2.3.117 Problems 11601 to 11700

Table 2.807: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

11601

16386

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

0.926

11602

17682

\begin{align*} \left (x^{2}-4\right ) y^{\prime \prime }+16 \left (x +2\right ) y^{\prime }-y&=0 \\ \end{align*}

Series expansion around \(x=1\).

0.926

11603

18225

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

0.926

11604

25986

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

0.926

11605

2397

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

0.927

11606

2660

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

Series expansion around \(t=0\).

0.927

11607

8536

\begin{align*} 4 x^{2} y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}-25\right ) y&=0 \\ \end{align*}

Series expansion around \(x=0\).

0.927

11608

11745

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

0.927

11609

12990

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

0.927

11610

20652

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

0.927

11611

22279

\begin{align*} x_{1}^{\prime }&=x_{2} \\ x_{2}^{\prime }&=x_{3} \\ x_{3}^{\prime }&=6 t \\ \end{align*}

With initial conditions

\begin{align*} x_{1} \left (0\right ) &= 0 \\ x_{2} \left (0\right ) &= 0 \\ x_{3} \left (0\right ) &= 12 \\ \end{align*}

0.927

11612

24850

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

0.927

11613

1965

\begin{align*} 6 x^{2} y^{\prime \prime }+x \left (10-x \right ) y^{\prime }-\left (x +2\right ) y&=0 \\ \end{align*}

Series expansion around \(x=0\).

0.928

11614

2105

\begin{align*} 4 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+4 x \left (x^{2}+2\right ) y^{\prime }-\left (x^{2}+15\right ) y&=0 \\ \end{align*}

Series expansion around \(x=0\).

0.928

11615

2451

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

Series expansion around \(t=0\).

0.928

11616

8587

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

Series expansion around \(x=0\).

0.928

11617

20455

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

0.928

11618

21921

\begin{align*} 4 y+y^{\prime \prime }&=x \sin \left (x \right ) \\ y \left (0\right ) &= {\frac {7}{9}} \\ y \left (\frac {\pi }{2}\right ) &= \frac {\pi }{6}-1 \\ \end{align*}

0.928

11619

22884

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

0.928

11620

23687

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

Series expansion around \(x=-3\).

0.928

11621

24066

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

0.928

11622

27579

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

0.928

11623

989

\begin{align*} x_{1}^{\prime }&=5 x_{1}+5 x_{2}+2 x_{3} \\ x_{2}^{\prime }&=-6 x_{1}-6 x_{2}-5 x_{3} \\ x_{3}^{\prime }&=6 x_{1}+6 x_{2}+5 x_{3} \\ \end{align*}

0.929

11624

14803

\(\left [\begin {array}{ccc} 1 & -1 & -1 \\ 1 & 3 & 1 \\ -3 & 1 & -1 \end {array}\right ]\)

N/A

N/A

N/A

0.929

11625

18750

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

0.929

11626

25353

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

Series expansion around \(t=0\).

0.929

11627

25596

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

0.929

11628

8820

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

0.930

11629

12457

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

0.930

11630

2806

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

0.931

11631

6523

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

0.931

11632

7301

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

0.931

11633

7789

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

0.931

11634

10267

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

0.931

11635

10307

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

0.931

11636

14540

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

0.931

11637

16674

\begin{align*} y^{\prime \prime }-6 y^{\prime }+9 y&=27 \,{\mathrm e}^{6 x}+25 \sin \left (6 x \right ) \\ \end{align*}

0.931

11638

22169

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

0.931

11639

23098

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

0.931

11640

24814

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

0.931

11641

1852

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

Series expansion around \(x=0\).

0.932

11642

18263

\begin{align*} y^{\prime \prime }-6 y^{\prime }+9 y&=9 x^{2}-12 x +2 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 3 \\ \end{align*}

0.932

11643

19505

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

0.932

11644

27163

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

0.932

11645

820

\begin{align*} x^{2} y^{\prime \prime }+2 x y^{\prime }-6 y&=0 \\ y \left (2\right ) &= 10 \\ y^{\prime }\left (2\right ) &= 15 \\ \end{align*}

0.933

11646

3903

\begin{align*} x_{1}^{\prime }&=2 x_{1}-4 x_{2}+3 x_{3} \\ x_{2}^{\prime }&=-9 x_{1}-3 x_{2}-9 x_{3} \\ x_{3}^{\prime }&=4 x_{1}+4 x_{2}+3 x_{3} \\ \end{align*}

0.933

11647

8605

\begin{align*} 9 x^{2} y^{\prime \prime }+9 x y^{\prime }+\left (36 x^{4}-16\right ) y&=0 \\ \end{align*}

Series expansion around \(x=0\).

