Let s > 0. (a) Find the solution m(x, e) to the boundary value problem - u

Question:

Let s > 0.
(a) Find the solution m(x, e) to the boundary value problem - u" + e2 u = 1, u(0) = u(l) = 0.
(b) Show that as ∈ -> 0+, the solution u(x. s) -> u.(x) converges uniformly to the solution to - u"= 1, n,(0) = u(1) = 0. This is a special case of a general fact about solutions to a regular perturbation of a boundary value problem, [36],