Sturm-Liouville theorem states that for ODE of the following form (p(x)y')' + [q(x) + Aw(x)]y = 0 Suppose ym(x) and yn(x) are solutions satisfying certain boundary condition to this ODE with corresponding eigen value 2m and n. (You can think of m and n are indices to label eigenvalues.) (a) (20%) Find the solution to the Sturm-Liouville type ODE (y')' + 2y = 0 with the boundary condition y(0) =0 and y'(a)=0 and their corresponding eigen values. (b) (20%) Find the solution to the Sturm-Liouville type ODE (y')' + 2y = 0 with the boundary condition y(0) =0 and y'(1)+y(1)=0 and their corresponding lowest eigen values. You need to find precise numerical value with one decimal digit. Hint: In this case, you cannot find exact value for eigen values without numerical method. So all you need is to find an algebra equation that determines the eigen value. Then solve it with calculator.