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

6524

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

1.239

13302

15144

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

1.239

13303

26620

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

1.239

13304

5414

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

1.240

13305

9640

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

Using Laplace transform method.

1.240

13306

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*}

1.240

13307

16675

\begin{align*} y^{\prime \prime }+9 y&=25 x \cos \left (2 x \right )+3 \sin \left (3 x \right ) \\ \end{align*}

1.240

13308

18093

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

1.240

13309

20162

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

1.240

13310

20172

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

1.240

13311

24754

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

1.240

13312

25189

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

1.240

13313

159

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

1.241

13314

1293

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

1.242

13315

14741

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

Series expansion around \(x=1\).

1.242

13316

15300

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

1.242

13317

25554

\begin{align*} y^{\prime \prime }+c y&={\mathrm e}^{i \omega t} \\ \end{align*}

1.242

13318

1673

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

1.243

13319

3401

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

Series expansion around \(x=0\).

1.243

13320

9838

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

Series expansion around \(x=0\).

1.243

13321

17711

\begin{align*} 9 x y^{\prime \prime }+14 y^{\prime }+\left (x -1\right ) y&=0 \\ \end{align*}

Series expansion around \(x=0\).

1.243

13322

18238

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

1.243

13323

18243

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

1.243

13324

21908

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

Series expansion around \(x=0\).

1.243

13325

22213

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

Series expansion around \(x=0\).

1.243

13326

12877

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

1.244

13327

4029

\begin{align*} x^{2} y^{\prime \prime }-\left (2 \sqrt {5}-1\right ) x y^{\prime }+\left (\frac {19}{4}-3 x^{2}\right ) y&=0 \\ \end{align*}

Series expansion around \(x=0\).

1.246

13328

5905

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

1.246

13329

6156

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

1.246

13330

12992

\begin{align*} 8 \left (-x^{3}+1\right ) y y^{\prime \prime }-4 \left (-x^{3}+1\right ) {y^{\prime }}^{2}-12 x^{2} y y^{\prime }+3 x y^{2}&=0 \\ \end{align*}

1.246

13331

18222

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

1.246

13332

20783

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

1.246

13333

25318

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

Using Laplace transform method.

1.246

13334

497

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

Series expansion around \(x=0\).

1.247

13335

3139

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

1.247

13336

3399

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

Series expansion around \(x=0\).

1.247

13337

8327

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

1.247

13338

25227

\begin{align*} t^{2} y^{\prime \prime }-3 t y^{\prime }-21 y&=0 \\ \end{align*}

1.247

13339

27732

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

1.247

13340

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.

1.248

13341

20475

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

1.248

13342

21542

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

1.248

13343

22

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

1.250

13344

18331

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

1.250

13345

20149

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

Series expansion around \(x=0\).

1.250

13346

23620

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

1.250

13347

27352

\begin{align*} \left (y^{\prime }+1\right )^{3}&=27 \left (x +y\right )^{2} \\ \end{align*}

1.250

13348

5932

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

1.251

13349

6187

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

1.251

13350

9567

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

1.251

13351

13171

\(\left [\begin {array}{cccc} 22 & -9 & -8 & -8 \\ 10 & -7 & -14 & 2 \\ 10 & 0 & 8 & -10 \\ 29 & -9 & -3 & -15 \end {array}\right ]\)

N/A

N/A

N/A

1.251

13352

15813

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

1.251

13353

15814

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

1.251

13354

15835

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

1.251

13355

21896

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

With initial conditions

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

1.251

13356

25472

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

1.251

13357

647

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

1.252

13358

19524

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

1.252

13359

26056

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

1.252

13360

6876

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

1.253

13361

7005

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

1.253

13362

9404

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

Series expansion around \(x=0\).

1.253

13363

9643

\begin{align*} y^{\prime \prime }+16 y&=\delta \left (t -2 \pi \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

Using Laplace transform method.

1.253

13364

13825

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

1.253

13365

17750

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

1.253

13366

20125

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

1.253

13367

21672

\begin{align*} 8 x^{2} y^{\prime \prime }+10 x y^{\prime }+\left (x -1\right ) y&=0 \\ \end{align*}

Series expansion around \(x=0\).

1.253

13368

12906

\begin{align*} 24+12 y x +x^{3} \left (y y^{\prime }+y^{\prime \prime }-y^{3}\right )&=0 \\ \end{align*}

1.254

13369

12976

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

1.254

13370

23131

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

1.254

13371

25593

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

1.254

13372

2431

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

1.255

13373

3394

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

Series expansion around \(x=0\).

1.255

13374

4037

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

Series expansion around \(x=0\).

1.255

13375

4387

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

1.255

13376

172

\begin{align*} x^{\prime }&=10 x-x^{2} \\ x \left (0\right ) &= 1 \\ \end{align*}

1.256

13377

516

\begin{align*} x y^{\prime \prime }-y^{\prime }+36 x^{3} y&=0 \\ \end{align*}

1.256

13378

8508

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

Series expansion around \(x=0\).

1.256

13379

9434

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

Series expansion around \(x=0\).

1.256

13380

23234

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

1.256

13381

1007

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

1.257

13382

6717

\begin{align*} 2 y x +2 x^{3} y^{\prime \prime }+x^{4} y^{\prime \prime \prime }&=10 x^{2}+10 \\ \end{align*}

1.257

13383

12314

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

1.257

13384

20785

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

1.257

13385

23054

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

1.257

13386

2290

\begin{align*} y_{1}^{\prime }&=-3 y_{1}+3 y_{2}+y_{3} \\ y_{2}^{\prime }&=y_{1}-5 y_{2}-3 y_{3} \\ y_{3}^{\prime }&=-3 y_{1}+7 y_{2}+3 y_{3} \\ \end{align*}

1.258

13387

11763

\begin{align*} 9 y {y^{\prime }}^{2}+4 x^{3} y^{\prime }-4 x^{2} y&=0 \\ \end{align*}

1.258

13388

22832

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

Series expansion around \(x=2\).

1.258

13389

25336

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

Series expansion around \(t=0\).

1.258

13390

8423

\begin{align*} 3 y^{\prime }+12 y&=4 \\ \end{align*}

1.259

13391

8866

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

1.259

13392

16394

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

1.259

13393

26428

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

1.259

13394

26467

\begin{align*} y^{\prime \prime }&=\frac {1}{4 \sqrt {y}} \\ \end{align*}

1.259

13395

2432

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

1.260

13396

8998

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

Series expansion around \(x=0\).

1.260

13397

10276

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

1.260

13398

14110

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

1.260

13399

21144

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

1.260

13400

21471

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

1.260