Solve the Dirichlet problem in the circle of radius 3 using polar coordinates:
PDE: $\quad \nabla^2 u = u_{rr} + \frac{1}{r} u_r + \frac{1}{r^2} u_{\theta\theta} = 0$ for $0 < r < 3$.
BC: $\quad u(3,\theta) = 6 \sin (8 \theta )$

$u(r,\theta) = {}$
(Write theta for $\theta$)

help (formulas)