Question: Write down all solutions to the following boundary value problems. Label your answer as (i) Unique solution, (ii) No solution, (iii) Infinitely many solutions. (a)

Write down all solutions to the following boundary value problems. Label your answer as
(i) Unique solution,
(ii) No solution,
(iii) Infinitely many solutions.
(a) u" + 2u = 2a, u(0) = 0, u(π) = 0
(b) u" + 4u = cos x, u(-π) = 0, u(π) = 1
(c) u" - 2u' + u = x - 2, u(0) = -1, u(1) = 1
(d) u" + 2u' + 2u = 1, u(0) = 1/2, u(π) = 1/2
(e) u" - 3u' + 2u = 4x, u(0) = 0, u(1) = 0
(f) x2u" + xu' - u = 0, u(0) = 1, u(1) = 0
(g) x2u" - 6u = 0, u(1) = 1, u(2) = -1
(h) x2u" - 2xu′ + 2u = 0, u(0) = 0, u(1) = 1

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