2.3.224 Problems 22301 to 22400

Table 2.991: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

22301

7322

\begin{align*} x^{2} y^{\prime \prime }-5 y^{\prime } x +9 y&=2 x^{3} \\ \end{align*}

10.055

22302

5861

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

10.056

22303

25887

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

10.057

22304

22952

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

10.064

22305

4818

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

10.065

22306

24397

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

10.071

22307

22319

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

10.077

22308

1645

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

10.088

22309

2869

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

10.088

22310

11623

\begin{align*} y^{m} x^{n} \left (a x y^{\prime }+b y\right )+\alpha x y^{\prime }+\beta y&=0 \\ \end{align*}

10.089

22311

5061

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

10.091

22312

17109

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

10.093

22313

19714

\begin{align*} x^{\prime }&=k \left (A -n x\right ) \left (M -m x\right ) \\ \end{align*}

10.093

22314

12234

\begin{align*} y^{\prime }&=\frac {150 x^{3}+125 \sqrt {x}+125+125 y^{2}-100 x^{3} y-500 \sqrt {x}\, y+20 x^{6}+200 x^{{7}/{2}}+500 x +125 y^{3}-150 x^{3} y^{2}-750 y^{2} \sqrt {x}+60 x^{6} y+600 y x^{{7}/{2}}+1500 y x -8 x^{9}-120 x^{{13}/{2}}-600 x^{4}-1000 x^{{3}/{2}}}{125 x} \\ \end{align*}

10.094

22315

22076

\begin{align*} y^{\prime }+\frac {2 y}{x}&=-x^{9} y^{5} \\ y \left (-1\right ) &= 2 \\ \end{align*}

10.094

22316

23957

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

10.096

22317

24249

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

10.098

22318

5707

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

10.112

22319

20258

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

10.113

22320

792

\begin{align*} y^{\prime } x&=6 y+12 x^{4} y^{{2}/{3}} \\ \end{align*}

10.115

22321

22446

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

10.115

22322

5103

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

10.119

22323

2883

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

10.122

22324

5874

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

10.124

22325

19077

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

10.132

22326

17268

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

10.139

22327

24395

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

10.140

22328

24377

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

10.146

22329

13315

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

10.151

22330

7414

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

10.154

22331

5187

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

10.155

22332

23971

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

10.164

22333

21370

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

10.169

22334

24165

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

10.185

22335

1162

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

10.186

22336

7955

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

10.191

22337

6486

\begin{align*} 3 y y^{\prime \prime }&=36 y^{2}+2 {y^{\prime }}^{2} \\ \end{align*}

10.192

22338

22448

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

10.197

22339

7256

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

10.205

22340

13394

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

10.205

22341

11725

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

10.209

22342

1725

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

10.211

22343

6914

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

10.213

22344

21358

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

10.221

22345

2982

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

10.224

22346

24211

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

10.225

22347

22518

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

10.229

22348

8231

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

10.233

22349

7416

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

10.237

22350

23166

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

10.249

22351

20232

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

10.255

22352

20760

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

10.257

22353

759

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

10.261

22354

5367

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

10.266

22355

20405

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

10.267

22356

17840

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

10.270

22357

3005

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

10.273

22358

14241

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

10.274

22359

13465

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

10.286

22360

5418

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

10.290

22361

11885

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

10.293

22362

17222

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

10.295

22363

3555

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

10.306

22364

16356

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

10.306

22365

6988

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

10.309

22366

145

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

10.313

22367

17980

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

10.314

22368

22586

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

10.316

22369

14765

\begin{align*} x^{2} y^{\prime \prime }-y^{\prime } x +8 \left (x^{2}-1\right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

10.328

22370

7160

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

10.329

22371

19712

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

10.332

22372

23245

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

10.339

22373

12987

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

10.340

22374

17910

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

10.343

22375

13640

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

10.346

22376

7464

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

10.348

22377

24341

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

10.348

22378

17075

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

10.350

22379

8874

\begin{align*} L y^{\prime }+R y&=E \,{\mathrm e}^{i \omega x} \\ y \left (0\right ) &= 0 \\ \end{align*}

10.352

22380

16218

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

10.355

22381

760

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

10.358

22382

14770

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

10.359

22383

119

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

10.362

22384

7224

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

10.363

22385

7456

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

10.379

22386

4794

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

10.382

22387

13442

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

10.384

22388

5196

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

10.387

22389

5839

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

10.387

22390

16146

\begin{align*} y^{\prime \prime }+y^{\prime }+8 y&=\left (1-\operatorname {Heaviside}\left (t -4\right )\right ) \cos \left (t -4\right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}
Using Laplace transform method.

10.388

22391

3470

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

10.391

22392

7405

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

10.396

22393

17220

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

10.402

22394

22332

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

10.408

22395

21359

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

10.409

22396

21159

\begin{align*} x^{\prime \prime }-p \left (t \right ) x&=q \left (t \right ) \\ x \left (a \right ) &= 0 \\ x \left (b \right ) &= 0 \\ \end{align*}

10.412

22397

21395

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

10.413

22398

19958

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

10.414

22399

4826

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

10.429

22400

10129

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

10.431