2.3.144 Problems 14301 to 14400

Table 2.861: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

14301

20167

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

1.191

14302

26473

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

1.191

14303

6531

\begin{align*} 4 f \left (x \right ) y y^{\prime \prime }&=4 f \left (x \right )^{2} y+3 f \left (x \right ) g \left (x \right ) y^{2}-f \left (x \right ) y^{4}+2 y^{3} f^{\prime }\left (x \right )+\left (-6 f \left (x \right ) y^{2}+2 f^{\prime }\left (x \right )\right ) y^{\prime }+3 f \left (x \right ) {y^{\prime }}^{2} \\ \end{align*}

1.192

14304

24099

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

Series expansion around \(x=0\).

1.192

14305

25421

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

1.192

14306

993

\begin{align*} x_{1}^{\prime }&=2 x_{1} \\ x_{2}^{\prime }&=-21 x_{1}-5 x_{2}-27 x_{3}-9 x_{4} \\ x_{3}^{\prime }&=5 x_{3} \\ x_{4}^{\prime }&=-21 x_{3}-2 x_{4} \\ \end{align*}

1.193

14307

9724

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

1.193

14308

17884

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

1.193

14309

23749

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

Series expansion around \(x=0\).

1.193

14310

2707

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

With initial conditions

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

1.194

14311

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 \(x=0\).

1.194

14312

14717

\begin{align*} x^{2} y^{\prime \prime }-2 y^{\prime } x -10 y&=0 \\ y \left (1\right ) &= 5 \\ y^{\prime }\left (1\right ) &= 4 \\ \end{align*}

1.194

14313

19847

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

1.194

14314

20907

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

Series expansion around \(x=0\).

1.194

14315

21479

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

1.194

14316

24848

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

1.194

14317

25289

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

Using Laplace transform method.

1.194

14318

1673

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

1.195

14319

19849

\begin{align*} e y^{\prime \prime }&=-\frac {\left (w L +P \right ) x}{2}-\frac {w \,x^{2}}{2} \\ \end{align*}

1.195

14320

7171

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

Series expansion around \(x=0\).

1.196

14321

9867

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

Series expansion around \(x=0\).

1.196

14322

20176

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

1.196

14323

23750

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

Series expansion around \(x=0\).

1.196

14324

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 \(x=0\).

1.197

14325

8333

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

1.197

14326

9919

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

Series expansion around \(x=0\).

1.197

14327

9957

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

Series expansion around \(x=0\).

1.197

14328

14363

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

Using Laplace transform method.

1.197

14329

26734

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

1.197

14330

27118

\(\left [\begin {array}{cccc} 1 & 0 & 0 & 0 \\ 0 & 4 & 1 & 0 \\ 0 & 0 & -3 & 1 \\ 0 & 0 & 1 & -2 \end {array}\right ]\)

N/A

N/A

N/A

1.197

14331

5719

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

1.198

14332

9918

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

Series expansion around \(x=0\).

1.198

14333

16423

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

1.198

14334

17435

\begin{align*} y^{\prime \prime }-4 y^{\prime }+13 y&=2 t \,{\mathrm e}^{-2 t} \sin \left (3 t \right ) \\ \end{align*}

1.198

14335

21314

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

1.198

14336

27172

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

With initial conditions

\begin{align*} x_{1} \left (0\right ) &= 6 \\ x_{2} \left (0\right ) &= 2 \\ x_{3} \left (0\right ) &= 3 \\ \end{align*}

1.198

14337

7119

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

1.199

14338

14539

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

1.199

14339

16388

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

1.199

14340

17486

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

1.199

14341

4611

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

1.200

14342

6959

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

1.200

14343

16674

\begin{align*} y^{\prime \prime }-6 y^{\prime }+9 y&=27 \,{\mathrm e}^{6 x}+25 \sin \left (6 x \right ) \\ \end{align*}

1.200

14344

23249

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

1.200

14345

26701

\begin{align*} y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }+2 y^{\prime \prime }-2 y^{\prime }+y&=\cos \left (2 x \right ) \\ y \left (0\right ) &= {\frac {1}{25}} \\ y \left (\pi \right ) &= {\frac {1}{25}} \\ y^{\prime }\left (0\right ) &= {\frac {2}{15}} \\ y^{\prime }\left (\pi \right ) &= {\frac {2}{25}} \\ \end{align*}

1.200

14346

3222

\begin{align*} 4 x^{2} y^{\prime \prime }-16 y^{\prime } x +25 y&=0 \\ \end{align*}

1.201

14347

8119

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

Series expansion around \(x=0\).

