2.3.184 Problems 18301 to 18400

Table 2.941: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

18301

13208

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

3.226

18302

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*}

3.227

18303

2096

\begin{align*} 4 x^{2} y^{\prime \prime }+8 x y^{\prime }-\left (-x^{2}+35\right ) y&=0 \\ \end{align*}

Series expansion around \(x=0\).

3.229

18304

15847

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

3.229

18305

26320

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

3.229

18306

15558

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

3.230

18307

20417

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

3.230

18308

25517

\begin{align*} y^{\prime \prime }&=-9 y \\ \end{align*}

3.230

18309

2303

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

3.231

18310

4075

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

Series expansion around \(x=0\).

3.231

18311

5033

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

3.231

18312

5435

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

3.231

18313

22067

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

3.232

18314

2318

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

3.233

18315

4206

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

3.233

18316

6959

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

3.233

18317

23106

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

3.233

18318

24032

\begin{align*} y^{\left (8\right )}+8 y^{\left (7\right )}+28 y^{\left (6\right )}+56 y^{\left (5\right )}+70 y^{\prime \prime \prime \prime }+56 y^{\prime \prime \prime }+28 y^{\prime \prime }+8 y^{\prime }&={\mathrm e}^{-x} x^{9} \\ \end{align*}

3.233

18319

6467

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

3.234

18320

17865

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

3.234

18321

20276

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

3.234

18322

23667

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

Series expansion around \(x=0\).

3.234

18323

11872

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

3.235

18324

8859

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

3.236

18325

15294

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

With initial conditions

\begin{align*} x \left (0\right ) &= 1 \\ y \left (0\right ) &= 2 \\ z \left (0\right ) &= 3 \\ \end{align*}

3.236

18326

1523

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

3.237

18327

1703

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

3.237

18328

7709

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

3.237

18329

15807

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

3.237

18330

20025

\begin{align*} a {y^{\prime }}^{3}&=27 y \\ \end{align*}

3.237

18331

24242

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

3.237

18332

2354

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

3.238

18333

22065

\begin{align*} y^{\prime }-7 y&={\mathrm e}^{x} \\ \end{align*}

3.238

18334

16898

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

Series expansion around \(x=0\).

3.239

18335

17844

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

3.239

18336

715

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

3.240

18337

1166

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

3.240

18338

18530

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

3.240

18339

12038

\begin{align*} y^{\prime }&=\frac {2 x^{3} y+x^{6}+x^{2} y^{2}+y^{3}}{x^{4}} \\ \end{align*}

3.242

18340

20826

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

3.242

18341

24112

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

Series expansion around \(x=0\).

3.242

18342

7219

\begin{align*} \sin \left (x \right ) y^{\prime }&=\ln \left (y\right ) y \\ y \left (\frac {\pi }{3}\right ) &= {\mathrm e} \\ \end{align*}

3.243

18343

17056

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

3.243

18344

92

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

3.244

18345

6328

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

3.244

18346

12060

\begin{align*} y^{\prime }&=\frac {-3 x^{2} y+1+x^{6} y^{2}+y^{3} x^{9}}{x^{3}} \\ \end{align*}

3.244

18347

19726

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

3.244

18348

17858

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

3.245

18349

14847

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

3.246

18350

18529

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

3.246

18351

22369

\begin{align*} i^{\prime }+5 i&=10 \\ i \left (0\right ) &= 0 \\ \end{align*}

3.246

18352

26885

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

3.246

18353

80

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

3.247

18354

1138

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

3.247

18355

16360

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

3.247

18356

183

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

3.248

18357

7420

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

3.249

18358

24952

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

3.249

18359

208

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

3.250

18360

749

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

3.250

18361

3598

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

3.250

18362

10431

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

3.250

18363

18026

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

3.250

18364

5649

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

3.251

18365

1672

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

3.252

18366

14260

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

3.252

18367

16921

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

Series expansion around \(x=0\).

3.252

18368

25440

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

3.252

18369

25672

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

3.253

18370

26870

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

3.253

18371

27252

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

3.253

18372

14510

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

3.254

18373

25404

\begin{align*} y^{\prime }-9 y&=90 \\ y \left (0\right ) &= 1 \\ \end{align*}

3.254

18374

26086

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

3.254

18375

13988

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

3.255

18376

2978

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

3.256

18377

11473

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

3.256

18378

21065

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

3.256

18379

23884

\begin{align*} \frac {2 x}{y}+5 y^{2}-4 x +\left (3 y^{2}-\frac {x^{2}}{y^{2}}+10 y x \right ) y^{\prime }&=0 \\ \end{align*}

3.256

18380

2093

\begin{align*} 4 x^{2} y^{\prime \prime }+2 x \left (x^{2}+8\right ) y^{\prime }+\left (3 x^{2}+5\right ) y&=0 \\ \end{align*}

Series expansion around \(x=0\).

3.257

18381

8106

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

Series expansion around \(x=0\).

3.257

18382

12182

\begin{align*} y^{\prime }&=\frac {-x y^{2}+x^{3}-x -y^{6}+3 x^{2} y^{4}-3 y^{2} x^{4}+x^{6}}{\left (x^{2}-y^{2}-1\right ) y} \\ \end{align*}

3.257

18383

24486

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

3.257

18384

26396

\begin{align*} y^{\prime } \left (3 x^{2}-2 x \right )-y \left (6 x -2\right )+\frac {18 x -8}{x}&=0 \\ \end{align*}

3.257

18385

2958

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

3.258

18386

3472

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

3.259

18387

26397

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

3.259

18388

3269

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

3.260

18389

23850

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

3.260

18390

4871

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

3.261

18391

17157

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

3.261

18392

16692

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

3.263

18393

17160

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

3.263

18394

18307

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

3.263

18395

27434

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

3.263

18396

52

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

3.264

18397

4405

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

3.264

18398

5430

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

3.264

18399

4622

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

3.265

18400

24145

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

3.265