2.3.254 Problems 25301 to 25400

Table 2.1081: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

25301

21307

\begin{align*} x_{1}^{\prime }&=x_{2} \\ x_{2}^{\prime }&=x_{3} \\ x_{3}^{\prime }&=-a x_{3}-b x_{2}-c x_{1} \\ \end{align*}

20.982

25302

18610

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

21.014

25303

21840

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

21.015

25304

10528

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

21.021

25305

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*}

21.038

25306

20984

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

21.053

25307

25744

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

21.074

25308

11361

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

21.086

25309

3031

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

21.096

25310

11935

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

21.138

25311

12245

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

21.140

25312

9018

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

21.145

25313

11794

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

21.191

25314

6423

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

21.204

25315

17023

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

21.208

25316

23843

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

21.217

25317

6845

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

21.222

25318

20834

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

21.276

25319

15648

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

21.301

25320

25508

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

21.307

25321

27520

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

21.314

25322

17922

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

21.321

25323

7519

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

21.344

25324

20221

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

21.372

25325

5685

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

21.381

25326

1687

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

21.383

25327

15289

\begin{align*} x^{\prime }&=7 x-4 y+10 \,{\mathrm e}^{t} \\ y^{\prime }&=3 x+14 y+6 \,{\mathrm e}^{2 t} \\ \end{align*}

With initial conditions

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

21.385

25328

15155

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

21.411

25329

2771

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

21.421

25330

25210

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

21.434

25331

21067

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

21.436

25332

15536

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

21.445

25333

23215

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

21.463

25334

21420

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

21.466

25335

22424

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

21.475

25336

14079

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

21.478

25337

2770

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

21.481

25338

11490

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

21.487

25339

4745

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

21.488

25340

20127

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

21.541

25341

25897

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

21.544

25342

1615

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

21.569

25343

13475

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

21.584

25344

11848

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

21.585

25345

5059

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

21.594

25346

4853

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

21.595

25347

6981

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

21.606

25348

164

\begin{align*} y^{\prime }&=\frac {2 y-x +7}{4 x -3 y-18} \\ \end{align*}

21.608

25349

22015

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

21.612

25350

6353

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

21.628

25351

15355

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

21.640

25352

4362

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

21.688

25353

1668

\begin{align*} y^{\prime }&=\frac {-x +3 y-14}{x +y-2} \\ \end{align*}

21.691

25354

17211

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

21.697

25355

10316

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

21.702

25356

11413

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

21.751

25357

17269

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

21.751

25358

21850

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

21.754

25359

13645

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

21.765

25360

22010

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

21.774

25361

22431

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

21.781

25362

20219

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

21.783

25363

20255

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

21.786

25364

2685

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

Using Laplace transform method.

21.807

25365

4710

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

21.820

25366

26869

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

21.828

25367

2876

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

21.832

25368

20950

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

21.832

25369

5125

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

21.833

25370

22461

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

21.836

25371

5261

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

21.852

25372

6995

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

21.859

25373

24169

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

21.861

25374

5255

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

21.872

25375

7385

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

21.899

25376

20449

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

21.902

25377

18559

\begin{align*} y^{\prime }&=-\frac {4 t}{y} \\ y \left (0\right ) &= y_{0} \\ \end{align*}

21.904

25378

21927

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

21.909

25379

25881

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

21.928

25380

4682

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

21.935

25381

4419

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

21.946

25382

11536

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

21.955

25383

5160

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

21.964

25384

19372

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

21.967

25385

17224

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

21.994

25386

11520

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

22.015

25387

25006

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

22.048

25388

11823

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

22.052

25389

13473

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

22.111

25390

17891

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

22.116

25391

5527

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

22.135

25392

8732

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

22.151

25393

11905

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

22.167

25394

17345

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

22.181

25395

7498

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

22.227

25396

25752

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

22.228

25397

4440

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

22.239

25398

2506

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

22.276

25399

14021

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

22.279

25400

11502

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

22.286