2.3.233 Problems 23201 to 23300

Table 2.997: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

23201

19567

\begin{align*} 12 y-7 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{2 x} \left (x^{3}-5 x^{2}\right ) \\ \end{align*}

29.028

23202

16591

\begin{align*} y^{\prime \prime }+6 y^{\prime }+9 y&=169 \sin \left (2 x \right ) \\ y \left (0\right ) &= -10 \\ y^{\prime }\left (0\right ) &= 9 \\ \end{align*}

29.032

23203

12144

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

29.036

23204

18102

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

29.037

23205

21033

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

29.037

23206

12287

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

29.042

23207

14415

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

29.045

23208

24007

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

29.047

23209

16111

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

29.056

23210

21425

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

29.061

23211

20350

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

29.072

23212

21816

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

29.079

23213

19562

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

29.092

23214

7766

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

29.094

23215

24038

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

29.099

23216

8796

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

29.106

23217

19755

\begin{align*} v^{\prime \prime }-6 v^{\prime }+13 v&={\mathrm e}^{-2 u} \\ \end{align*}

29.115

23218

16114

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

29.116

23219

11341

\begin{align*} y^{\prime }-\operatorname {a3} y^{3}-\operatorname {a2} y^{2}-\operatorname {a1} y-\operatorname {a0}&=0 \\ \end{align*}

29.118

23220

15436

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

29.119

23221

13284

\begin{align*} y^{\prime }&=\sigma y^{2}+a y+b \,{\mathrm e}^{x}+c \\ \end{align*}

29.149

23222

14296

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

29.154

23223

8939

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

29.156

23224

18535

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

29.162

23225

24068

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

29.162

23226

6109

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

29.170

23227

8022

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

29.179

23228

15074

\begin{align*} x^{\prime \prime }-4 x^{\prime }+4 x&={\mathrm e}^{t}+{\mathrm e}^{2 t}+1 \\ \end{align*}

29.183

23229

12930

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

29.186

23230

18243

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

29.188

23231

12195

\begin{align*} y^{\prime }&=-\frac {-y^{3}-y+4 y^{2} \ln \left (x \right )-4 \ln \left (x \right )^{2} y^{3}-1+6 y \ln \left (x \right )-12 \ln \left (x \right )^{2} y^{2}+8 \ln \left (x \right )^{3} y^{3}}{y x} \\ \end{align*}

29.189

23232

21835

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

29.204

23233

24042

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

29.213

23234

14572

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

29.234

23235

20061

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

29.237

23236

18254

\begin{align*} y^{\prime \prime }+6 y^{\prime }+9 y&=18 \,{\mathrm e}^{-3 x}+8 \sin \left (x \right )+6 \cos \left (x \right ) \\ \end{align*}

29.243

23237

16337

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

29.251

23238

23987

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

29.254

23239

25113

\begin{align*} y^{\prime \prime }-3 y^{\prime }-10 y&=7 \,{\mathrm e}^{2 t} \\ \end{align*}

29.259

23240

17917

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

29.269

23241

17022

\begin{align*} 12 y-7 y^{\prime }+y^{\prime \prime }&=2 \\ \end{align*}

29.275

23242

15442

\begin{align*} y^{\prime \prime }-7 y^{\prime }+6 y&=\sin \left (x \right ) \\ \end{align*}

29.278

23243

14849

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

29.318

23244

9263

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

29.323

23245

21519

\begin{align*} y^{\prime \prime }+y^{\prime }-6 y&=2 x^{3}+5 x^{2}-7 x +2 \\ \end{align*}

29.329

23246

9040

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

29.336

23247

12573

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

29.347

23248

19196

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

29.355

23249

14555

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

29.362

23250

6108

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

29.369

23251

18601

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

29.370

23252

12599

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

29.375

23253

8030

\begin{align*} -12 y-2 \left (2 x +1\right ) y^{\prime }+\left (2 x +1\right )^{2} y^{\prime \prime }&=6 x \\ \end{align*}

29.395

23254

13576

\begin{align*} y y^{\prime }&=\frac {3 y}{\left (a x +b \right )^{{1}/{3}} x^{{5}/{3}}}+\frac {3}{\left (a x +b \right )^{{2}/{3}} x^{{7}/{3}}} \\ \end{align*}

29.403

23255

12426

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

29.409

23256

25559

\begin{align*} m y^{\prime \prime }+b y^{\prime }+k y&={\mathrm e}^{c t} \\ \end{align*}

29.414

23257

25564

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

29.423

23258

12206

\begin{align*} y^{\prime }&=\frac {-8 x^{2} y^{3}+16 x y^{2}+16 x y^{3}-8+12 y x -6 y^{2} x^{2}+x^{3} y^{3}}{16 \left (-2+y x -2 y\right ) x} \\ \end{align*}

29.424

23259

8002

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

29.430

23260

14119

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

29.444

23261

18245

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

29.464

23262

9998

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

29.467

23263

5792

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

29.468

23264

25598

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

29.469

23265

23479

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

29.480

23266

9153

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

29.494

23267

13905

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

29.496

23268

12540

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

29.500

23269

9256

\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*}

29.503

23270

23476

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

29.509

23271

14522

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

29.517

23272

16115

\begin{align*} y^{\prime \prime }+6 y^{\prime }+8 y&=-4 \cos \left (3 t \right ) \\ \end{align*}

29.524

23273

12544

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

29.528

23274

14324

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

29.530

23275

25112

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

29.533

23276

18158

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

29.540

23277

18828

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

29.540

23278

12478

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

29.574

23279

23457

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

29.579

23280

15067

\begin{align*} y^{\prime \prime }-6 y^{\prime }+10 y&=100 \\ y \left (0\right ) &= 10 \\ y^{\prime }\left (0\right ) &= 5 \\ \end{align*}

29.584

23281

21525

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

29.600

23282

6059

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

29.609

23283

9260

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

29.619

23284

17048

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

29.632

23285

14108

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

29.695

23286

17509

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

29.696

23287

13295

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

29.698

23288

2963

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

29.705

23289

18326

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

29.709

23290

16624

\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&=\left (-6 x -8\right ) \cos \left (2 x \right )+\left (8 x -11\right ) \sin \left (2 x \right ) \\ \end{align*}

29.721

23291

12411

\begin{align*} \left (\operatorname {a2} x +\operatorname {b2} \right ) y^{\prime \prime }+\left (\operatorname {a1} x +\operatorname {b1} \right ) y^{\prime }+\left (\operatorname {a0} x +\operatorname {b0} \right ) y&=0 \\ \end{align*}

29.723

23292

25572

\begin{align*} m y^{\prime \prime }+k y&=\cos \left (\sqrt {\frac {k}{m}}\, t \right ) \\ \end{align*}

29.723

23293

14957

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

29.746

23294

18840

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

29.755

23295

21479

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

29.756

23296

9881

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

29.766

23297

8795

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

29.785

23298

22407

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

29.793

23299

23488

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

29.802

23300

18244

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

29.807