1.201

14348

8149

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

Series expansion around \(x=0\).

1.201

14349

8209

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

1.201

14350

9145

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

1.201

14351

20525

\begin{align*} \left (2 x^{2}+3 x \right ) y^{\prime \prime }+\left (3+6 x \right ) y^{\prime }+2 y&={\mathrm e}^{x} \left (x +1\right ) \\ \end{align*}

1.201

14352

23286

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

1.201

14353

23470

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

1.201

14354

23565

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

1.202

14355

24101

\begin{align*} x^{2} y^{\prime \prime }-\left (3 x^{4}+5 x \right ) y^{\prime }+\left (6 x^{3}+5\right ) y&=0 \\ \end{align*}

Series expansion around \(x=0\).

1.202

14356

16406

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

1.203

14357

20093

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

1.203

14358

2292

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

1.204

14359

7888

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

1.204

14360

17589

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

1.204

14361

19618

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

Series expansion around \(x=-1\).

1.204

14362

25562

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

1.204

14363

7166

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

Series expansion around \(x=0\).

1.205

14364

7374

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

Series expansion around \(x=0\).

1.205

14365

26438

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

1.205

14366

7440

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

1.206

14367

16653

\begin{align*} 6 y-5 y^{\prime }+y^{\prime \prime }&=x^{2} \cos \left (2 x \right ) \\ \end{align*}

1.206

14368

25494

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

1.206

14369

16839

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

Series expansion around \(x=0\).

1.207

14370

18161

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

1.207

14371

20236

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

1.207

14372

1036

\begin{align*} x_{1}^{\prime }&=-x_{1}+x_{2}+x_{3}-2 x_{4} \\ x_{2}^{\prime }&=7 x_{1}-4 x_{2}-6 x_{3}+11 x_{4} \\ x_{3}^{\prime }&=5 x_{1}-x_{2}+x_{3}+3 x_{4} \\ x_{4}^{\prime }&=6 x_{1}-2 x_{2}-2 x_{3}+6 x_{4} \\ \end{align*}

1.208

14373

13076

\begin{align*} 4 x^{\prime }+9 y^{\prime }+44 x+49 y&=t \\ 3 x^{\prime }+7 y^{\prime }+34 x+38 y&={\mathrm e}^{t} \\ \end{align*}

1.208

14374

14489

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

1.208

14375

20906

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

Series expansion around \(x=0\).

1.208

14376

26549

\begin{align*} y^{\prime \prime }+8 y^{\prime }&=8 x \\ \end{align*}

1.208

14377

26996

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

1.208

14378

156

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

1.209

14379

3955

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

Using Laplace transform method.

1.209

14380

9871

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

Series expansion around \(x=0\).

1.209

14381

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 \(x=0\).

1.209

14382

18084

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

1.209

14383

2475

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

1.210

14384

4245

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

1.210

14385

5725

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

1.210

14386

9413

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

Series expansion around \(x=0\).

1.210

14387

21794

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

1.210

14388

22341

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

1.210

14389

22928

\begin{align*} 2 x^{\prime }-x+7 y^{\prime }+3 y&=90 \sin \left (2 t \right ) \\ x^{\prime }-5 x+8 y^{\prime }-3 y&=0 \\ \end{align*}

1.210

14390

8976

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

1.211

14391

16726

\begin{align*} x^{2} y^{\prime \prime }+2 y^{\prime } x -30 y&=0 \\ \end{align*}

1.211

14392

23736

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

Series expansion around \(x=0\).

1.211

14393

4215

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

1.212

14394

27558

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

1.212

14395

9751

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

1.213

14396

20211

\begin{align*} 4 x^{\prime }+9 y^{\prime }+2 x+31 y&={\mathrm e}^{t} \\ 3 x^{\prime }+7 y^{\prime }+x+24 y&=3 \\ \end{align*}

1.213

14397

262

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

1.214

14398

1114

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

1.214

14399

4012

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

Series expansion around \(x=0\).

1.214

14400

5401

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

1.214