2.3.134 Problems 13301 to 13400

Table 2.811: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

13301

20727

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

1.211

13302

9398

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

1.212

13303

9637

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

1.212

13304

23452

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

1.212

13305

23669

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

1.212

13306

2465

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

1.213

13307

8149

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

1.213

13308

9624

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

1.213

13309

9942

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

1.213

13310

18364

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

1.213

13311

20022

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

1.213

13312

7772

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

1.214

13313

9210

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

1.214

13314

12536

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

1.214

13315

20629

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

1.214

13316

20968

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

1.214

13317

165

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

1.215

13318

6803

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

1.215

13319

9969

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

1.215

13320

15660

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

1.215

13321

15885

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

1.215

13322

21339

\begin{align*} \sqrt {x}\, y^{\prime }+1&=0 \\ \end{align*}

1.215

13323

24876

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

1.215

13324

23633

\begin{align*} y^{\prime }-3 y&=13 \cos \left (2 t \right ) \\ y \left (0\right ) &= -1 \\ \end{align*}
Using Laplace transform method.

1.216

13325

23663

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

1.216

13326

3558

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

1.217

13327

7312

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

1.217

13328

12366

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

1.217

13329

7377

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

1.218

13330

9142

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

1.218

13331

14943

\begin{align*} x^{\prime \prime }+x^{\prime }-2 x&=12 \,{\mathrm e}^{-t}-6 \,{\mathrm e}^{t} \\ \end{align*}

1.218

13332

10015

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

1.219

13333

14776

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

1.219

13334

19005

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

1.219

13335

23049

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

1.219

13336

23701

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

1.219

13337

26122

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

1.219

13338

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.

1.220

13339

7082

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

1.220

13340

12428

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

1.220

13341

14656

\begin{align*} y^{\prime \prime \prime }-4 y^{\prime \prime }+y^{\prime }+6 y&=3 x \,{\mathrm e}^{x}+2 \,{\mathrm e}^{x}-\sin \left (x \right ) \\ y \left (0\right ) &= {\frac {33}{40}} \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime \prime }\left (0\right ) &= 0 \\ \end{align*}

1.220

13342

19506

\begin{align*} 4 y+y^{\prime \prime }&=4 \cos \left (2 x \right )+6 \cos \left (x \right )+8 x^{2}-4 x \\ \end{align*}

1.220

13343

20880

\begin{align*} x^{2} y^{\prime \prime }+3 y^{\prime } x -15 y&={\mathrm e}^{x} x^{4} \\ y \left (1\right ) &= 1 \\ y^{\prime }\left (1\right ) &= 0 \\ \end{align*}

1.220

13344

14409

\begin{align*} x^{\prime }&=-5 x+3 y+{\mathrm e}^{-t} \\ y^{\prime }&=2 x-10 y \\ \end{align*}

1.221

13345

25284

\begin{align*} y^{\prime \prime }-\left (a +b \right ) y^{\prime }+a b y&=f \left (t \right ) \\ \end{align*}
Using Laplace transform method.

1.221

13346

8765

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

1.222

13347

9908

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

1.222

13348

22931

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

1.222

13349

23659

\begin{align*} y^{\prime \prime }+2 y^{\prime }+5 y&=8 \,{\mathrm e}^{t}+5 t \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*}
Using Laplace transform method.

1.222

13350

845

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

1.223

13351

6406

\begin{align*} -6+x y \left (12+3 y x -2 y^{2} x^{2}\right )+x^{2} \left (9+2 y x \right ) y^{\prime }+2 x^{3} y^{\prime \prime }&=0 \\ \end{align*}

1.223

13352

6408

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

1.223

13353

11819

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

1.223

13354

16925

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

1.223

13355

22860

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

1.224

13356

25218

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

1.224

13357

25758

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

1.224

13358

7689

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

1.225

13359

8668

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

1.225

13360

21956

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

1.225

13361

6419

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

1.226

13362

8745

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

1.226

13363

10378

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

1.226

13364

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*}

1.226

13365

23627

\begin{align*} x^{\prime }&=-10 x+y+7 z \\ y^{\prime }&=-9 x+4 y+5 z \\ z^{\prime }&=-17 x+y+12 z \\ \end{align*}
With initial conditions
\begin{align*} x \left (0\right ) &= 6 \\ y \left (0\right ) &= 1 \\ z \left (0\right ) &= 10 \\ \end{align*}

1.226

13366

25584

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

1.226

13367

2700

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

1.227

13368

14740

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

1.227

13369

18361

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

1.227

13370

21314

\begin{align*} x^{\prime }&=\lambda x-x^{3}-x^{5} \\ \end{align*}

1.227

13371

22057

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

1.227

13372

3440

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

1.228

13373

3913

\begin{align*} x_{1}^{\prime }&=7 x_{1}-x_{4} \\ x_{2}^{\prime }&=6 x_{2} \\ x_{3}^{\prime }&=-x_{3} \\ x_{4}^{\prime }&=2 x_{1}+5 x_{4} \\ \end{align*}

1.228

13374

18077

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

1.228

13375

384

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

1.229

13376

3847

\begin{align*} x_{1}^{\prime }&=x_{1}+2 x_{2}+3 x_{3}+4 x_{4} \\ x_{2}^{\prime }&=4 x_{1}+3 x_{2}+2 x_{3}+x_{4} \\ x_{3}^{\prime }&=4 x_{1}+5 x_{2}+6 x_{3}+7 x_{4} \\ x_{4}^{\prime }&=7 x_{1}+6 x_{2}+5 x_{3}+4 x_{4} \\ \end{align*}

1.229

13377

6035

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

1.229

13378

9940

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

1.229

13379

3329

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

1.230

13380

14787

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

1.230

13381

14790

\begin{align*} x^{\prime }&=5 x+2 y+5 t \\ y^{\prime }&=3 x+4 y+17 t \\ \end{align*}

1.230

13382

18537

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

1.230

13383

20503

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

1.230

13384

1056

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

1.231

13385

3226

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

1.231

13386

9399

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

1.231

13387

11432

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

1.231

13388

14727

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

1.231

13389

22104

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

1.231

13390

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 \(x=0\).

1.232

13391

7193

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

1.232

13392

8293

\begin{align*} y^{\prime }&={\mathrm e}^{-\frac {x y^{2}}{100}} \\ y \left (-6\right ) &= 0 \\ \end{align*}

1.232

13393

9645

\begin{align*} y^{\prime \prime }+y&=\delta \left (t -2 \pi \right )+\delta \left (t -4 \pi \right ) \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}
Using Laplace transform method.

1.232

13394

16178

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

1.232

13395

24739

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

1.232

13396

6784

\begin{align*} y^{\prime }+2 y^{\prime \prime \prime }+y^{\left (5\right )}&=a x +b \cos \left (x \right )+c \sin \left (x \right ) \\ \end{align*}

1.233

13397

8640

\begin{align*} y^{\prime \prime }+9 y&=\left \{\begin {array}{cc} 8 \sin \left (t \right ) & 0<t <\pi \\ 0 & \pi <t \end {array}\right . \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 4 \\ \end{align*}
Using Laplace transform method.

1.233

13398

10165

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

1.233

13399

21848

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

1.233

13400

23677

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

1.233