2.3.206 Problems 20501 to 20600

Table 2.985: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

20501

15870

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

4.758

20502

17870

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

4.761

20503

25046

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

4.761

20504

50

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

4.763

20505

5659

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

4.763

20506

14561

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

4.766

20507

7163

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

4.767

20508

10254

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

4.767

20509

24206

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

4.769

20510

7694

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

4.770

20511

2538

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

4.772

20512

2515

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

4.773

20513

4723

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

4.773

20514

6974

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

4.774

20515

11786

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

4.774

20516

14053

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

4.775

20517

25026

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

4.775

20518

3534

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

4.777

20519

7256

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

4.779

20520

3040

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

4.780

20521

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*}

4.780

20522

5316

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

4.781

20523

26378

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

4.781

20524

9774

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

4.782

20525

14966

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

4.783

20526

21342

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

4.783

20527

22340

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

4.783

20528

21843

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

4.785

20529

21348

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

4.786

20530

24240

\begin{align*} \left (3 x -1\right ) y^{\prime }&=6 y-10 \left (3 x -1\right )^{{1}/{3}} \\ \end{align*}

4.786

20531

25465

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

4.786

20532

18540

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

4.788

20533

26324

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

4.790

20534

15021

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

4.791

20535

8391

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

4.792

20536

22539

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

4.792

20537

5291

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

4.795

20538

9814

\begin{align*} 4 x^{5} {y^{\prime }}^{2}+12 x^{4} y y^{\prime }+9&=0 \\ \end{align*}

4.796

20539

15257

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

4.796

20540

17124

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

4.796

20541

11615

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

4.797

20542

9395

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

Series expansion around \(x=0\).

4.798

20543

17247

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

4.798

20544

26299

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

4.799

20545

17119

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

4.800

20546

25024

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

4.800

20547

10375

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

4.801

20548

20230

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

4.801

20549

12084

\begin{align*} y^{\prime }&=-\frac {-\frac {1}{x}-\textit {\_F1} \left (y+\frac {1}{x}\right )}{x} \\ \end{align*}

4.803

20550

14829

\begin{align*} t x^{\prime \prime }-2 x^{\prime }+9 t^{5} x&=0 \\ \end{align*}

4.804

20551

6018

\begin{align*} \operatorname {a2} y+\operatorname {a1} x y^{\prime }+x^{2} y^{\prime \prime }&=0 \\ \end{align*}

4.806

20552

9091

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

4.806

20553

11596

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

4.806

20554

6002

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

4.807

20555

4089

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

4.809

20556

15236

\begin{align*} y^{\prime \prime }-2 y^{\prime }&=\left \{\begin {array}{cc} 4 & 0\le t <1 \\ 6 & 1\le t \end {array}\right . \\ y \left (0\right ) &= -6 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}

Using Laplace transform method.

4.811

20557

2836

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

4.812

20558

15563

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

4.813

20559

21011

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

4.813

20560

26218

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

4.813

20561

5314

\begin{align*} \left (2-10 x^{2} y^{3}+3 y^{2}\right ) y^{\prime }&=x \left (1+5 y^{4}\right ) \\ \end{align*}

4.815

20562

12141

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

4.815

20563

5633

\begin{align*} {y^{\prime }}^{3}+a_{0} {y^{\prime }}^{2}+a_{1} y^{\prime }+a_{2} +a_{3} y&=0 \\ \end{align*}

4.816

20564

12100

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

4.816

20565

1577

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

4.819

20566

19356

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

4.820

20567

19711

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

4.820

20568

14462

\begin{align*} \left ({\mathrm e}^{v}+1\right ) \cos \left (u \right )+{\mathrm e}^{v} \left (1+\sin \left (u \right )\right ) v^{\prime }&=0 \\ \end{align*}

4.823

20569

5451

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

4.824

20570

11870

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

4.825

20571

22468

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

4.826

20572

25719

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

4.826

20573

750

\begin{align*} x^{2} y^{\prime }+2 y x&=5 y^{4} \\ \end{align*}

4.829

20574

7409

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

4.829

20575

11621

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

4.829

20576

11949

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

4.830

20577

8359

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

4.831

20578

15915

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

4.832

20579

9209

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

4.835

20580

18549

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

4.836

20581

23949

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

4.836

20582

9725

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

4.837

20583

14224

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

4.839

20584

25606

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

4.839

20585

11978

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

4.840

20586

2299

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

4.841

20587

2984

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

4.842

20588

9364

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

4.842

20589

21084

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

4.842

20590

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*}

4.843

20591

20171

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

4.845

20592

15586

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

4.849

20593

25738

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

4.850

20594

20781

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

4.851

20595

8596

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

Series expansion around \(t=0\).

4.853

20596

15863

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

4.853

20597

20293

\begin{align*} \left (20 x^{2}+8 y x +4 y^{2}+3 y^{3}\right ) y+4 \left (x^{2}+y x +y^{2}+y^{3}\right ) x y^{\prime }&=0 \\ \end{align*}

4.853

20598

21170

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

4.855

20599

11435

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

4.857

20600

3602

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

4.858