2.3.234 Problems 23301 to 23400

Table 2.1011: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

23301

11656

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

15.031

23302

11543

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

15.050

23303

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*}

15.064

23304

4348

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

15.072

23305

23167

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

15.075

23306

13651

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

15.081

23307

11713

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

15.083

23308

15551

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

15.106

23309

1662

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

15.121

23310

21983

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

15.122

23311

24957

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

15.133

23312

9656

\begin{align*} x^{\prime }&=-3 x+4 y-9 z \\ y^{\prime }&=6 x-y \\ z^{\prime }&=10 x+4 y+3 z \\ \end{align*}

15.145

23313

4949

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

15.156

23314

7314

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

15.160

23315

9179

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

15.173

23316

2892

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

15.188

23317

22537

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

15.196

23318

22038

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

15.197

23319

12140

\begin{align*} y^{\prime }&=-\frac {-x -\textit {\_F1} \left (y^{2}-2 x \right )}{\sqrt {y^{2}}\, x} \\ \end{align*}

15.226

23320

1663

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

15.257

23321

4695

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

15.262

23322

14449

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

15.272

23323

4352

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

15.273

23324

5032

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

15.292

23325

3886

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

15.293

23326

7143

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

15.299

23327

2939

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

15.306

23328

21156

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

15.306

23329

12122

\begin{align*} y^{\prime }&=\frac {b \,x^{3}+c^{2} \sqrt {a}-2 c b \,x^{2} \sqrt {a}+2 c y^{2} a^{{3}/{2}}+b^{2} x^{4} \sqrt {a}-2 y^{2} a^{{3}/{2}} b \,x^{2}+a^{{5}/{2}} y^{4}}{a \,x^{2} y} \\ \end{align*}

15.312

23330

4429

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

15.322

23331

4931

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

15.345

23332

17837

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

15.358

23333

14544

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

15.361

23334

4942

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

15.365

23335

20262

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

15.367

23336

14895

\begin{align*} m v^{\prime }&=-m g +k v^{2} \\ \end{align*}

15.379

23337

12164

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

15.395

23338

7515

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

15.401

23339

11456

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

15.403

23340

4920

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

15.404

23341

21455

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

15.408

23342

12440

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

15.441

23343

17129

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

15.460

23344

4260

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

15.467

23345

15172

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

15.494

23346

4945

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

15.497

23347

21421

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

15.498

23348

5101

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

15.502

23349

23852

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

15.531

23350

740

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

15.533

23351

1685

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

15.562

23352

11361

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

15.568

23353

19770

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

15.571

23354

19411

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

15.589

23355

25693

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

15.599

23356

1654

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

15.600

23357

7874

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

15.604

23358

8836

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

15.612

23359

5685

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

15.618

23360

13808

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

15.622

23361

17295

\begin{align*} 2 t +3 y+1+\left (4 t +6 y+1\right ) y^{\prime }&=0 \\ \end{align*}

15.624

23362

18554

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

15.624

23363

16858

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

15.638

23364

19900

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

15.644

23365

4316

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

15.655

23366

11591

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

15.663

23367

25717

\begin{align*} y^{\prime }&=\sqrt {y^{2}-9} \\ y \left (2\right ) &= -3 \\ \end{align*}

15.666

23368

14246

\begin{align*} x x^{\prime }&=1-t x \\ \end{align*}

15.672

23369

11589

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

15.681

23370

14034

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

15.683

23371

4404

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

15.698

23372

24828

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

15.705

23373

3655

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

15.722

23374

12235

\begin{align*} y^{\prime }&=\frac {-150 x^{3} y+60 x^{6}+350 x^{{7}/{2}}-150 x^{3}-125 \sqrt {x}\, y+250 x -125 \sqrt {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}}}{25 \left (-5 y+2 x^{3}+10 \sqrt {x}-5\right ) x} \\ \end{align*}

15.729

23375

14447

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

15.730

23376

20284

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

15.744

23377

5213

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

15.760

23378

7846

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

15.763

23379

20251

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

15.776

23380

14887

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

15.789

23381

12473

\begin{align*} x^{2} y^{\prime \prime }+\left (a x +b \right ) y^{\prime } x +\left (\operatorname {a1} \,x^{2}+\operatorname {b1} x +\operatorname {c1} \right ) y&=0 \\ \end{align*}

15.791

23382

9206

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

15.809

23383

7147

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

15.813

23384

20788

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

15.822

23385

11510

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

15.823

23386

15784

\begin{align*} y^{\prime }&=t y^{{1}/{3}} \\ \end{align*}

15.837

23387

12056

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

15.839

23388

10408

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

15.869

23389

25503

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

15.882

23390

14517

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

15.891

23391

25746

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

15.902

23392

11573

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

15.910

23393

20502

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

15.934

23394

5016

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

15.941

23395

19936

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

15.943

23396

4905

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

15.947

23397

2504

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

15.951

23398

4906

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

15.960

23399

12085

\begin{align*} y^{\prime }&=\frac {\textit {\_F1} \left (y^{2}-2 \ln \left (x \right )\right )}{\sqrt {y^{2}}\, x} \\ \end{align*}

15.961

23400

22461

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

15.961