2.3.243 Problems 24201 to 24300

Table 2.1017: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

24201

11973

\begin{align*} y^{\prime }&=\frac {-x^{2}+1+4 x^{3} \sqrt {x^{2}-2 x +1+8 y}}{4 x +4} \\ \end{align*}

18.375

24202

21440

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

18.382

24203

19109

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

18.423

24204

23893

\begin{align*} 20 y-20 x y^{2}+\left (5 x -8 x^{2} y\right ) y^{\prime }&=0 \\ \end{align*}

18.464

24205

5273

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

18.486

24206

13430

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

18.486

24207

17976

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

18.510

24208

23224

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

18.582

24209

19670

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

18.639

24210

11789

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

18.641

24211

4810

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

18.663

24212

21345

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

18.682

24213

11959

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

18.685

24214

13982

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

18.698

24215

15645

\begin{align*} y^{\prime }&=x \sqrt {1-y^{2}} \\ y \left (0\right ) &= {\frac {9}{10}} \\ \end{align*}

18.702

24216

14555

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

18.713

24217

13828

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

18.734

24218

12273

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

18.736

24219

24179

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

18.740

24220

7724

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

18.804

24221

12074

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

18.805

24222

21358

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

18.820

24223

7498

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

18.833

24224

11544

\begin{align*} \left (3 x +2\right ) \left (y-2 x -1\right ) y^{\prime }-y^{2}+y x -7 x^{2}-9 x -3&=0 \\ \end{align*}

18.833

24225

14915

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

18.859

24226

13563

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

18.863

24227

20394

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

18.877

24228

4811

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

18.906

24229

12226

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

18.913

24230

13257

\begin{align*} x^{2} y^{\prime }&=\left (\alpha \,x^{2 n}+\beta \,x^{n}+\gamma \right ) y^{2}+\left (a \,x^{n}+b \right ) x y+c \,x^{2} \\ \end{align*}

18.927

24231

12193

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

18.944

24232

7517

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

18.958

24233

11994

\begin{align*} y^{\prime }&=\frac {x^{2}+2 x +1+2 x^{3} \sqrt {x^{2}+2 x +1-4 y}}{2 x +2} \\ \end{align*}

18.967

24234

21066

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

19.030

24235

18051

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

19.040

24236

24394

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

19.047

24237

24152

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

19.068

24238

20977

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

19.078

24239

13577

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

19.083

24240

24364

\begin{align*} x +y-4-\left (3 x -y-4\right ) y^{\prime }&=0 \\ y \left (3\right ) &= 7 \\ \end{align*}

19.108

24241

12196

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

19.126

24242

24407

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

19.141

24243

12064

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

19.163

24244

8824

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

19.196

24245

11519

\begin{align*} \left (2 y+x +7\right ) y^{\prime }-y+2 x +4&=0 \\ \end{align*}

19.197

24246

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*}

19.242

24247

19369

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

19.247

24248

21873

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

19.283

24249

24336

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

19.288

24250

5951

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

19.291

24251

12233

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

19.293

24252

13769

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

19.309

24253

24355

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

19.360

24254

11977

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

19.388

24255

24381

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

19.398

24256

6296

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

19.406

24257

16858

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

19.421

24258

12212

\begin{align*} y^{\prime }&=\frac {\left (27 y^{3}+27 \,{\mathrm e}^{3 x^{2}} y+18 \,{\mathrm e}^{3 x^{2}} y^{2}+3 y^{3} {\mathrm e}^{3 x^{2}}+27 \,{\mathrm e}^{\frac {9 x^{2}}{2}}+27 \,{\mathrm e}^{\frac {9 x^{2}}{2}} y+9 \,{\mathrm e}^{\frac {9 x^{2}}{2}} y^{2}+{\mathrm e}^{\frac {9 x^{2}}{2}} y^{3}\right ) {\mathrm e}^{3 x^{2}} x \,{\mathrm e}^{-\frac {9 x^{2}}{2}}}{243 y} \\ \end{align*}

19.479

24259

17841

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

19.487

24260

13345

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

19.509

24261

5340

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

19.522

24262

5706

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

19.543

24263

11701

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

19.590

24264

6920

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

19.592

24265

24178

\begin{align*} y \left (9 x -2 y\right )-x \left (6 x -y\right ) y^{\prime }&=0 \\ y \left (1\right ) &= 1 \\ \end{align*}

19.645

24266

6900

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

19.661

24267

19966

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

19.698

24268

2535

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

19.727

24269

21076

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

19.754

24270

11468

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

19.764

24271

21055

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

19.829

24272

4891

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

19.966

24273

21428

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

19.972

24274

6092

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

19.978

24275

12012

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

20.019

24276

5109

\begin{align*} \left (x +4 x^{3}+5 y\right ) y^{\prime }+7 x^{3}+3 x^{2} y+4 y&=0 \\ \end{align*}

20.063

24277

5060

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

20.078

24278

6073

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

20.084

24279

23875

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

20.098

24280

21421

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

20.110

24281

4112

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

20.131

24282

7895

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

20.138

24283

5062

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

20.139

24284

6366

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

20.201

24285

21829

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

20.203

24286

19374

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

20.256

24287

14866

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

20.315

24288

24409

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

20.315

24289

5457

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

20.323

24290

15042

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

20.332

24291

11625

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

20.385

24292

13367

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

20.423

24293

19383

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

20.469

24294

13565

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

20.477

24295

5063

\begin{align*} \left (3-x +y\right ) y^{\prime }&=11-4 x +3 y \\ \end{align*}

20.486

24296

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*}

20.500

24297

5249

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

20.525

24298

13418

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

20.542

24299

17267

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

20.555

24300

7029

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

20.595