2.3.226 Problems 22501 to 22600

Table 2.983: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

22501

23872

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

6.386

22502

9975

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

6.387

22503

1665

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

6.388

22504

12021

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

6.388

22505

25768

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

6.389

22506

11523

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

6.395

22507

6423

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

6.396

22508

13970

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

6.400

22509

12305

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

6.401

22510

21099

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

6.402

22511

7464

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

6.410

22512

21010

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

6.410

22513

16354

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

6.412

22514

17946

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

6.419

22515

20264

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

6.419

22516

23163

\begin{align*} y^{\prime } y-7 y&=6 x \\ \end{align*}

6.419

22517

14442

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

6.420

22518

14474

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

6.420

22519

3255

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

6.421

22520

11881

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

6.421

22521

17323

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

6.421

22522

4738

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

6.424

22523

5000

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

6.424

22524

1663

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

6.434

22525

21044

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

6.441

22526

12013

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

6.445

22527

24257

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

6.445

22528

2884

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

6.456

22529

19291

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

6.460

22530

10235

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

6.463

22531

11975

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

6.466

22532

12204

\begin{align*} y^{\prime }&=-\frac {\left (-\frac {\ln \left (y\right )^{2}}{2 x}-\textit {\_F1} \left (x \right )\right ) y}{\ln \left (y\right )} \\ \end{align*}

6.467

22533

19096

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

6.468

22534

14554

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

6.469

22535

19229

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

6.472

22536

11980

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

6.474

22537

19362

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

6.475

22538

13754

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

6.476

22539

3011

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

6.480

22540

12105

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

6.480

22541

13794

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

6.483

22542

13242

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

6.484

22543

5367

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

6.491

22544

7500

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

6.492

22545

22358

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

6.492

22546

4664

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

6.497

22547

792

\begin{align*} y^{\prime } x&=6 y+12 x^{4} y^{{2}/{3}} \\ \end{align*}

6.505

22548

11866

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

6.510

22549

6919

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

6.514

22550

4085

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

6.516

22551

10434

\begin{align*} y^{\prime \prime } x -y^{\prime }+4 x^{3} y&=8 x^{3} \sin \left (x \right )^{2} \\ \end{align*}

6.516

22552

2345

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

6.517

22553

5073

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

6.517

22554

6881

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

6.517

22555

6909

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

6.517

22556

14232

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

6.517

22557

13323

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

6.521

22558

13489

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

6.525

22559

12170

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

6.535

22560

17862

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

6.539

22561

761

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

6.542

22562

19597

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

6.543

22563

19713

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

6.546

22564

4932

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

6.551

22565

11887

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

6.554

22566

4393

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

6.555

22567

11981

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

6.556

22568

19343

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

6.556

22569

11496

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

6.565

22570

1661

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

6.572

22571

3651

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

6.577

22572

5856

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

6.579

22573

12060

\begin{align*} y^{\prime }&=\frac {-3 x^{2} y+1+x^{6} y^{2}+y^{3} x^{9}}{x^{3}} \\ \end{align*}

6.586

22574

19614

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

6.592

22575

20247

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

6.592

22576

4693

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

6.595

22577

22597

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

6.598

22578

19145

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

6.599

22579

24135

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

6.602

22580

10373

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

6.603

22581

20572

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

6.609

22582

8245

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

6.617

22583

13651

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

6.617

22584

4689

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

6.622

22585

5309

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

6.632

22586

14235

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

6.632

22587

14529

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

6.632

22588

17046

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

6.632

22589

4399

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

6.635

22590

4733

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

6.635

22591

11884

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

6.636

22592

23947

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

6.636

22593

13859

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

6.640

22594

17928

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

6.642

22595

13213

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

6.651

22596

2533

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

6.652

22597

4731

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

6.652

22598

11521

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

6.655

22599

11656

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

6.655

22600

137

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

6.661