## How do I solve two nonlinear algebraic equations i...

f1 := 0.001;
f2 := 0.002;
c1 := 0.002;
c2 := 0.005;
w1 := 0.1;
W := 0.14;
p1 := 0.65;
p2 := 0.28;
p := 1.167;
r := 0.004;
alpha := 0.2;
ze := 0.14;
mu := 0.05;
ga := 0.01;
cp := 9.3;
Rp := 100;
sigma2 := 0;
l[1] := 3*W^2*(-1+W^2)/(4*(-1+4*W^2));
l[2] := Rp^2*w1^2*mu*ga*cp/(2*(Rp^2*w1^2*cp^2+1));
l[3] := (Rp.w1.mu.ga)/(2*(Rp^2*w1^2*cp^2+1));
l[4] := W*(-1-7*W^2+8*W^4)/(8*(-2+8*W^2));
eq1 := (-x*t+l[2]*x+l[1]*x*y^2+(3/2)*alpha*ze^2*x)^2+((1/2)*c1*x+l[3]*x)^2-(1/4)*f1^2;
eq2 := (-l[4]*y^3+l[1]*x^2*y)^2+(1/4)*y^2*c2^2-f2^2/(4*W^2);

I need to solve these two equation for the variable x and y in terms of  t because I want to plot x with a range for t

and the same plot y with a range for t and if it is possible to plot x vs y for the previuos same range for t

## dsolve event continue the simulation after "halt"...

I want to contnue the simulation from the point (time) that the event accure

how can I do it ?

## Problem with this proc...

proctes.mw

load this Maple code done'nt work!!!

## how do I integrate HeunB function with complex arg...

I am trying to calculate the following integra
r*rr*g1^2*h1^2*f1^2*fh1^2*exp(-2*t)/t

here g1 is a kummerM functin in s, and also h1 is another kummerM function  in ss, and f1 and fh1 are the HeunB functions with complex arguments in r and rr. and t=sqrt((r-rr)^2+(s-ss)^2).I would like to integte over dr drr ds dss

## Why Minus an Integras Sign Places parentheses Arou...

I am using an integal sign using Int. If there is a minus sign in front of it, then

I get the expression -(Int ... dx). Why is the parenthesis there? Can we avoind it?

Thank you!

mapleatha

## Why Does Maple Give Me the Answer Like This?...

Why does Maple give me an answer like this?

How do I force Maple to automatically multiply the exponents in the denominator and eliminate the factor y^2?

Simplify will not do it.

Thank you!

mapleatha

## Getting Rid of _F1, _F2, Etc., in the Solution of...

I am solving a PDE whose solution is the integrating factor MU of a given 1st order ODE. I get

I only need one of these solutions. How do I get rid of _F1? Can I make it to be the identity function? That is exactly what I need.

Thank you, as always!

mapleatha

## Why Doesn't Maple Solve This System?...

I cannot get the answer (m=2,n=2) to the following problem on two equations from Maple 13.

(13/4)*m-(7/4)*n-3 = 0,
-(17/2)*n*2^n +34*m= 0

I get:

{m = (7/13)*RootOf(13*_Z*2^_Z-28*_Z-48)+12/13, n = RootOf(13*_Z*2^_Z-28*_Z-48)}

Thank you very much.

mapleatha

## I try to invert this Matrix and get error...

Way I get this error ?

 >
 >
 >
 (1)
 >
 (2)
 >
 >

## how do i plot a probabilitry function in 3 variabl...

How can i plot a probability function such as cos(x-y)*cos(y-z)*cos^3(x-2z)=0.6 where

x=0..5, y=0..x, z=0..y.

## How do I plot f(x,y,z) = x^3*y*z, constrained to x...

i have a probability function f(x,y,z)=x^3*y*z and constraint on its ranges x<y , y<z. how can i plot it fot f(x,y,z)=0.5

## Shooting method in maple...

Hi

Im going to solve mixing layer boundary layer equation in maple but Its this error: "Error, (in Shoot:-shoot) invalid boundary conditions, must be given at one point"

