2.3.265 Problems 26401 to 26500

Table 2.1103: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

26401

19303

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

39.875

26402

6904

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

39.883

26403

5347

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

39.959

26404

22328

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

39.967

26405

24179

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

39.986

26406

19295

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

39.999

26407

13911

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

40.000

26408

11843

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

40.004

26409

17916

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

40.005

26410

23901

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

40.078

26411

5781

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

40.085

26412

14329

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

40.150

26413

4961

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

40.164

26414

17292

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

40.165

26415

17967

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

40.166

26416

6564

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

40.191

26417

6903

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

40.250

26418

15046

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

40.259

26419

8721

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

40.325

26420

13448

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

40.376

26421

21384

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

40.387

26422

5113

\begin{align*} \left (1+x +9 y\right ) y^{\prime }+1+x +5 y&=0 \\ \end{align*}

40.445

26423

19294

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

40.450

26424

30

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

40.462

26425

4321

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

40.511

26426

12126

\begin{align*} y^{\prime }&=\frac {3 x^{3}+\sqrt {-9 x^{4}+4 y^{3}}+x^{2} \sqrt {-9 x^{4}+4 y^{3}}+x^{3} \sqrt {-9 x^{4}+4 y^{3}}}{y^{2}} \\ \end{align*}

40.640

26427

20427

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

40.855

26428

21248

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

40.904

26429

20213

\begin{align*} x^{\prime }&=n y-m z \\ y^{\prime }&=L z-m x \\ z^{\prime }&=m x-L y \\ \end{align*}

40.952

26430

4079

\begin{align*} 4 x y^{2}+6 y+\left (5 x^{2} y+8 x \right ) y^{\prime }&=0 \\ \end{align*}

41.040

26431

27239

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

41.047

26432

3323

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

41.124

26433

23295

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

41.158

26434

13412

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

41.167

26435

12249

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

41.267

26436

24043

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

41.287

26437

13257

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

41.385

26438

13502

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

41.391

26439

14478

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

41.424

26440

13981

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

41.441

26441

15555

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

41.475

26442

15522

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

41.508

26443

8696

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

41.555

26444

23871

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

41.565

26445

13410

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

41.582

26446

15142

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

41.583

26447

5085

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

41.601

26448

5985

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

41.661

26449

25839

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

41.665

26450

13393

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

41.803

26451

17065

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

41.807

26452

19113

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

41.871

26453

22524

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

41.917

26454

24176

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

42.006

26455

22420

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

42.015

26456

15258

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

42.055

26457

24317

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

42.103

26458

25728

\begin{align*} y^{\prime \prime }+9 y&=0 \\ y \left (0\right ) &= 0 \\ y \left (\pi \right ) &= 4 \\ \end{align*}

42.109

26459

13500

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

42.132

26460

6041

\begin{align*} \left (\operatorname {c2} \,x^{2}+\operatorname {b2} x +\operatorname {a2} \right ) y+x \left (\operatorname {b1} x +\operatorname {a1} \right ) y^{\prime }+x^{2} y^{\prime \prime }&=0 \\ \end{align*}

42.146

26461

1623

\begin{align*} y^{\prime }&=3 x \left (-1+y\right )^{{1}/{3}} \\ y \left (0\right ) &= 9 \\ \end{align*}

42.148

26462

21361

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

42.184

26463

13543

\begin{align*} y y^{\prime }-y&=\frac {15 x}{4}+\frac {A}{x^{7}} \\ \end{align*}

42.186

26464

5307

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

42.197

26465

18569

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

42.231

26466

12623

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

42.332

26467

13290

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

42.379

26468

5273

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

42.397

26469

8282

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

42.400

26470

14028

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

42.439

26471

14037

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

42.540

26472

2946

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

42.589

26473

5150

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

42.600

26474

24282

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

42.677

26475

13985

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

42.765

26476

8157

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

42.875

26477

20601

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

42.957

26478

10526

\begin{align*} \left (x^{8}+1\right ) y^{\prime \prime }-16 x^{7} y^{\prime }+72 x^{6} y&=0 \\ \end{align*}

42.967

26479

3303

\begin{align*} 8 x +1&=y {y^{\prime }}^{2} \\ \end{align*}

42.984

26480

11650

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

43.100

26481

22973

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

43.102

26482

4415

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

43.130

26483

11686

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

43.134

26484

7489

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

43.142

26485

23757

\begin{align*} y^{\prime \prime }+9 y&=0 \\ y \left (0\right ) &= 1 \\ y \left (\pi \right ) &= 2 \\ \end{align*}

43.242

26486

15629

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

43.302

26487

15551

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

43.339

26488

21276

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

43.345

26489

4311

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

43.392

26490

15544

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

43.434

26491

5166

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

43.512

26492

21788

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

43.527

26493

15381

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

43.544

26494

23754

\begin{align*} y^{\prime \prime }+9 y&=0 \\ y \left (0\right ) &= 1 \\ y \left (\pi \right ) &= B \\ \end{align*}

43.544

26495

25236

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

43.649

26496

12520

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

43.701

26497

13440

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

43.747

26498

13566

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

43.762

26499

72

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

43.796

26500

6895

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

43.831