Solving Uxx + Uyy + U = 0 with mixed boundary conditions

[whatwhat1127]

Can't seem to work this out,
any solutions would be greatly appreciated!
Thanks in advance!

Solve the boundary-value problem

Uxx + Uyy + U = 0 , 0<x<1,0<y<1
U(0,y) = 0 , Ux(a,y)= f(y)
U(x,0) = 0 , Uy(x,1)= sin(3*pi*x)

 

[HallsofIvy]

Well, this is your problem and, presumably, you are taking, or have taken, a course in partial differential equations. What have you done on this?

(One's first thought for a problem like this would be to write U as a Fourier series in one of the variables with coefficients in terms of the other but that "U(x, 1)= sin(3pi x)" makes me think the whole Fourier series is not needed. Try U(x,y)= Y(y)sin(3pi x).
Now I will shut up. I have said too much already.)