Consider the second order linear ODE (1 − x²)y" — xy + X²y = 0 0 ≤ x ≤ 1/2, - with boundary conditions (a) y(0) = 0 y(1/2) = 0. Demonstrate that this ODE can be rewritten in Sturm-Liouville form: d dy p(x) - + q(x)y — X²r(x)y = 0, dx dx (b) and identify p(x), q(x), and r(x). Characterize this boundary value problem as a regular or singular Sturm-Liouville problem.