[3+12+15=30] a) Explain a Sturm-Liouville problem. b) Expand the function f(x)=ex in terms of the eigenfunctions of the Sturm-Liouville problem yn+y=0(1) with boundary conditions: y(0)=0(2); and y()=0(3). c) Consider a diffusive-reactive system of a species B, which gets produced when A reacts. AB is an elementary first order reaction with specific rate constant for production of B being kB. Using the eigenfunctions of CB+kBCB=0CB(0)=0CB(1)=0 (3) expand the function CB(x)=1