## how to solve an ode numerically?...

hey guys.. i have put input this in maple.. but it doesn't seem to solve it..

ode:= D(D(y(t)))- u*(1-(y(t)^2))*D(y(t)) + y(t)=0;
ics:=y(0)=0.2, D(y)(0)=0;
y(0) = 0.2, D(y)(0) = 0
dsolve({ode,ics},numeric);

Error, (in unknown) invalid input: op expects 1 or 2 arguments, but received 0

## Percentage points of the F-distribution...

The F-distribution (also known as Snedecor's F distribution or the Fisher-Snedecor distribution) depends on two separate degrees of freedom, m and n. It is defined by (Eq. 2 in MathWorld):

In Maple notation:

> fdist:=(x,m,n)->GAMMA((m+n)/2)*(m/n)^(m/2)/GAMMA(m/2)/GAMMA(n/2)*x^(m/2-1)/(1+m*x/n)^((m+n)/2);

In order to calculate the percentage points of the F-distribution we need to find the area under the curve. For example, for known m, n the integral

defines the percentage of points under curve for x, since

This can be done easily in Maple, if we wish to find, say, 95 % confidence level for m=4, n=3, we (could) do the following:

> Fstat:=proc(perc,m,n) fsolve(int(fdist(u,m,n),u=0..x)-perc,x=0..infinity); end proc:

> Fstat(0.95,4,3);

9.117182253

Is there a Maple built-in function I can use to calculate these values in a more elegant form instead of defining fdist and Fstat?

Is there something similar for the evaluation of the percentage points of the t-Distribution?

Graph the surfaces  y= x + z and y = 1 - z on the same axes using the domain |x| < or = 1.2 , |z| < or = 1.2 , and observe the curve of intersection of both surfaces. Show that the projection of this curve onto the xz-plane is an ellipse.

So that's that problem. I am so lost on what to do. I know it has to do something with implicitplot3d.

## Plot Riemann sums for double integals...

I know that student[middlebox] can graph an approximation of an integral.
For example,
with(plots):
with(student):
f:=x->sin(x)+0.2*x+0.5:
a:=0: b:=16: N:=10:
C:=plot(f(x), x=a..b):
R:=middlebox(f(x), x=a..b, N):
display(C,R);

I need to know how to use Maple to do the same plotting for double integrals. Thanks for your help.

## Maple Solve Command...

Hello everyone.

I believe I have come across some kind of bug in Maple 11, and I was wondering if anyone could confirm that I am not crazy and that I am not using the software incorrectly.  When using the solve command, I get some very weird stuff:

evalf(solve(x^3+1/4 = x))

evalf(solve(x^3+.25 = x))

The second gives the correct answers.  The first gives three complex roots.  Am I doing something wrong?

Thanks,

John

## plot both an arrow and a function....

O.k. so I can plot an arrow.  And I can plot a function.  Now how do I get them on the same plot?  Any simple example that shows how to do this will help me.  Thanks.

## notation for subtraction...

For describing intermediate steps when calculating a definite integral, often in textbooks or other literature people use a square bracket on the right of an equation with the lower and upper bounds of the integral as sub- and super-script to the right of the square bracket to mean that the equation should first have the upper bound substituted into the equation and then the lower bound should be substituted into the equation and the latter subtracted from the former.  Is there any way to write this in Maple in a way that is visually the same?  I don't see anything similar in the

## Differential equations...

Find the general solution for the differential equation

x"(t) - 4 x'(t) + 4 x(t) = t * exp(2*t)

## how to solve a system of linear equations + 1 tran...

Hi

To find the deflection of a bar under buckling I am trying to solve a set of 10 unknowns and 10 equations, with equations like this one:

eq3 := C1*cos(P^(1/2))+sin(P^(1/2))+5*C3+C4 = C5*cos(P^(1/2))+sin(P^(1/2))+5*C7+C8

(the complete file is included)

When I try to solve the system, Maple is able to evaluate all the C's but not P. That makes sense, because P will be a solution of a transcendental equation (something like tan(x)=x) as opposed to the the C's all being linearly dependant.

## Sequence by induction...

Hey guys,

Now I'm encountering another problem. I'm trying to assign a[n] as:

a[1]=1

a[n]=a[n-1]+1/2^(n-1)

I tried the following:

a:=[1, seq(a[n-1]+1/2^(n-1),n=2..10);

The result is "Recursive error".

The problem is this is a good recursive. Maple seems to simply not recognize recursive input at all.

I tried another way:

a[1]:=1

a:=[seq(a[n-1]+1/2^(n-1),n=2..10);

Result is the same.

I tried another way

a[1]:=1

a[n]:=[seq(a[n-1]+1/2^(n-1),n=2..10]

## Orthogonal polynomials and Gauss Quadrature: s.th....

There is a Mathematica package OrthogonalPolynomials by Milovanovic sketched in facta.junis.ni.ac.yu/mai/mai19/f19-017-036.pdf
( ~ 200 kb and 20 pages). Is anybody aware of something similar for Maple?

## LinearAlgebra Matrix won't work...

I'm trying to do some work with a large matrix. I was using with(linalg), but I need to use LinearAlgebra now. However, if I don't use the command "matrix" (lowercase m) then I get this as an output:

## Using DEplot to plot a phase portrait...

Hi there.

I am having a little bother plotting a phase portrait of the following system:

DEs := [diff(u(t),t)=-a*u(t)+v(t), diff(v(t),t)=u(t)^2/(1+u(t)^2)-v(t)];

where 'a' denotes any real number.  I am trying to draw the phase portrait but I have know initial conditions. 'a' must also be from -0.5..0.5.

Any hints/tips would be greatly appreciated.  Thanks.

## Lauricella function...

Hi

I need to evalaute the Lauricella function of type F for arbitrary value of   n , say around 2 to 10 or so. I think maple does not provide the ready function for the same and its is restricted to single variable series. Is there any method for computing the Lauricella functions in maple?

Thanks for any help

Vish

## german language pack...

where can i get a german language pack? is one available?

I recently got my copy of maple in the university, but i cant choose german as my language.

To make everything a little easier (cause im new to maple), i was trying to find a language pack.  I hope there is a pack for download anywhere.