Given the second-order linear homogeneous ordinary differential equa- tion with variable coefficients dạy d.x2 2.0 (1 – 2:2) d?y dy +m(m+1)y = 0, MER, 0, dc use y(x) = ananth to obtain n=0 8 P}(k)aoxk-2 + P3(k)a1.mk-1 + branth - 0, n=0 - where Pi} (k), P2 (k) are polynomials of degree 2 to be determined. Find the roots of the polynomial equation P) (k) = 0 and comment on the coefficients ao and a, in light of the smaller one of these two roots. Next, using the smaller root, establish an explicit expression for the general term bn, and thus derive a recurrence relation between an+2 and an Finally, using the recurrence relation you have found above, obtain the first three terms of two linearly independent series solutions in their simplest form, one with even and one with odd powers of x.