Hi,

Coul anyone help with this question?

Thanks

Your job is to test several forms of dampening coefficients to determine the ``best'' to use for safety
and comfort. You are to consider a modification of the harmonic motion differential equation
my"+ b(v) y'+ ky = 0

where m is the mass of the driver, k is the spring constant, and b(v) is the variable dampening coefficient.
For the first part of the problem, assume that m = k = 1. We will also be letting v = y' .

b(v)= v^4

Solve the ODE:

I have maple 12 and i am wondering how to approach a Newton's Method type problem. General help would be fine, but i m gonna supply a specific example that im interested in solving.

If anyone knows how to do this please respond as soon as possible, I am really having trouble with this

How the several packages for the dsolve(numeric) chose the step size? what are the criteria?

Hi there,

So my problem is to find the solution(s) of a 3-D system. I can get Maple to spit out a solution (at times), but I am looking for reassurance that this is indeed the solution (if unique, and if not what the other solutions may be). Increasing Digits makes Maple "lose" the solution and return a blank-- normal behavior? Looking at the 3-D plot of the system offers something to puzzle over.

I set up the system in  (x,c,q):

xd := x^.5-.1*x-c;
cd := (.5/x^.5-.1-q)*c;
qd := -(q-.2e-1)*(q-.3e-1)+(q-.25e-1)*(.5/x^.5-.1-q)*c/(x^.5-.1*x-c);
 

I look for a solution with fsolve:

Digits:=10: interface(displayprecision=10):
ss:= fsolve({xd,cd/c,qd}, {x,c,q}, avoid={x=0, c=0, q=0});
xs:=subs(ss,x): cs:=subs(ss,c): qs:=subs(ss,q):

Maple gives:

ss := {c = 2.399289639, q = .2511089584e-1, x = 15.97164840}

If I raise digits to 15, Maple can't solve it anymore. Perhaps this is normal behavior.

I'd like some reassurance that this solution is indeed a solution. Simply feeding the fsolve output back into the system will not work because of a division by zero:

eval(xd,{x=xs,c=cs,q=qs}); eval(cd,{x=xs,c=cs,q=qs}); eval(qd,{x=xs,c=cs,q=qs});

yields:

0.
-.9597158556e-10
Float(-infinity)

I decided to look at the 3-D plot. The plot of the system suggests that there may be several solutions.

The plot:

plotopts:=style=patchcontour, shading=none,lightmodel=light3,axes=boxed:
px:=implicitplot3d({xd}, x=0..25,c=0..5,q=0.02..0.05, numpoints=10000, plotopts, colour=brown): pc:=implicitplot3d({cd/c}, x=0..25,c=0..5,q=0.02..0.05, numpoints=10000, plotopts, colour=green):
pq:=implicitplot3d({qd}, x=0..25,c=0..5,q=0.02..0.05, numpoints=10000, plotopts, colour=blue):
display3d({pq}, orientation=[-25,70]);
display3d({px,pc,pq}, orientation=[95,90], projection=1);

plot of third equation
plot of 3-D system

The plot is not very clean, and no matter how hard I've tried, by turning it around and zooming near the Maple solution, it is not clear that there are no other solutions. (well perhaps it is clear from the equations themselves, but I couldn't work it out and resorted to the numerical approach)

Does somebody have a sheet covering that algorithm for continous
anti-derivatives of rational functions (Bronstein's book §2.8
"Integration of transcendental functions")?

Or can show me, how to extract it from Maple's library in case
it is there (and I guess Maple covers that ...) for explicite
use?

Hello,

I am trying to change the variable in an integral and I have two problems with it:

My first problem is that I can't get the integrand of the new integral with GetIntegrand when I use IntegrationTools[Change] :

restart;

a1:=Int(1/(2*A),x=-A..A);

D1:=IntegrationTools[Change](a1,x=20*log[10](u));

View 8939_simplify_CRRA.mw on MapleNet or Download 8939_simplify_CRRA.mw
View file details

Dear all:

    I am wondering if there is any way in Maple you can do prettyprint with the printf?  Printf gives me more power but the output format of printf is "C-style". For example,

f := exp(x) + 3*sqrt(exp(x));

f1 := subs(exp(x)=y,f);

printf("Transformation is %a s.t %a => %a\n", f,f1 );

gives a display which is very hard to read. Is there any way to do a prettyprint with this kind of things?

Thanks,

Peter

Hi all,

I have a function defined as a sum:

with(PDEtools): mfx:=(x,y,ufx)->sum(ufx[k]*(x-x[k])*(y-y[k]),k);

I want to declare mfx(x,y,ufx) so that it would appear as mfx in subsequent displays. However, when I tried

declare(mfx(x,y,ufx));

Maple tells me that "Error, (in PDEtools:-declare) cannot declare objects as sum(ufx[k]*(x-x[k])*(y-y[k]), k)".

How can I solve this problem?

Thanks.

I am having a problem differentiating a function. I have a fluid in a channel with moving walls corresponding to y=a(t) (upper wall) and y=-a(t) (lower wall). The fluid is driven by suction out of the walls. The speed of the fluid being sucked out of the walls is the constant v_w. I am using the variable eta=y/a(t) to model the fluid. y is the normal direction to teh channel and x is the streamwise direction of the channel. So I have

x=streamwise direction of the channel

y=normal direction of the channel

a(t)=height of the channel

v_w=constant

This is inspired by MapleTA, but applies to Maple in general.  According to the documentation, bitmap plot devices do not allow for font selection, meaning the recommended textplot(...,font=[SYMBOL]) fails to render greek characters such as π in plots which are rendered for embedding in web pages.  This seems like a gaping omission, so we're hoping we've just missed something here.  Is there any way to get the symbol for pi onto a jpeg or gif plot?

Hi all,

I have little (almost zero) experience with Maple. Nonetheless I wish to use Maple 8 to solve a set of 5 equations for 8 unknowns.

At the moment my strategy is to input each equation, make a set of the 5 equations, and then use the 'solve' command to determine the variables. I then refine the answer using 'allvalues' and 'evalf'. Is this the best approach?

Any help or guidance on this is greatly appreciated.