(a) Show that any regular second order linear ordinary differential equation
a(x)u" + b(x)u' -I- c(x)u = f(x),
with a (x) ≠ 0, can be placed in Sturm- Liouville form (11.143) by multiplying theequation by a suitable integrating factor qlx).
(b) Use this method to place the following differential equations in Sturm-Liouviile form:
(i) -u´´-2u' + u = ex,
(ii) -x2u" + 2xu' + 3u = 1,
(iii) xu" -t- (1 - x)u' + u -0.
(c) In each case, write down a minimization principle that characterizes the solutions to the Dirichlet boundary value problem on the interval [1,2],