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