2.3.245 Problems 24401 to 24500

Table 2.1021: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

24401

23877

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

23.133

24402

5149

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

23.160

24403

25213

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

23.261

24404

16265

\begin{align*} y^{\prime } x +\cos \left (x^{2}\right )&=827 y \\ \end{align*}

23.283

24405

764

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

23.292

24406

11778

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

23.342

24407

140

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

23.365

24408

15932

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

23.392

24409

6316

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

23.438

24410

17102

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

23.464

24411

12250

\begin{align*} y^{\prime }&=-\frac {216 y \left (-2 y^{4}-3 y^{3}-6 y^{2}-6 y+6 x +6\right )}{-648 x^{2} y-1296 y x +2484 y^{6}-216 x^{2} y^{4}-1296 y-1944 x y^{2}+2808 y^{4}-648 x y^{3}-18 y^{8}-648 y^{2} x^{2}+216 y^{7} x +1728 y^{3}+72 y^{8} x +216 x^{3}-1296 y^{2}+4428 y^{5}-324 x^{2} y^{3}+594 x y^{6}+1080 x y^{5}-432 y^{4} x +594 y^{7}-126 y^{10}-8 y^{12}-36 y^{11}-315 y^{9}} \\ \end{align*}

23.492

24412

5551

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

23.502

24413

21825

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

23.538

24414

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*}

23.550

24415

22025

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

23.582

24416

14003

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

23.608

24417

21560

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

23.627

24418

24866

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

23.658

24419

13453

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

23.670

24420

19745

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

23.713

24421

24302

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

23.723

24422

25443

\begin{align*} y^{\prime }-3 y&=5 \,{\mathrm e}^{2 i t} \\ \end{align*}

23.757

24423

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*}

23.769

24424

19397

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

23.794

24425

2874

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

23.800

24426

19335

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

23.807

24427

19411

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

23.863

24428

21565

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

23.924

24429

20127

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

23.947

24430

6192

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

24.008

24431

13456

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

24.010

24432

5635

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

24.022

24433

21263

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

24.089

24434

19236

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

24.105

24435

21040

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

24.148

24436

19389

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

24.172

24437

3024

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

24.173

24438

19964

\begin{align*} 3 y+2 x +4-\left (4 x +6 y+5\right ) y^{\prime }&=0 \\ \end{align*}

24.232

24439

6338

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

24.253

24440

19339

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

24.260

24441

13589

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

24.284

24442

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

24.301

24443

14063

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

24.378

24444

20427

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

24.388

24445

15834

\begin{align*} \theta ^{\prime }&=\frac {11}{10}-\frac {9 \cos \left (\theta \right )}{10} \\ \end{align*}

24.395

24446

15832

\begin{align*} \theta ^{\prime }&=\frac {9}{10}-\frac {11 \cos \left (\theta \right )}{10} \\ \end{align*}

24.396

24447

23887

\begin{align*} \frac {1-6 x^{2} y}{x}+\frac {\left (2+5 y-3 x^{2} y\right ) y^{\prime }}{y}&=0 \\ \end{align*}

24.409

24448

13557

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

24.411

24449

9159

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

24.447

24450

12863

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

24.464

24451

6441

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

24.467

24452

11512

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

24.487

24453

6802

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

24.498

24454

20237

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

24.509

24455

1686

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

24.514

24456

20823

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

24.533

24457

13905

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

24.564

24458

15170

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

24.576

24459

21821

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

24.636

24460

2923

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

24.637

24461

13542

\begin{align*} y^{\prime } y-y&=20 x +\frac {A}{\sqrt {x}} \\ \end{align*}

24.646

24462

11961

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

24.654

24463

21607

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

24.696

24464

3055

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

24.710

24465

24324

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

24.714

24466

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*}

24.731

24467

13492

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

24.749

24468

2908

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

24.761

24469

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*}

24.761

24470

6585

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

24.763

24471

21328

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

24.784

24472

19816

\begin{align*} \left (3 x +2 y-7\right ) y^{\prime }&=2 x -3 y+6 \\ \end{align*}

24.824

24473

13464

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

24.825

24474

12168

\begin{align*} y^{\prime }&=\frac {6 x^{2} y-2 x +1-5 x^{3} y^{2}-2 y x +y^{3} x^{4}}{x^{2} \left (x^{2} y-x +1\right )} \\ \end{align*}

24.835

24475

21028

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

24.842

24476

19707

\begin{align*} v^{\prime \prime }&=\left (\frac {1}{v}+{v^{\prime }}^{4}\right )^{{1}/{3}} \\ \end{align*}

24.846

24477

8360

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

24.852

24478

15131

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

24.861

24479

5415

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

24.875

24480

20316

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

24.884

24481

25444

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

24.916

24482

12568

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

25.033

24483

18499

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

25.050

24484

17972

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

25.052

24485

7408

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

25.092

24486

14450

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

25.110

24487

15631

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

25.158

24488

20960

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

25.166

24489

12264

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

25.181

24490

2903

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

25.210

24491

13465

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

25.233

24492

25044

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

25.266

24493

11982

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

25.306

24494

5003

\begin{align*} x^{7} y^{\prime }+5 x^{3} y^{2}+2 \left (x^{2}+1\right ) y^{3}&=0 \\ \end{align*}

25.318

24495

21814

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

25.327

24496

20021

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

25.339

24497

11620

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

25.359

24498

25485

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

25.374

24499

5301

\begin{align*} \left (3 x^{3}+6 x^{2} y-3 x y^{2}+20 y^{3}\right ) y^{\prime }+4 x^{3}+9 x^{2} y+6 x y^{2}-y^{3}&=0 \\ \end{align*}

25.446

24500

4321

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

25.449