## Solution of second order differential equation...

Dear Users!

Hope you would be fine with everying. I want to solve the following 2nd order linear differential equation.

(1+B)*(diff(theta(eta), eta, eta))+C*A*(diff(theta(eta), eta)) = 0;
where A is given as

A := -(alpha*exp(-sqrt((omega+1)*omega*(M^2+alpha+1))*eta/(omega+1))*omega+alpha*exp(-sqrt((omega+1)*omega*(M^2+alpha+1))*eta/(omega+1))+exp(-sqrt((omega+1)*omega*(M^2+alpha+1))*eta/(omega+1))*omega-alpha*omega+exp(-sqrt((omega+1)*omega*(M^2+alpha+1))*eta/(omega+1))-alpha-omega-1)/sqrt((omega+1)*omega*(M^2+alpha+1));
I want solution for any values of omega, alpha, M, B, C and L. The BCs are below:

BCs := (D(theta))(0) = -1, theta(L) = 0.

## how can i obtain this ?...

Write a command maple to count each two elements distincts of a list L ?

## Error, (in unknown) invalid arguments to divide: 4...

Hello,

There is a error happened when i use the command "eliminate" ,

And,the target two equations is:

[190.0315457*d^6-7.601261828*d^4+344.0*c^2*d^2-2.677685950*c^4, 0.6830134554e-2*c^4+2084.317025*d^8-166.7453620*d^6+3.334907240*d^4-c^2*d^2]

The error is happened like that shown below.

Error, (in unknown) invalid arguments to divide: 4903.60312, 1.000000000 to use eliminate command!

I wonder why this error happened, could anyone help me!

Thanks!!!

## how can i substitute these elements ?...

to get the list where all the elements of a list L equal to its largest element are replaced by 0 ?

## How can I find the inverse of a function over a gi...

Hi everyone,

I have a x -> y = f(x) function from R to R (you may suppose f is C(infinity)),  given by an explicit relation.
This function is not strictly monotonic over R.

I want to construct the global inverse of f over R by putting "side by side" local inverse functions.
Let a__0, ..., a__n values of x such that:

1. -infinity =a__0 < a__1 < ... a__(n-1) < a__n = + infinity
2. f is monotonic over ] a__p, a__(p+1) [   for each p=0..n-1

The idea is to define the global inverse g of f over R by
g := y ->  piecewise(y < f(a__1), g__0(y), ..., y < f(a__n), g__(n-1)(y))
where g__p(y), is the inverse function of the restriction of f to ] a__p, a__(p+1) [

Toy problem
f := x ->1-(1-x)^2;
x__1 := solve(diff(f(x), x);
y__1 := f(x__1);

# I thought one of these commands could work (but they don't return me a single branch as I had expected)
solve(f(x)=y, x) assuming y < y__1;
solve({f(x)=y, x < x__1}, x);

How can I obtain the inverse of a function f over an interval where f is bijective ?

TIA

## latex code too long...

I think that maple is actually evaluating this series into what ever ridiculously long closed form expression the expansion of the series has, but i just want the latex for what i have entered.

How do i tell maple to not evaluate something?

