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

18500

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

3.966

20502

25841

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

3.966

20503

4946

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

3.967

20504

8410

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

3.967

20505

20201

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

3.968

20506

18011

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

3.969

20507

17210

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

3.970

20508

20957

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

3.970

20509

19726

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

3.971

20510

20820

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

3.971

20511

21975

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

3.971

20512

6431

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

3.973

20513

23850

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

3.973

20514

687

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

3.974

20515

12354

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

3.974

20516

26475

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

3.974

20517

26614

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

3.974

20518

6838

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

3.976

20519

15789

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

3.977

20520

2992

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

3.978

20521

4027

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

Series expansion around \(x=0\).

3.978

20522

4994

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

3.978

20523

19989

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

3.981

20524

8903

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

3.983

20525

15342

\begin{align*} 1+s^{2}-\sqrt {t}\, s^{\prime }&=0 \\ \end{align*}

3.983

20526

12148

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

3.985

20527

12091

\begin{align*} y^{\prime }&=\frac {-125+300 x -240 x^{2}+64 x^{3}-80 y^{2}+64 x y^{2}+64 y^{3}}{\left (4 x -5\right )^{3}} \\ \end{align*}

3.986

20528

4048

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

Series expansion around \(x=0\).

3.989

20529

8997

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

Series expansion around \(x=0\).

3.990

20530

9342

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

3.991

20531

9365

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

3.991

20532

20269

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

3.991

20533

5431

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

3.992

20534

21377

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

3.992

20535

27471

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

3.992

20536

16213

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

3.993

20537

22954

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

3.994

20538

17042

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

3.996

20539

26035

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

Series expansion around \(x=0\).

3.996

20540

27372

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

3.996

20541

9924

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

Series expansion around \(x=0\).

3.997

20542

19963

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

3.997

20543

4038

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

Series expansion around \(x=0\).

3.998

20544

15953

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

3.998

20545

8292

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

3.999

20546

7007

\begin{align*} y^{\prime }+8 x^{3} y^{3}+2 y x&=0 \\ \end{align*}

4.000

20547

8061

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

4.001

20548

19162

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

4.001

20549

19919

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

4.001

20550

8233

\begin{align*} y^{\prime }&=\sqrt {y^{2}-9} \\ y \left (5\right ) &= 3 \\ \end{align*}

4.003

20551

9936

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

Series expansion around \(x=0\).

4.003

20552

11431

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

4.003

20553

673

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

4.004

20554

24111

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

Series expansion around \(x=0\).

4.004

20555

5751

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

4.006

20556

7753

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

4.006

20557

7878

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

4.006

20558

16223

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

4.006

20559

15397

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

4.007

20560

21089

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

4.007

20561

750

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

4.009

20562

12176

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

4.010

20563

19890

\begin{align*} z^{\prime }+7 y-9 z&={\mathrm e}^{x} \\ y^{\prime }-y-3 z&={\mathrm e}^{2 x} \\ \end{align*}

4.010

20564

3561

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

4.011

20565

7149

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

4.013

20566

16592

\begin{align*} x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y&=10 x +12 \\ y \left (1\right ) &= 6 \\ y^{\prime }\left (1\right ) &= 8 \\ \end{align*}

4.013

20567

18791

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

4.013

20568

23855

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

4.013

20569

15365

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

4.015

20570

4916

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

4.017

20571

5026

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

4.018

20572

7960

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

4.018

20573

8180

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

4.018

20574

17473

\begin{align*} y^{\prime }-4 y&=t^{2} \\ \end{align*}

4.019

20575

4439

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

4.021

20576

19409

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

4.021

20577

27563

\begin{align*} 5 {y^{\prime \prime \prime }}^{2}-3 y^{\prime \prime } y^{\prime \prime \prime \prime }&=0 \\ \end{align*}

4.024

20578

17640

\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +36 y&=x^{2} \\ \end{align*}

4.026

20579

26895

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

4.026

20580

14447

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

4.027

20581

16697

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

4.028

20582

3015

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

4.029

20583

23159

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

4.029

20584

20027

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

4.030

20585

8885

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

4.031

20586

19808

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

4.031

20587

15925

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

4.032

20588

15346

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

4.035

20589

27265

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

4.035

20590

23942

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

4.037

20591

23953

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

4.037

20592

24397

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

4.037

20593

15917

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

4.038

20594

17779

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

4.042

20595

19387

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

4.042

20596

62

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

4.043

20597

8356

\begin{align*} y^{\prime }&=\frac {y x +3 x -y-3}{y x -2 x +4 y-8} \\ \end{align*}

4.043

20598

11637

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

4.044

20599

9928

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

Series expansion around \(x=0\).

4.045

20600

14473

\begin{align*} \left (3 x +8\right ) \left (4+y^{2}\right )-4 y \left (x^{2}+5 x +6\right ) y^{\prime }&=0 \\ y \left (1\right ) &= 2 \\ \end{align*}

4.046