2.3.216 Problems 21501 to 21600

Table 2.963: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

21501

4677

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

4.540

21502

12342

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

4.540

21503

2982

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

4.542

21504

6302

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

4.543

21505

1647

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

4.544

21506

25022

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

4.545

21507

2882

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

4.547

21508

6914

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

4.548

21509

14451

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

4.548

21510

16350

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

4.548

21511

10007

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

4.549

21512

11780

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

4.549

21513

21327

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

4.549

21514

11483

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

4.551

21515

14039

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

4.551

21516

12355

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

4.552

21517

25720

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

4.552

21518

2953

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

4.553

21519

5894

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

4.554

21520

11485

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

4.556

21521

14417

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

4.559

21522

24061

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

4.559

21523

1656

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

4.563

21524

4827

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

4.563

21525

8903

\begin{align*} y^{\prime \prime }+10 y&=0 \\ y \left (0\right ) &= \pi \\ y^{\prime }\left (0\right ) &= \pi ^{2} \\ \end{align*}

4.563

21526

2947

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

4.566

21527

735

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

4.567

21528

2850

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

4.572

21529

17875

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

4.572

21530

16224

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

4.577

21531

8825

\begin{align*} \phi ^{\prime }-\frac {\phi ^{2}}{2}-\phi \cot \left (\theta \right )&=0 \\ \end{align*}

4.580

21532

11539

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

4.580

21533

2344

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

4.582

21534

2871

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

4.582

21535

3000

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

4.582

21536

4357

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

4.583

21537

13308

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

4.585

21538

7752

\begin{align*} \frac {r \tan \left (\theta \right ) r^{\prime }}{a^{2}-r^{2}}&=1 \\ r \left (\frac {\pi }{4}\right ) &= 0 \\ \end{align*}

4.586

21539

11713

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

4.587

21540

11627

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

4.589

21541

19302

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

4.591

21542

6346

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

4.592

21543

1570

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

4.594

21544

7350

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

4.594

21545

19334

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

4.595

21546

5129

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

4.596

21547

5084

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

4.598

21548

3476

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

4.599

21549

15355

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

4.601

21550

2951

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

4.602

21551

22604

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

4.605

21552

12165

\begin{align*} y^{\prime }&=-\frac {i \left (32 i x +64+64 y^{4}+32 y^{2} x^{2}+4 x^{4}+64 y^{6}+48 x^{2} y^{4}+12 x^{4} y^{2}+x^{6}\right )}{128 y} \\ \end{align*}

4.607

21553

23213

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

4.607

21554

19325

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

4.609

21555

21031

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

4.612

21556

4291

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

4.616

21557

4886

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

4.618

21558

4947

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

4.620

21559

7023

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

4.623

21560

12692

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

4.624

21561

14536

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

4.625

21562

15923

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

4.625

21563

17953

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

4.627

21564

13939

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

4.628

21565

7222

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

4.629

21566

12942

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

4.631

21567

7630

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

4.632

21568

16146

\begin{align*} y^{\prime \prime }+y^{\prime }+8 y&=\left (1-\operatorname {Heaviside}\left (t -4\right )\right ) \cos \left (t -4\right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}
Using Laplace transform method.

4.632

21569

21320

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

4.634

21570

7199

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

4.635

21571

19004

\begin{align*} x_{1}^{\prime }&=-3 x_{2}-2 x_{3}+3 x_{4}+2 x_{5} \\ x_{2}^{\prime }&=8 x_{1}+6 x_{2}+4 x_{3}-8 x_{4}-16 x_{5} \\ x_{3}^{\prime }&=-8 x_{1}-8 x_{2}-6 x_{3}+8 x_{4}-16 x_{5} \\ x_{4}^{\prime }&=8 x_{1}+7 x_{2}+4 x_{3}-9 x_{4}-16 x_{5} \\ x_{5}^{\prime }&=-3 x_{1}-5 x_{2}-3 x_{3}+5 x_{4}+7 x_{5} \\ \end{align*}

4.635

21572

11464

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

4.636

21573

19326

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

4.636

21574

11898

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

4.637

21575

2505

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

4.638

21576

8237

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

4.638

21577

4920

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

4.642

21578

11897

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

4.642

21579

14499

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

4.642

21580

19527

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

4.647

21581

3327

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

4.648

21582

22420

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

4.648

21583

3548

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

4.651

21584

11510

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

4.651

21585

17915

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

4.651

21586

23204

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

4.651

21587

3646

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

4.652

21588

17198

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

4.652

21589

8785

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

4.658

21590

2937

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

4.662

21591

210

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

4.663

21592

4963

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

4.665

21593

21342

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

4.666

21594

23181

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

4.667

21595

1691

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

4.670

21596

20000

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

4.672

21597

2970

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

4.675

21598

6349

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

4.677

21599

6918

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

4.677

21600

12349

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

4.681