Hello! This is my first post to this excellent forum! I would like some help with this exercise:
u_{xx} (x,y) + u_{yy} (x,y) = 0, with 0 < x < 2 \pi , 0 < y < 4 \pi
u_x (0,y) = 0, \, u_x(2 \pi, y) = 0, \, 0< y < 4 \pi
u(x,0) = a \cos(2x), \, u(x, 4 \pi) = a \cos^3(x), \, 0<x<2\pi...