0.933

11648

10093

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

0.933

11649

14821

\begin{align*} y^{\prime \prime \prime }-5 y^{\prime \prime }+7 y^{\prime }-3 y&=20 \sin \left (t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime \prime }\left (0\right ) &= -2 \\ \end{align*}

Using Laplace transform method.

0.933

11650

20551

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

0.933

11651

23401

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

0.933

11652

27341

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

0.933

11653

27699

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

0.933

11654

2653

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

Series expansion around \(t=0\).

0.934

11655

3358

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

Series expansion around \(x=0\).

0.934

11656

3590

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

0.934

11657

5518

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

0.934

11658

7445

\begin{align*} u^{\prime }&=\alpha \left (1-u\right )-\beta u \\ \end{align*}

0.934

11659

13000

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

0.934

11660

19159

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

0.934

11661

20536

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

0.934

11662

2248

\begin{align*} y_{1}^{\prime }&=y_{1}-y_{2}+2 y_{3} \\ y_{2}^{\prime }&=12 y_{1}-4 y_{2}+10 y_{3} \\ y_{3}^{\prime }&=-6 y_{1}+y_{2}-7 y_{3} \\ \end{align*}

0.935

11663

2646

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

Series expansion around \(t=0\).

0.935

11664

7947

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

0.935

11665

8063

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

0.935

11666

8555

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

Series expansion around \(x=0\).

0.935

11667

22780

\begin{align*} i^{\prime \prime }+2 i^{\prime }+5 i&=34 \cos \left (2 t \right ) \\ \end{align*}

0.935

11668

3746

\begin{align*} y^{\prime \prime }+9 y&=18 \sec \left (3 x \right )^{3} \\ \end{align*}

0.936

11669

6707

\begin{align*} -\left (-a \,x^{3}+12\right ) y+6 x^{2} y^{\prime \prime }+x^{3} y^{\prime \prime \prime }&=0 \\ \end{align*}

0.936

11670

9380

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

Series expansion around \(x=0\).

0.936

11671

22829

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

Series expansion around \(x=0\).

0.936

11672

23467

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

0.936

11673

26027

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

Series expansion around \(x=0\).

0.936

11674

3362

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

Series expansion around \(x=0\).

0.937

11675

5523

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

0.937

11676

8518

\begin{align*} x^{2} y^{\prime \prime }-\left (x -\frac {2}{9}\right ) y&=0 \\ \end{align*}

Series expansion around \(x=0\).

0.937

11677

8943

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

0.937

11678

13163

\(\left [\begin {array}{cccc} 4 & 0 & 0 & -3 \\ 0 & 2 & 0 & 0 \\ 0 & 0 & -1 & 0 \\ 6 & 0 & 0 & -5 \end {array}\right ]\)

N/A

N/A

N/A

0.937

11679

16229

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

0.937

11680

18678

\begin{align*} x^{\prime }&=\frac {5 x}{4}+\frac {3 y}{4} \\ y^{\prime }&=a x+\frac {5 y}{4} \\ \end{align*}

0.937

11681

21694

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

Series expansion around \(x=0\).

0.937

11682

22275

\begin{align*} x_{1}^{\prime }&=x_{2} \\ x_{2}^{\prime }&=6 x_{1}+4 \\ \end{align*}

With initial conditions

\begin{align*} x_{1} \left (1\right ) &= 0 \\ x_{2} \left (1\right ) &= 0 \\ \end{align*}

0.937

11683

24786

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

0.937

11684

26021

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

Series expansion around \(x=0\).

0.937

11685

1961

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

Series expansion around \(x=0\).

0.938

11686

3583

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

0.938

11687

3732

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

0.938

11688

8607

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

Series expansion around \(x=0\).

0.938

11689

10396

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

0.938

11690

12361

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

0.938

11691

15085

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

0.938

11692

16810

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

Using Laplace transform method.

0.938

11693

19604

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

Series expansion around \(x=0\).

0.938

11694

20623

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

0.938

11695

7316

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

0.939

11696

14649

\begin{align*} y^{\prime \prime }-10 y^{\prime }+29 y&=8 \,{\mathrm e}^{5 x} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 8 \\ \end{align*}

0.939

11697

16696

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

0.939

11698

27486

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

0.939

11699

6879

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

0.940

11700

8608

\begin{align*} x y^{\prime \prime }+y^{\prime }+36 y&=0 \\ \end{align*}

Series expansion around \(x=0\).

0.940