2.3.255 Problems 25401 to 25500

Table 2.1083: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

25401

11536

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

18.565

25402

11997

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

18.568

25403

26399

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

18.586

25404

27327

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

18.607

25405

24170

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

18.622

25406

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*}

18.623

25407

14028

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

18.644

25408

5017

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

18.648

25409

5879

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

18.668

25410

11811

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

18.673

25411

11656

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

18.687

25412

12438

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

18.691

25413

6414

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

18.711

25414

23248

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

18.724

25415

4877

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

18.725

25416

12128

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

18.743

25417

1601

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

18.751

25418

6906

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

18.760

25419

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*}

18.762

25420

22554

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

18.766

25421

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*}

18.796

25422

24321

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

18.815

25423

3772

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

18.816

25424

11713

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

18.842

25425

9128

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

18.845

25426

22462

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

18.846

25427

5265

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

18.851

25428

5147

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

18.858

25429

12143

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

18.885

25430

12568

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

18.924

25431

22773

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

18.937

25432

27293

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

18.963

25433

12138

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

18.979

25434

17149

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

18.987

25435

12454

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

19.006

25436

22411

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

19.028

25437

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*}

19.032

25438

25040

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

19.075

25439

13427

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

19.083

25440

22790

\begin{align*} x^{2} y^{\prime \prime }-4 y^{\prime } x +4 y&=24 x +24 \\ \end{align*}

19.093

25441

17225

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

19.095

25442

25029

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

19.102

25443

7532

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

19.108

25444

19372

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

19.125

25445

14478

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

19.132

25446

3652

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

19.191

25447

12245

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

19.201

25448

12098

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

19.231

25449

6170

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

19.234

25450

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*}

19.244

25451

12197

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

19.261

25452

11361

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

19.283

25453

21361

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

19.296

25454

4083

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

19.306

25455

24158

\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*}

19.317

25456

6901

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

19.318

25457

3225

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

19.322

25458

19942

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

19.362

25459

5530

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

19.375

25460

16294

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

19.399

25461

15784

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

19.419

25462

13492

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

19.427

25463

27295

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

19.437

25464

15852

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

19.444

25465

4357

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

19.445

25466

27483

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

19.451

25467

13016

\begin{align*} 2 \left (y-a \right ) \left (y-b \right ) \left (y-c \right ) y^{\prime \prime }-\left (\left (y-a \right )^{2} \left (y-b \right ) \left (y-c \right )+\left (y-b \right ) \left (y-c \right )\right ) {y^{\prime }}^{2}+\left (y-a \right )^{2} \left (y-b \right )^{2} \left (y-c \right )^{2} \left (A_{0} +\frac {B_{0}}{\left (y-a \right )^{2}}+\frac {C_{1}}{\left (y-b \right )^{2}}+\frac {D_{0}}{\left (y-c \right )^{2}}\right )&=0 \\ \end{align*}

19.464

25468

13466

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

19.492

25469

14475

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

19.514

25470

19144

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

19.519

25471

11969

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

19.528

25472

3655

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

19.530

25473

11623

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

19.533

25474

11519

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

19.539

25475

4319

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

19.542

25476

6573

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

19.552

25477

2946

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

19.554

25478

15555

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

19.556

25479

19954

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

19.566

25480

3777

\begin{align*} x^{2} y^{\prime \prime }+6 y^{\prime } x +6 y&=4 \,{\mathrm e}^{2 x} \\ \end{align*}

19.580

25481

6918

\begin{align*} 3 x -2 y+4-\left (2 x +7 y-1\right ) y^{\prime }&=0 \\ \end{align*}

19.582

25482

7714

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

19.606

25483

5264

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

19.612

25484

24152

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

19.628

25485

12439

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

19.634

25486

5179

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

19.641

25487

13875

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

19.677

25488

23187

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

19.686

25489

27476

\begin{align*} 2 x^{2} y+2 \sqrt {1+y^{2} x^{4}}+x^{3} y^{\prime }&=0 \\ \end{align*}

19.690

25490

7876

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

19.704

25491

18733

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

19.705

25492

5148

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

19.709

25493

8752

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

19.714

25494

7873

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

19.717

25495

15940

\begin{align*} y^{\prime }&=-\sin \left (y\right )^{5} \\ \end{align*}

19.719

25496

17198

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

19.727

25497

7870

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

19.738

25498

23354

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

19.753

25499

3278

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

19.761

25500

12390

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

19.780