For each the following boundary value problems,
(i) write down a minimization principle, carefully specifying the space of functions, and
(ii) find the solution:
a. -u" = cosx, u(0) = 1, u(Ï€) = -2
b.

u(1) = 1
c. ex(u" + u') = 1, u(0) = 1, u(1) =0
d. xu" + 2u' = 1 - x, u(l) = -1, u(3) = 2