2.3.254 Problems 25301 to 25400

Table 2.1051: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

25301

24272

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

58.550

25302

6315

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

58.612

25303

11660

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

58.763

25304

20480

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

58.789

25305

2820

\begin{align*} z^{\prime \prime }+z+z^{5}&=0 \\ \end{align*}

58.867

25306

4774

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

58.944

25307

21326

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

59.008

25308

4810

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

59.181

25309

2874

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

59.191

25310

13501

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

59.261

25311

12017

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

59.329

25312

5015

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

59.549

25313

6560

\begin{align*} \left (\left (-y+a \right ) \left (-y+b \right )+\left (-y+a \right ) \left (c -y\right )+\left (-y+b \right ) \left (c -y\right )\right ) {y^{\prime }}^{2}+2 \left (-y+a \right ) \left (-y+b \right ) \left (c -y\right ) y^{\prime \prime }&=\operatorname {a3} \left (-y+a \right )^{2} \left (-y+b \right )^{2}+2 \operatorname {a2} \left (-y+a \right )^{2} \left (c -y\right )^{2}+\operatorname {a1} \left (-y+b \right )^{2} \left (c -y\right )^{2}+\operatorname {a0} \left (-y+a \right )^{2} \left (-y+b \right )^{2} \left (c -y\right )^{2} \\ \end{align*}

59.551

25314

21076

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

59.565

25315

17903

\begin{align*} x^{2} y^{\prime }+\cos \left (2 y\right )&=1 \\ y \left (\infty \right ) &= \frac {10 \pi }{3} \\ \end{align*}

59.645

25316

11793

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

59.683

25317

12503

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

59.760

25318

21106

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

59.761

25319

12870

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

59.927

25320

11961

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

59.947

25321

4961

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

59.966

25322

15357

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

60.000

25323

15153

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

60.009

25324

21283

\begin{align*} x^{\prime \prime }-4 x^{\prime }+3 x&=1 \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*}
Using Laplace transform method.

60.037

25325

14247

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

60.183

25326

23212

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

60.202

25327

20256

\begin{align*} \left (6 x -5 y+4\right ) y^{\prime }+y-2 x -1&=0 \\ \end{align*}

60.400

25328

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*}

60.422

25329

13215

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

60.469

25330

22773

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

60.492

25331

17010

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

60.570

25332

14006

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

60.584

25333

13268

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

60.641

25334

20457

\begin{align*} \left (8 {y^{\prime }}^{3}-27\right ) x&=\frac {12 {y^{\prime }}^{2}}{x} \\ \end{align*}

60.705

25335

21385

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

60.755

25336

784

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

60.769

25337

11732

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

60.800

25338

25214

\begin{align*} y^{\prime \prime }+\sqrt {t}\, y^{\prime }-\sqrt {t -3}\, y&=0 \\ y \left (10\right ) &= y_{1} \\ y^{\prime }\left (10\right ) &= y_{1} \\ \end{align*}

60.806

25339

14532

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

60.908

25340

13446

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

60.912

25341

25185

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

61.001

25342

13375

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

61.048

25343

13985

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

61.079

25344

23220

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

61.118

25345

21368

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

61.334

25346

5181

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

61.339

25347

24348

\begin{align*} x -4 y-3-\left (x -6 y-5\right ) y^{\prime }&=0 \\ \end{align*}

61.383

25348

7547

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

61.469

25349

12533

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

61.493

25350

13559

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

61.518

25351

23216

\begin{align*} y^{\prime }&=\frac {3 x -2 y+7}{2 x +3 y+9} \\ \end{align*}

61.604

25352

14550

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

61.704

25353

5986

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

61.727

25354

12094

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

61.729

25355

23461

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

61.847

25356

2903

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

61.912

25357

6105

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

62.126

25358

12067

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

62.281

25359

13307

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

62.332

25360

17277

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

62.357

25361

22013

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

62.363

25362

24302

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

62.411

25363

11681

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

62.437

25364

15976

\begin{align*} p^{\prime }&=3 p-2 q-7 r \\ q^{\prime }&=-2 p+6 r \\ r^{\prime }&=\frac {73 q}{100}+2 r \\ \end{align*}

62.449

25365

22602

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

62.558

25366

12107

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

62.565

25367

26087

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

62.566

25368

12113

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

62.578

25369

7489

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

62.723

25370

21327

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

62.753

25371

4707

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

62.776

25372

19074

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

62.776

25373

5695

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

62.823

25374

19739

\begin{align*} \phi ^{\prime \prime }&=\frac {4 \pi n c}{\sqrt {v_{0}^{2}+\frac {2 e \left (\phi -V_{0} \right )}{m}}} \\ \end{align*}

62.836

25375

11931

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

62.850

25376

16198

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

62.884

25377

19819

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

62.944

25378

13476

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

63.020

25379

5193

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

63.021

25380

13421

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

63.037

25381

22077

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

63.063

25382

19122

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

63.079

25383

10410

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

63.111

25384

12597

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

63.130

25385

7125

\begin{align*} r^{\prime \prime }&=-\frac {k}{r^{2}} \\ \end{align*}

63.222

25386

13434

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

63.243

25387

25648

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

63.310

25388

17967

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

63.337

25389

13030

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

63.348

25390

13431

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

63.381

25391

22532

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

63.412

25392

14834

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

63.505

25393

19048

\begin{align*} x_{1}^{\prime }&=2 x_{1}+x_{2}+1 \\ x_{2}^{\prime }&=x_{1}-2 x_{2}+x_{3} \\ x_{3}^{\prime }&=x_{2}-x_{3} \\ \end{align*}
With initial conditions
\begin{align*} x_{1} \left (0\right ) &= 0 \\ x_{2} \left (0\right ) &= 0 \\ x_{3} \left (0\right ) &= 0 \\ \end{align*}

63.587

25394

17250

\begin{align*} 2 t +\frac {19 y}{10}+\left (\frac {19 t}{10}+2 y\right ) y^{\prime }&=0 \\ \end{align*}

63.632

25395

11815

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

63.808

25396

19870

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

63.848

25397

24321

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

63.945

25398

4876

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

63.951

25399

25653

\begin{align*} R^{\prime \prime }&=-\frac {k}{R^{2}} \\ \end{align*}

63.974

25400

6192

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

64.072