Please answer part f) and show your steps

for part a) I got T''(t) / T(t) - 1 = X''(x) / X(x)

for part e) I got Xn(x) = An*sin(k*x) with k=n*pi

In this problem we will use separation of variables to solve the PDE 2 6t2 65:2 with boundary conditions y(0, t) = y(1, t) = 0. (a) Assume a separable solution y(:r:, t) = X (m)T(t) and plug it into the PDE. Divide both sides by X (:c)T(t) and separate variables so that all the t dependence is on the left and all the 5: dependence is on the right. Put the constant term on the t dependent side. (b) Explain why both sides of the separated equation you found in (a) must equal a constant. (c) Set the 5: side of the separated equation equal to a constant P. Find the general solution to this ODE for two cases: P > 0 and P = 0, and P 0 and P = 0 unless X (1:) = 0. (d) Since P must be negative, set P = k2 and write your solution for X (:3) [using the P