 >
 a_{{p,q}}= \left( -4\, \left( \cos \left( {\frac {\pi }{q}} \right)  \right) ^{2}+8\, \left( \cos \left( {\frac {\pi \,p}{q}} \right)  \right) ^{2} \left( \cos \left( {\frac {\pi }{q}} \right)  \right) ^{ 2}-8\,\sin \left( {\frac {\pi \,p}{q}} \right) \cos \left( {\frac { \pi \,p}{q}} \right) \sin \left( {\frac {\pi }{q}} \right) \cos  \left( {\frac {\pi }{q}} \right) +3-4\, \left( \cos \left( {\frac { \pi \,p}{q}} \right)  \right) ^{2} \right)  \left( \cos \left( {\frac {\pi \, \left( q+1 \right) }{q}} \right)  \right) ^{2}+ \left( -4\,  \left( \cos \left( {\frac {\pi }{q}} \right)  \right) ^{2}+8\,  \left( \cos \left( {\frac {\pi \,p}{q}} \right)  \right) ^{2} \left( \cos \left( {\frac {\pi }{q}} \right)  \right) ^{2}-8\,\sin \left( { \frac {\pi \,p}{q}} \right) \cos \left( {\frac {\pi \,p}{q}} \right) \sin \left( {\frac {\pi }{q}} \right) \cos \left( {\frac {\pi }{q}}  \right) +3-4\, \left( \cos \left( {\frac {\pi \,p}{q}} \right)  \right) ^{2} \right)  \left( \cos \left( {\frac {\pi \, \left( q+1  \right) p}{q}} \right)  \right) ^{2}+ \left( 8\, \left( \cos \left( { \frac {\pi }{q}} \right)  \right) ^{2}-16\, \left( \cos \left( {\frac {\pi \,p}{q}} \right)  \right) ^{2} \left( \cos \left( {\frac {\pi }{q }} \right)  \right) ^{2}+16\,\sin \left( {\frac {\pi \,p}{q}} \right) \cos \left( {\frac {\pi \,p}{q}} \right) \sin \left( {\frac {\pi }{q}}  \right) \cos \left( {\frac {\pi }{q}} \right) -6+8\, \left( \cos  \left( {\frac {\pi \,p}{q}} \right)  \right) ^{2} \right)  \left( \cos \left( {\frac {\pi \, \left( q+1 \right) p}{q}} \right)  \right) ^{2} \left( \cos \left( {\frac {\pi \, \left( q+1 \right) }{q}}  \right)  \right) ^{2}+ \left( 8\,\sin \left( {\frac {\pi \,p}{q}}  \right) \cos \left( {\frac {\pi \,p}{q}} \right)  \left( \cos \left( {\frac {\pi }{q}} \right)  \right) ^{4}-4\, \left( \cos \left( {\frac {\pi }{q}} \right)  \right) ^{3}\sin \left( {\frac {\pi }{q}} \right) +8\, \left( \cos \left( {\frac {\pi \,p}{q}} \right)  \right) ^{2}  \left( \cos \left( {\frac {\pi }{q}} \right)  \right) ^{3}\sin  \left( {\frac {\pi }{q}} \right) -4\,\sin \left( {\frac {\pi \,p}{q}}  \right) \cos \left( {\frac {\pi \,p}{q}} \right)  \left( \cos \left( {\frac {\pi }{q}} \right)  \right) ^{2}-8\,\sin \left( {\frac {\pi \,p }{q}} \right)  \left( \cos \left( {\frac {\pi \,p}{q}} \right)  \right) ^{3} \left( \cos \left( {\frac {\pi }{q}} \right)  \right) ^{ 2}-8\,\sin \left( {\frac {\pi }{q}} \right) \cos \left( {\frac {\pi }{ q}} \right)  \left( \cos \left( {\frac {\pi \,p}{q}} \right)  \right) ^{4}+\sin \left( {\frac {\pi }{q}} \right) \cos \left( {\frac {\pi }{q }} \right) +4\, \left( \cos \left( {\frac {\pi \,p}{q}} \right)  \right) ^{2}\sin \left( {\frac {\pi }{q}} \right) \cos \left( {\frac {\pi }{q}} \right) +4\,\sin \left( {\frac {\pi \,p}{q}} \right)  \left( \cos \left( {\frac {\pi \,p}{q}} \right)  \right) ^{3}-\sin  \left( {\frac {\pi \,p}{q}} \right) \cos \left( {\frac {\pi \,p}{q}}  \right)  \right) \sin \left( {\frac {\pi \, \left( q+1 \right) }{q}}  \right) \cos \left( {\frac {\pi \, \left( q+1 \right) }{q}} \right)  \left( - \left( \cos \left( {\frac {\pi \,p}{q}} \right)  \right) ^{2 }+ \left( \cos \left( {\frac {\pi }{q}} \right)  \right) ^{2} \right) ^{-1}+ \left( 8\,\sin \left( {\frac {\pi \,p}{q}} \right) \cos \left( {\frac {\pi \,p}{q}} \right)  \left( \cos \left( {\frac {\pi }{q}}  \right)  \right) ^{4}-4\, \left( \cos \left( {\frac {\pi }{q}}  \right)  \right) ^{3}\sin \left( {\frac {\pi }{q}} \right) +8\,  \left( \cos \left( {\frac {\pi \,p}{q}} \right)  \right) ^{2} \left( \cos \left( {\frac {\pi }{q}} \right)  \right) ^{3}\sin \left( {\frac {\pi }{q}} \right) -4\,\sin \left( {\frac {\pi \,p}{q}} \right) \cos  \left( {\frac {\pi \,p}{q}} \right)  \left( \cos \left( {\frac {\pi } {q}} \right)  \right) ^{2}-8\,\sin \left( {\frac {\pi \,p}{q}}  \right)  \left( \cos \left( {\frac {\pi \,p}{q}} \right)  \right) ^{3 } \left( \cos \left( {\frac {\pi }{q}} \right)  \right) ^{2}-8\,\sin  \left( {\frac {\pi }{q}} \right) \cos \left( {\frac {\pi }{q}}  \right)  \left( \cos \left( {\frac {\pi \,p}{q}} \right)  \right) ^{4 }+\sin \left( {\frac {\pi }{q}} \right) \cos \left( {\frac {\pi }{q}}  \right) +4\, \left( \cos \left( {\frac {\pi \,p}{q}} \right)  \right) ^{2}\sin \left( {\frac {\pi }{q}} \right) \cos \left( {\frac {\pi }{q}} \right) +4\,\sin \left( {\frac {\pi \,p}{q}} \right)  \left( \cos \left( {\frac {\pi \,p}{q}} \right)  \right) ^{3}-\sin  \left( {\frac {\pi \,p}{q}} \right) \cos \left( {\frac {\pi \,p}{q}}  \right)  \right) \sin \left( {\frac {\pi \, \left( q+1 \right) p}{q}}  \right) \cos \left( {\frac {\pi \, \left( q+1 \right) p}{q}} \right)  \left( - \left( \cos \left( {\frac {\pi \,p}{q}} \right)  \right) ^{2 }+ \left( \cos \left( {\frac {\pi }{q}} \right)  \right) ^{2} \right) ^{-1}-2\, \left( 8\,\sin \left( {\frac {\pi \,p}{q}} \right) \cos  \left( {\frac {\pi \,p}{q}} \right)  \left( \cos \left( {\frac {\pi } {q}} \right)  \right) ^{4}-4\, \left( \cos \left( {\frac {\pi }{q}}  \right)  \right) ^{3}\sin \left( {\frac {\pi }{q}} \right) +8\,  \left( \cos \left( {\frac {\pi \,p}{q}} \right)  \right) ^{2} \left( \cos \left( {\frac {\pi }{q}} \right)  \right) ^{3}\sin \left( {\frac {\pi }{q}} \right) -4\,\sin \left( {\frac {\pi \,p}{q}} \right) \cos  \left( {\frac {\pi \,p}{q}} \right)  \left( \cos \left( {\frac {\pi } {q}} \right)  \right) ^{2}-8\,\sin \left( {\frac {\pi \,p}{q}}  \right)  \left( \cos \left( {\frac {\pi \,p}{q}} \right)  \right) ^{3 } \left( \cos \left( {\frac {\pi }{q}} \right)  \right) ^{2}-8\,\sin  \left( {\frac {\pi }{q}} \right) \cos \left( {\frac {\pi }{q}}  \right)  \left( \cos \left( {\frac {\pi \,p}{q}} \right)  \right) ^{4 }+\sin \left( {\frac {\pi }{q}} \right) \cos \left( {\frac {\pi }{q}}  \right) +4\, \left( \cos \left( {\frac {\pi \,p}{q}} \right)  \right) ^{2}\sin \left( {\frac {\pi }{q}} \right) \cos \left( {\frac {\pi }{q}} \right) +4\,\sin \left( {\frac {\pi \,p}{q}} \right)  \left( \cos \left( {\frac {\pi \,p}{q}} \right)  \right) ^{3}-\sin  \left( {\frac {\pi \,p}{q}} \right) \cos \left( {\frac {\pi \,p}{q}}  \right)  \right)  \left( \cos \left( {\frac {\pi \, \left( q+1  \right) p}{q}} \right)  \right) ^{2}\sin \left( {\frac {\pi \,  \left( q+1 \right) }{q}} \right) \cos \left( {\frac {\pi \, \left( q+ 1 \right) }{q}} \right)  \left( - \left( \cos \left( {\frac {\pi \,p}{ q}} \right)  \right) ^{2}+ \left( \cos \left( {\frac {\pi }{q}}  \right)  \right) ^{2} \right) ^{-1}-2\, \left( 8\,\sin \left( {\frac {\pi \,p}{q}} \right) \cos \left( {\frac {\pi \,p}{q}} \right)  \left( \cos \left( {\frac {\pi }{q}} \right)  \right) ^{4}-4\,  \left( \cos \left( {\frac {\pi }{q}} \right)  \right) ^{3}\sin  \left( {\frac {\pi }{q}} \right) +8\, \left( \cos \left( {\frac {\pi \,p}{q}} \right)  \right) ^{2} \left( \cos \left( {\frac {\pi }{q}}  \right)  \right) ^{3}\sin \left( {\frac {\pi }{q}} \right) -4\,\sin  \left( {\frac {\pi \,p}{q}} \right) \cos \left( {\frac {\pi \,p}{q}}  \right)  \left( \cos \left( {\frac {\pi }{q}} \right)  \right) ^{2}-8 \,\sin \left( {\frac {\pi \,p}{q}} \right)  \left( \cos \left( {\frac {\pi \,p}{q}} \right)  \right) ^{3} \left( \cos \left( {\frac {\pi }{q }} \right)  \right) ^{2}-8\,\sin \left( {\frac {\pi }{q}} \right) \cos  \left( {\frac {\pi }{q}} \right)  \left( \cos \left( {\frac {\pi \,p} {q}} \right)  \right) ^{4}+\sin \left( {\frac {\pi }{q}} \right) \cos  \left( {\frac {\pi }{q}} \right) +4\, \left( \cos \left( {\frac {\pi \,p}{q}} \right)  \right) ^{2}\sin \left( {\frac {\pi }{q}} \right) \cos \left( {\frac {\pi }{q}} \right) +4\,\sin \left( {\frac {\pi \,p} {q}} \right)  \left( \cos \left( {\frac {\pi \,p}{q}} \right)  \right) ^{3}-\sin \left( {\frac {\pi \,p}{q}} \right) \cos \left( { \frac {\pi \,p}{q}} \right)  \right) \sin \left( {\frac {\pi \,  \left( q+1 \right) p}{q}} \right) \cos \left( {\frac {\pi \, \left( q +1 \right) p}{q}} \right)  \left( \cos \left( {\frac {\pi \, \left( q+ 1 \right) }{q}} \right)  \right) ^{2} \left( - \left( \cos \left( { \frac {\pi \,p}{q}} \right)  \right) ^{2}+ \left( \cos \left( {\frac { \pi }{q}} \right)  \right) ^{2} \right) ^{-1}+ \left( -8\, \left( \cos  \left( {\frac {\pi }{q}} \right)  \right) ^{2}+16\, \left( \cos  \left( {\frac {\pi \,p}{q}} \right)  \right) ^{2} \left( \cos \left( {\frac {\pi }{q}} \right)  \right) ^{2}-16\,\sin \left( {\frac {\pi \, p}{q}} \right) \cos \left( {\frac {\pi \,p}{q}} \right) \sin \left( { \frac {\pi }{q}} \right) \cos \left( {\frac {\pi }{q}} \right) +6-8\,  \left( \cos \left( {\frac {\pi \,p}{q}} \right)  \right) ^{2}  \right) \sin \left( {\frac {\pi \, \left( q+1 \right) p}{q}} \right) \cos \left( {\frac {\pi \, \left( q+1 \right) p}{q}} \right) \sin  \left( {\frac {\pi \, \left( q+1 \right) }{q}} \right) \cos \left( { \frac {\pi \, \left( q+1 \right) }{q}} \right) - \left( -4\, \left( \cos \left( {\frac {\pi }{q}} \right)  \right) ^{2}+8\, \left( \cos  \left( {\frac {\pi \,p}{q}} \right)  \right) ^{2} \left( \cos \left( {\frac {\pi }{q}} \right)  \right) ^{2}-8\,\sin \left( {\frac {\pi \,p }{q}} \right) \cos \left( {\frac {\pi \,p}{q}} \right) \sin \left( { \frac {\pi }{q}} \right) \cos \left( {\frac {\pi }{q}} \right) +3-4\,  \left( \cos \left( {\frac {\pi \,p}{q}} \right)  \right) ^{2}  \right)  \left( \cos \left( {\frac {\pi }{q}} \right)  \right) ^{2}-  \left( -4\, \left( \cos \left( {\frac {\pi }{q}} \right)  \right) ^{2 }+8\, \left( \cos \left( {\frac {\pi \,p}{q}} \right)  \right) ^{2}  \left( \cos \left( {\frac {\pi }{q}} \right)  \right) ^{2}-8\,\sin  \left( {\frac {\pi \,p}{q}} \right) \cos \left( {\frac {\pi \,p}{q}}  \right) \sin \left( {\frac {\pi }{q}} \right) \cos \left( {\frac { \pi }{q}} \right) +3-4\, \left( \cos \left( {\frac {\pi \,p}{q}}  \right)  \right) ^{2} \right)  \left( \cos \left( {\frac {\pi \,p}{q} } \right)  \right) ^{2}- \left( 8\, \left( \cos \left( {\frac {\pi }{q }} \right)  \right) ^{2}-16\, \left( \cos \left( {\frac {\pi \,p}{q}}  \right)  \right) ^{2} \left( \cos \left( {\frac {\pi }{q}} \right)  \right) ^{2}+16\,\sin \left( {\frac {\pi \,p}{q}} \right) \cos  \left( {\frac {\pi \,p}{q}} \right) \sin \left( {\frac {\pi }{q}}  \right) \cos \left( {\frac {\pi }{q}} \right) -6+8\, \left( \cos  \left( {\frac {\pi \,p}{q}} \right)  \right) ^{2} \right)  \left( \cos \left( {\frac {\pi \,p}{q}} \right)  \right) ^{2} \left( \cos  \left( {\frac {\pi }{q}} \right)  \right) ^{2}- \left( 8\,\sin  \left( {\frac {\pi \,p}{q}} \right) \cos \left( {\frac {\pi \,p}{q}}  \right)  \left( \cos \left( {\frac {\pi }{q}} \right)  \right) ^{4}-4 \, \left( \cos \left( {\frac {\pi }{q}} \right)  \right) ^{3}\sin  \left( {\frac {\pi }{q}} \right) +8\, \left( \cos \left( {\frac {\pi \,p}{q}} \right)  \right) ^{2} \left( \cos \left( {\frac {\pi }{q}}  \right)  \right) ^{3}\sin \left( {\frac {\pi }{q}} \right) -4\,\sin  \left( {\frac {\pi \,p}{q}} \right) \cos \left( {\frac {\pi \,p}{q}}  \right)  \left( \cos \left( {\frac {\pi }{q}} \right)  \right) ^{2}-8 \,\sin \left( {\frac {\pi \,p}{q}} \right)  \left( \cos \left( {\frac {\pi \,p}{q}} \right)  \right) ^{3} \left( \cos \left( {\frac {\pi }{q }} \right)  \right) ^{2}-8\,\sin \left( {\frac {\pi }{q}} \right) \cos  \left( {\frac {\pi }{q}} \right)  \left( \cos \left( {\frac {\pi \,p} {q}} \right)  \right) ^{4}+\sin \left( {\frac {\pi }{q}} \right) \cos  \left( {\frac {\pi }{q}} \right) +4\, \left( \cos \left( {\frac {\pi \,p}{q}} \right)  \right) ^{2}\sin \left( {\frac {\pi }{q}} \right) \cos \left( {\frac {\pi }{q}} \right) +4\,\sin \left( {\frac {\pi \,p} {q}} \right)  \left( \cos \left( {\frac {\pi \,p}{q}} \right)  \right) ^{3}-\sin \left( {\frac {\pi \,p}{q}} \right) \cos \left( { \frac {\pi \,p}{q}} \right)  \right) \sin \left( {\frac {\pi }{q}}  \right) \cos \left( {\frac {\pi }{q}} \right)  \left( - \left( \cos  \left( {\frac {\pi \,p}{q}} \right)  \right) ^{2}+ \left( \cos  \left( {\frac {\pi }{q}} \right)  \right) ^{2} \right) ^{-1}- \left( 8\,\sin \left( {\frac {\pi \,p}{q}} \right) \cos \left( {\frac {\pi \, p}{q}} \right)  \left( \cos \left( {\frac {\pi }{q}} \right)  \right) ^{4}-4\, \left( \cos \left( {\frac {\pi }{q}} \right)  \right) ^{3} \sin \left( {\frac {\pi }{q}} \right) +8\, \left( \cos \left( {\frac { \pi \,p}{q}} \right)  \right) ^{2} \left( \cos \left( {\frac {\pi }{q} } \right)  \right) ^{3}\sin \left( {\frac {\pi }{q}} \right) -4\,\sin  \left( {\frac {\pi \,p}{q}} \right) \cos \left( {\frac {\pi \,p}{q}}  \right)  \left( \cos \left( {\frac {\pi }{q}} \right)  \right) ^{2}-8 \,\sin \left( {\frac {\pi \,p}{q}} \right)  \left( \cos \left( {\frac {\pi \,p}{q}} \right)  \right) ^{3} \left( \cos \left( {\frac {\pi }{q }} \right)  \right) ^{2}-8\,\sin \left( {\frac {\pi }{q}} \right) \cos  \left( {\frac {\pi }{q}} \right)  \left( \cos \left( {\frac {\pi \,p} {q}} \right)  \right) ^{4}+\sin \left( {\frac {\pi }{q}} \right) \cos  \left( {\frac {\pi }{q}} \right) +4\, \left( \cos \left( {\frac {\pi \,p}{q}} \right)  \right) ^{2}\sin \left( {\frac {\pi }{q}} \right) \cos \left( {\frac {\pi }{q}} \right) +4\,\sin \left( {\frac {\pi \,p} {q}} \right)  \left( \cos \left( {\frac {\pi \,p}{q}} \right)  \right) ^{3}-\sin \left( {\frac {\pi \,p}{q}} \right) \cos \left( { \frac {\pi \,p}{q}} \right)  \right) \sin \left( {\frac {\pi \,p}{q}}  \right) \cos \left( {\frac {\pi \,p}{q}} \right)  \left( - \left( \cos \left( {\frac {\pi \,p}{q}} \right)  \right) ^{2}+ \left( \cos  \left( {\frac {\pi }{q}} \right)  \right) ^{2} \right) ^{-1}+2\,  \left( 8\,\sin \left( {\frac {\pi \,p}{q}} \right) \cos \left( { \frac {\pi \,p}{q}} \right)  \left( \cos \left( {\frac {\pi }{q}}  \right)  \right) ^{4}-4\, \left( \cos \left( {\frac {\pi }{q}}  \right)  \right) ^{3}\sin \left( {\frac {\pi }{q}} \right) +8\,  \left( \cos \left( {\frac {\pi \,p}{q}} \right)  \right) ^{2} \left( \cos \left( {\frac {\pi }{q}} \right)  \right) ^{3}\sin \left( {\frac {\pi }{q}} \right) -4\,\sin \left( {\frac {\pi \,p}{q}} \right) \cos  \left( {\frac {\pi \,p}{q}} \right)  \left( \cos \left( {\frac {\pi } {q}} \right)  \right) ^{2}-8\,\sin \left( {\frac {\pi \,p}{q}}  \right)  \left( \cos \left( {\frac {\pi \,p}{q}} \right)  \right) ^{3 } \left( \cos \left( {\frac {\pi }{q}} \right)  \right) ^{2}-8\,\sin  \left( {\frac {\pi }{q}} \right) \cos \left( {\frac {\pi }{q}}  \right)  \left( \cos \left( {\frac {\pi \,p}{q}} \right)  \right) ^{4 }+\sin \left( {\frac {\pi }{q}} \right) \cos \left( {\frac {\pi }{q}}  \right) +4\, \left( \cos \left( {\frac {\pi \,p}{q}} \right)  \right) ^{2}\sin \left( {\frac {\pi }{q}} \right) \cos \left( {\frac {\pi }{q}} \right) +4\,\sin \left( {\frac {\pi \,p}{q}} \right)  \left( \cos \left( {\frac {\pi \,p}{q}} \right)  \right) ^{3}-\sin  \left( {\frac {\pi \,p}{q}} \right) \cos \left( {\frac {\pi \,p}{q}}  \right)  \right)  \left( \cos \left( {\frac {\pi \,p}{q}} \right)  \right) ^{2}\sin \left( {\frac {\pi }{q}} \right) \cos \left( {\frac {\pi }{q}} \right)  \left( - \left( \cos \left( {\frac {\pi \,p}{q}}  \right)  \right) ^{2}+ \left( \cos \left( {\frac {\pi }{q}} \right)  \right) ^{2} \right) ^{-1}+2\, \left( 8\,\sin \left( {\frac {\pi \,p} {q}} \right) \cos \left( {\frac {\pi \,p}{q}} \right)  \left( \cos  \left( {\frac {\pi }{q}} \right)  \right) ^{4}-4\, \left( \cos  \left( {\frac {\pi }{q}} \right)  \right) ^{3}\sin \left( {\frac { \pi }{q}} \right) +8\, \left( \cos \left( {\frac {\pi \,p}{q}}  \right)  \right) ^{2} \left( \cos \left( {\frac {\pi }{q}} \right)  \right) ^{3}\sin \left( {\frac {\pi }{q}} \right) -4\,\sin \left( { \frac {\pi \,p}{q}} \right) \cos \left( {\frac {\pi \,p}{q}} \right)  \left( \cos \left( {\frac {\pi }{q}} \right)  \right) ^{2}-8\,\sin  \left( {\frac {\pi \,p}{q}} \right)  \left( \cos \left( {\frac {\pi \,p}{q}} \right)  \right) ^{3} \left( \cos \left( {\frac {\pi }{q}}  \right)  \right) ^{2}-8\,\sin \left( {\frac {\pi }{q}} \right) \cos  \left( {\frac {\pi }{q}} \right)  \left( \cos \left( {\frac {\pi \,p} {q}} \right)  \right) ^{4}+\sin \left( {\frac {\pi }{q}} \right) \cos  \left( {\frac {\pi }{q}} \right) +4\, \left( \cos \left( {\frac {\pi \,p}{q}} \right)  \right) ^{2}\sin \left( {\frac {\pi }{q}} \right) \cos \left( {\frac {\pi }{q}} \right) +4\,\sin \left( {\frac {\pi \,p} {q}} \right)  \left( \cos \left( {\frac {\pi \,p}{q}} \right)  \right) ^{3}-\sin \left( {\frac {\pi \,p}{q}} \right) \cos \left( { \frac {\pi \,p}{q}} \right)  \right) \sin \left( {\frac {\pi \,p}{q}}  \right) \cos \left( {\frac {\pi \,p}{q}} \right)  \left( \cos \left( {\frac {\pi }{q}} \right)  \right) ^{2} \left( - \left( \cos \left( { \frac {\pi \,p}{q}} \right)  \right) ^{2}+ \left( \cos \left( {\frac { \pi }{q}} \right)  \right) ^{2} \right) ^{-1}- \left( -8\, \left( \cos  \left( {\frac {\pi }{q}} \right)  \right) ^{2}+16\, \left( \cos  \left( {\frac {\pi \,p}{q}} \right)  \right) ^{2} \left( \cos \left( {\frac {\pi }{q}} \right)  \right) ^{2}-16\,\sin \left( {\frac {\pi \, p}{q}} \right) \cos \left( {\frac {\pi \,p}{q}} \right) \sin \left( { \frac {\pi }{q}} \right) \cos \left( {\frac {\pi }{q}} \right) +6-8\,  \left( \cos \left( {\frac {\pi \,p}{q}} \right)  \right) ^{2}  \right) \sin \left( {\frac {\pi \,p}{q}} \right) \cos \left( {\frac { \pi \,p}{q}} \right) \sin \left( {\frac {\pi }{q}} \right) \cos  \left( {\frac {\pi }{q}} \right)
 >

