Question: 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.

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

1 du

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