> restart;
> alias(U = u(x, y), V = v(x, y)); PDE := {diff(U, x)+diff(V, y) = 0, U*(diff(U, x))+V*(diff(U, y))-nu*(diff(U, \$(y, 2))) = 0};
print(output redirected...); # input placeholder
// d   \   / d   \        / d   \     / d   \      / d  / d   \\    \
{ |--- U| + |--- V| = 0, U |--- U| + V |--- U| - nu |--- |--- U|| = 0 }
\\ dx  /   \ dy  /        \ dx  /     \ dy  /      \ dy \ dy  //    /
> simsubs := eta(x, y) = y*sqrt((1/2)*u[0]/(nu*x));
print(output redirected...); # input placeholder
(1/2)
1    (1/2) /u[0]\
eta(x, y) = - y 2      |----|
2          \nu x/
> stream := psi(x, y) = sqrt(2*nu*x*u[0])*f(eta(x, y));
print(output redirected...); # input placeholder
(1/2)            (1/2)
psi(x, y) = 2      (nu x u[0])      f(eta(x, y))
> Usubs := U = diff(rhs(stream), y);
print(output redirected...); # input placeholder
(1/2)            (1/2)                 / d           \
U = 2      (nu x u[0])      D(f)(eta(x, y)) |--- eta(x, y)|
\ dy          /
> Vsubs := V = -(diff(rhs(stream), x));
print(output redirected...); # input placeholder
(1/2)
2      f(eta(x, y)) nu u[0]
V = - ---------------------------
(1/2)
2 (nu x u[0])

(1/2)            (1/2)                 / d           \
- 2      (nu x u[0])      D(f)(eta(x, y)) |--- eta(x, y)|
\ dx          /
> ODE := simplify(subs(Usubs, Vsubs, simsubs, PDE));
print(output redirected...); # input placeholder
/                             /      /           /                 (1/2)\  /
|                  1          |    2 |           |1    (1/2) /u[0]\     |  |1
|0 = 0, - ------------------- |u[0]  |@@(D, 2)(f)|- y 2      |----|     | f|- y
<                        (1/2) \      \           \2          \nu x/     /  \2
|               2 /u[0]\
|         2 nu x  |----|
\                 \nu x/

(1/2)\          (1/2)
(1/2) /u[0]\     |    /u[0]\
2      |----|     | nu |----|      x
\nu x/     /    \nu x/

/                 (1/2)\\\    \
(1/2)            |1    (1/2) /u[0]\     |||    |
+ (nu x u[0])      @@(D, 3)(f)|- y 2      |----|     ||| = 0|
\2          \nu x/     ///     >
|
|
/
> simsubs2 := solve(subs(eta(x, y) = eta, simsubs), {y});
print(output redirected...); # input placeholder
/         (1/2) \
|    eta 2      |
|y = -----------|
<           (1/2) >
|    /u[0]\     |
|    |----|     |
\    \nu x/     /
> ODE := simplify(subs(simsubs2, ODE), symbolic);
print(output redirected...); # input placeholder
/             2                                                 \
|         u[0]  (@@(D, 2)(f)(eta) f(eta) + @@(D, 3)(f)(eta))    |
< 0 = 0, - -------------------------------------------------- = 0 >
|                                2 x                            |
\                                                               /

> shootlib := "C:\\Users/abbas/Desktop/maple9/"; libname := shootlib, libname; with(Shoot);
print(output redirected...); # input placeholder
[shoot]
> FNS := {f(eta), g(eta), h(eta)};
> ODE := {diff(f(eta), eta) = g(eta), diff(g(eta), eta) = h(eta), diff(h(eta), eta) = -f(eta)*h(eta)};
print(output redirected...); # input placeholder
/  d                      d                      d                          \
{ ----- f(eta) = g(eta), ----- g(eta) = h(eta), ----- h(eta) = -f(eta) h(eta) }
\ deta                   deta                   deta                        /
> IC := {f(0) = 0, g(0) = 0, h(0) = beta};
print(output redirected...); # input placeholder
{f(0) = 0, g(0) = 0, h(0) = beta}
> BC := {g(-10.) = 0, g(10.) = 1, limit(eta-f(eta), eta = 10) = 0};
print(output redirected...); # input placeholder
{10 - f(10) = 0, g(-10.) = 0, g(10.) = 1}
> infolevel[shoot] := 1;
print(output redirected...); # input placeholder
1
> S := shoot(ODE, IC, BC, FNS, beta = 0, abserr = 0.5e-6, output = listprocedure, method = taylorseries);
%;
Error, (in Shoot:-shoot) invalid boundary conditions, must be given at one point

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