Please help solve this Laplace Equation Problem.

\f(a) Use separation of variables to write down the two ODE's that need to be solved. Include their boundary conditions. (b) Solve the (IDES and nd the eigenvalues. (e) Write down the solution to the PDE. (d) Let HI) = :r:(l:r) for :t' E (0, l) with x) = f(:r} for :t' E (1.0) and x) = He: + 2). Find the Fourier series for f. (e) Use your answer to parts 03) and (e) to nd the solution to g + $ = n x e (0.1) lthy) = 0 = 1414;} y E {0,1} 143.0} = r) 141:,\" = at} (f ) Use your answer to the previous part to nd the solution to $+3=0 $6 (0.1) \"(0'3\" = -.f(y) y E (0', 1) u(1.y}= f(y) \"(3am = f{.'1') 143,1): HI)