Uppgift 5

Lös randvärdesproblemet

$$u_{xx}+u_{yy}=0,\qquad 0<x<a,\ 0<y<b\mathpunct{,}$$

$$u_x(0,y)=u_x(a,y)=0,\qquad u(x,0)=0,\qquad u(x,b)=1+\cos\frac{\pi x}{a}\mathpunct{.}$$