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

2.394

13390

27635

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

2.394

13391

4894

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

2.395

13392

8045

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

2.395

13393

24018

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

2.395

13394

4613

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

2.396

13395

23262

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

2.396

13396

27532

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

2.396

13397

10213

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

Series expansion around \(x=0\).

2.397

13398

24460

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

2.397

13399

4059

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

Series expansion around \(x=0\).

2.398

13400

4283

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

2.398