## Monte Carlo integration...

I am trying to use Monte Carlo integration example given at: https://www.maplesoft.com/products/maple/new_features/maple15/examples/montecarlo.aspx.

After coding the procedure, the statement approxint(x^2, x = 1 .. 3)

gives error: Error, (in approxint) invalid input: if expects 3 arguments, but received 1

But I have used in exactly the same way as given in the page. What is the problem

## Questions allowed...

Are we allowed to ask questions about only math or does it have to only be a problem with maple code?

## Measurement of torsional strain...

I have modeled a 3D flexible manipulator in Maplesim. I intend to measure the torsional strain of the flexible beams. How can I do this??

## Animating a 3-D vector field...

Hey guys, I have created this vector field at t=0. Now I would like to ask how can I animate this vector field changing to let say t=0 to 10. Thanks already! Check the code I already wrote and uploaded.upload.mw

## Is it possible to find a derivative at a point?...

Can there be approximate ways of calculating the derivative? Maybe I should count on some formula? Or can not it be calculated in any way at all?

## I want to solve transcendental equation in maple (...

I want to solve transcendental equation in maple and facing problem to plot  “β” vs “a” plot, using Eq. 8, 9, 10...

PDF file attached below:

Equation_file.pdf

## How to solve coupled singular boundary value probl...

restart; with(plots);
G := 1; M := .1; R := 1; P := .72; alpha := .1; phi := 1; K := 1; n := 2; beta := 1;
1
0.1
1
0.72
0.1
1
1
2
1
ode1 := {(1+(4/3)*R)*(diff(theta(x), x, x))+(1/2)*P*f(x)*(diff(theta(x), x))+alpha*theta(x) = 0, n*(diff(f(x), x, x))^(n-1)*(diff(f(x), x, x, x))+f(x)*(diff(f(x), x, x))/(n+1)+G*theta(x)-M*(diff(f(x), x)) = 0, f(0) = 0, theta(10) = 0, (D(f))(0) = beta*K*((D@@2)(f))(0), (D(f))(10) = 1, (D(theta))(0) = -phi*(1-theta(0))};
/7  d  / d          \                     / d          \
{ - --- |--- theta(x)| + 0.3600000000 f(x) |--- theta(x)|
\3  dx \ dx         /                     \ dx         /

/ d  / d      \\ / d  / d  / d      \\\
+ 0.1 theta(x) = 0, 2 |--- |--- f(x)|| |--- |--- |--- f(x)|||
\ dx \ dx     // \ dx \ dx \ dx     ///

1      / d  / d      \\                  / d      \
+ - f(x) |--- |--- f(x)|| + theta(x) - 0.1 |--- f(x)| = 0,
3      \ dx \ dx     //                  \ dx     /

f(0) = 0, theta(10) = 0, D(f)(0) = @@(D, 2)(f)(0),

\
D(f)(10) = 1, D(theta)(0) = -1 + theta(0) }
/
dsol := dsolve(ode1, numeric, method = bvp[midrich], range = 0 .. 10);
Error, (in dsolve/numeric/bvp) initial Newton iteration is not converging

## pdsolve ignores "assuming real", how to get real s...

I try to get real solutions for a PDE, i.e. real-valued functions depending on real variables. Maple computer complex solutions, i.e. complex-valued functions depending on complex variables.

Here is the example in question: (the four function f1, f2, f3, f4 depend on the four unknowns lam, mu, l, m)

assuming([pdsolve([diff(f2(lam, mu, l, m), m)-(diff(f1(lam, mu, l, m), l))-(diff(f4(lam, mu, l, m), mu))+diff(f3(lam, mu, l, m), lam) = 0, diff(f1(lam, mu, l, m), m)+diff(f2(lam, mu, l, m), l)-(diff(f3(lam, mu, l, m), mu))-(diff(f4(lam, mu, l, m), lam)) = 0])], [real])

How can I solve my problem and receive only real solutions to my PDE?

A similar problem had been posted before (see here), but I can only find a cached version of the post where no answers are displayed.

## Controlling plot range in a parametric 3D plot...

Hi,

I would like to control the extents of my 3D parametric plot. Increasing the grid creates too many gridlines and I just get a black plot  (and I still don't get the extent in the y-coordinate that I want).

Any suggestions how I might be able to get this plot from -360 to 0 and -20 to 60 completely filled in? (see attached workbook).

Any suggestions on how to control the gridlines?

An idea of what I am trying to do...I want to plot argument(z/(1+z)) vs. argument(z)*180/pi vs. 20*log10(abs(z)) with contours of argument(z/(1+z)) and 20*log10(abs(z/(1+z))
This is a 3D plot of the output phase of a Nichol's Chart (with the output contours of the Nichol's chart).

Thanks.

phaseplot.mw

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