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

5906

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

1.779

11602

5961

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

1.779

11603

7123

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

1.779

11604

10490

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

1.779

11605

14291

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

1.779

11606

23090

\begin{align*} 16 y+8 y^{\prime }+y^{\prime \prime }&=x \left (12-{\mathrm e}^{-4 x}\right ) \\ \end{align*}

1.779

11607

27698

\begin{align*} x^{2} y^{\prime \prime }-6 y&=5 x^{3}+8 x^{2} \\ \end{align*}

1.779

11608

2634

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

1.780

11609

5855

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

1.780

11610

8006

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

1.780

11611

8478

\begin{align*} \left (x^{2}-2 x +10\right ) y^{\prime \prime }+y^{\prime } x -4 y&=0 \\ \end{align*}

Series expansion around \(x=0\).

1.780

11612

10153

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

1.780

11613

10413

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

1.780

11614

27785

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

Series expansion around \(x=1\).

1.780

11615

14752

\begin{align*} x^{2} y^{\prime \prime }-y^{\prime } x +\left (2 x^{2}+\frac {5}{9}\right ) y&=0 \\ \end{align*}

Series expansion around \(x=0\).

1.781

11616

15890

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

1.782

11617

20236

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

1.782

11618

22722

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

1.782

11619

25625

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

1.782

11620

16089

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

1.783

11621

22728

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

1.783

11622

3131

\begin{align*} y^{\prime \prime }+9 y&=\left (1+\sin \left (3 x \right )\right ) \cos \left (2 x \right ) \\ \end{align*}

1.784

11623

14751

\begin{align*} x^{2} y^{\prime \prime }-y^{\prime } x +\left (x^{2}+\frac {8}{9}\right ) y&=0 \\ \end{align*}

Series expansion around \(x=0\).

1.785

11624

2062

\begin{align*} 2 x^{2} \left (2+x \right ) y^{\prime \prime }-x \left (4-7 x \right ) y^{\prime }-\left (5-3 x \right ) y&=0 \\ \end{align*}

Series expansion around \(x=0\).

1.786

11625

11757

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

1.786

11626

23442

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

Series expansion around \(x=0\).

1.786

11627

23995

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

1.786

11628

26643

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

1.786

11629

27113

\(\left [\begin {array}{cc} -5 & 3 \\ 0 & 9 \end {array}\right ]\)

N/A

N/A

N/A

1.786

11630

20852

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

1.787

11631

24536

\begin{align*} y^{\prime \prime }-6 y^{\prime }+9 y&={\mathrm e}^{x} \\ \end{align*}

1.787

11632

12664

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

1.788

11633

17672

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

1.788

11634

25965

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

1.788

11635

5983

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

1.789

11636

8074

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

Series expansion around \(x=0\).

1.789

11637

18449

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

1.789

11638

22814

\begin{align*} y^{\prime \prime \prime }+3 y^{\prime \prime }+3 y^{\prime }+y&=12 \,{\mathrm e}^{-t} \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime \prime }\left (0\right ) &= -3 \\ \end{align*}

Using Laplace transform method.

1.789

11639

8846

\begin{align*} x_{1}^{\prime }&=-2 x_{1}+x_{2}+2 \,{\mathrm e}^{-t} \\ x_{2}^{\prime }&=x_{1}-2 x_{2}+3 t \\ \end{align*}

1.790

11640

26355

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

1.790

11641

4740

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

1.791

11642

24881

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

1.791

11643

25

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

1.792

11644

121

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

1.792

11645

22274

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

With initial conditions

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

1.792

11646

23640

\begin{align*} y^{\prime \prime }-9 y^{\prime }+18 y&=54 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= -3 \\ \end{align*}

Using Laplace transform method.

1.792

11647

23793

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

1.792

11648

18232

\begin{align*} y^{\prime \prime }-3 y^{\prime }&=18 x -10 \cos \left (x \right ) \\ \end{align*}

1.793

11649

21269

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

Series expansion around \(t=0\).

1.793

11650

23636

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

Using Laplace transform method.

1.793

11651

24055

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

Using Laplace transform method.

1.793

11652

24119

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

Series expansion around \(x=0\).

1.793

11653

8946

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

1.794

11654

16177

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

1.794

11655

19203

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

1.794

11656

19505

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

1.794

11657

5773

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

1.795

11658

8509

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

Series expansion around \(x=0\).

1.795

11659

12908

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

1.795

11660

16078

\begin{align*} y^{\prime \prime }+6 y^{\prime }+8 y&={\mathrm e}^{-t} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

1.796

11661

14778

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

1.797

11662

16874

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

Series expansion around \(x=0\).

1.797

11663

21738

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

1.797

11664

6891

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

1.798

11665

14750

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

Series expansion around \(x=0\).

1.798

11666

21273

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

Series expansion around \(t=0\).

1.798

11667

5609

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

1.799

11668

17890

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

1.799

11669

20549

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

1.799

11670

11831

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

1.800

11671

23577

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

1.800

11672

25093

\begin{align*} y^{\prime \prime }+8 y&=t \\ \end{align*}

1.800

11673

3424

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

1.801

11674

14985

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

With initial conditions

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

1.801

11675

19029

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

1.801

11676

20289

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

1.802

11677

24600

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

1.802

11678

25621

\begin{align*} y^{\prime \prime }-5 y^{\prime }+6 y&=12 \\ \end{align*}

1.802

11679

1223

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

1.803

11680

12654

\begin{align*} y^{\prime \prime }&=\frac {\left (7 a \,x^{2}+5\right ) y^{\prime }}{x \left (a \,x^{2}+1\right )}-\frac {\left (15 a \,x^{2}+5\right ) y}{x^{2} \left (a \,x^{2}+1\right )} \\ \end{align*}

1.803

11681

21584

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

1.803

11682

24690

\begin{align*} y^{\prime \prime }-6 y^{\prime }+9 y&={\mathrm e}^{3 x} \\ \end{align*}

1.803

11683

3224

\begin{align*} 2 x^{2} y^{\prime \prime }-3 y^{\prime } x -18 y&=\ln \left (x \right ) \\ \end{align*}

1.804

11684

14294

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

1.806

11685

22874

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

Series expansion around \(x=0\).

1.806

11686

6516

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

1.807

11687

1264

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

1.808

11688

12474

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

1.808

11689

16657

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

1.808

11690

5535

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

1.809

11691

10505

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

1.809

11692

19851

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

1.809

11693

227

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

1.810

11694

14287

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

1.810

11695

25547

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

1.810

11696

14069

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

1.811

11697

16038

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

1.811

11698

7166

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

Series expansion around \(x=0\).

1.812

11699

8112

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

Series expansion around \(x=0\).

1.812

11700

12314

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

1.812