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

22064

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

48.338

25402

26887

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

48.353

25403

8720

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

48.415

25404

5236

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

48.434

25405

7955

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

48.454

25406

21082

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

48.458

25407

22382

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

48.459

25408

13426

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

48.493

25409

18285

\begin{align*} y^{\prime \prime }+4 y^{\prime }+3 y&=8 \,{\mathrm e}^{x}+9 \\ y \left (-\infty \right ) &= 3 \\ \end{align*}

48.502

25410

24127

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

48.522

25411

25895

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

48.705

25412

13347

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

48.716

25413

21430

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

48.741

25414

13727

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

48.763

25415

24207

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

48.764

25416

11582

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

48.783

25417

27301

\begin{align*} x \left (2-9 x y^{2}\right )+y \left (4 y^{2}-6 x^{3}\right ) y^{\prime }&=0 \\ \end{align*}

48.784

25418

13950

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

48.794

25419

5015

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

48.798

25420

18611

\begin{align*} 3 y^{\prime } t +9 y&=2 t y^{{5}/{3}} \\ \end{align*}

48.817

25421

22790

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

48.842

25422

11989

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

48.864

25423

13437

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

48.875

25424

1195

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

48.908

25425

10317

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

48.952

25426

7870

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

48.954

25427

6050

\begin{align*} y \left (\operatorname {a2} +\operatorname {b2} \,x^{k}+\operatorname {c2} \,x^{2 k}+\left (-1+\operatorname {a1} +\operatorname {b1} \,x^{k}\right ) f \left (x \right )+f \left (x \right )^{2}+f^{\prime }\left (x \right )\right )+x \left (\operatorname {a1} +\operatorname {b1} \,x^{k}+2 f \left (x \right )\right ) y^{\prime }+x^{2} y^{\prime \prime }&=0 \\ \end{align*}

49.019

25428

13964

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

49.046

25429

24997

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

49.056

25430

21810

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

49.088

25431

21248

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

49.102

25432

21395

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

49.104

25433

21805

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

49.115

25434

25851

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

49.141

25435

5624

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

49.143

25436

25047

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

49.148

25437

6167

\begin{align*} -\left (4 p^{2}+1\right ) y-8 y^{\prime } x +4 \left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\ \end{align*}

49.149

25438

9346

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

49.177

25439

5014

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

49.214

25440

9149

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

49.283

25441

7886

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

49.319

25442

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*}

49.321

25443

12512

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

49.334

25444

24142

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

49.347

25445

22412

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

49.353

25446

15540

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

49.424

25447

24326

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

49.456

25448

7244

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

49.493

25449

25489

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

49.542

25450

11528

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

49.546

25451

5323

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

49.552

25452

13955

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

49.552

25453

26432

\begin{align*} y^{\prime \prime }+6 y {y^{\prime }}^{3}&=0 \\ \end{align*}

49.578

25454

22957

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

49.585

25455

25030

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

49.593

25456

24390

\begin{align*} 5 x +3 \,{\mathrm e}^{y}+2 x \,{\mathrm e}^{y} y^{\prime }&=0 \\ \end{align*}

49.594

25457

1216

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

49.617

25458

27747

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

49.620

25459

11645

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

49.641

25460

15057

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

49.730

25461

5216

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

49.738

25462

24319

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

49.741

25463

15031

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

49.753

25464

23538

\begin{align*} 5 x^{2} y^{\prime \prime }-3 y^{\prime } x +3 y&=\sqrt {x} \\ \end{align*}

49.762

25465

25046

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

49.779

25466

20394

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

49.794

25467

26294

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

49.824

25468

6441

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

49.838

25469

1664

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

49.843

25470

1238

\begin{align*} \frac {-4+6 y x +2 y^{2}}{3 x^{2}+4 y x +3 y^{2}}+y^{\prime }&=0 \\ \end{align*}

49.845

25471

8787

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

49.848

25472

25479

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

49.868

25473

27303

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

49.877

25474

6888

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

49.881

25475

26665

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

49.950

25476

26179

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

49.990

25477

27504

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

50.030

25478

9054

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

50.046

25479

26696

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

50.104

25480

8170

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

50.122

25481

9205

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

50.139

25482

26213

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

50.221

25483

13982

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

50.263

25484

19107

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

50.277

25485

13425

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

50.322

25486

18605

\begin{align*} y^{\prime }&=\frac {x +y}{x -y} \\ y \left (5\right ) &= 8 \\ \end{align*}

50.324

25487

5243

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

50.329

25488

24323

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

50.330

25489

8751

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

50.335

25490

22738

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

50.351

25491

25648

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

50.376

25492

26331

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

50.411

25493

11557

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

50.421

25494

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*}

50.463

25495

6889

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

50.471

25496

22405

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

50.488

25497

21165

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

50.490

25498

22773

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

50.507

25499

13862

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

50.541

25500

5232

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

50.549