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## Homework Statement

a rectangular plate (15 x 30) with the following boundary conditions:

u_y(x,0) = 0

u_y(x,30) = 0

u_x(0,y) = 0

u_x(15,y) = y(20-y)

the derivative B.Cs describe the heat flux through the boundaries.

solve the the steady-state temp u(x,t)

## Homework Equations

steady-state: [tex]\nabla[/tex]^2 * u =0

## The Attempt at a Solution

I set u(x,y)=F(x)G(y)

with the BCs, I got

G'(0)=0

G'(30)=0

F'(0)=0

F'(15)=y(20-y)

let F=A*cos(px) + B*sin(px)

F'(0)=0; so B=0

F'(15)=-A*sin(15*p)=y(20-y)

this is where I got stock.

How can I solve for 'p' or A with the B.C. that has 'y' in there?

Am I doing the right thing?

Thank you very much!