[25 points] 2. Consider the differential equation and 2xy"-y'+y=0 (a) show that x=0 is a regular singular point of the differential equation. (b) solve the indicial equation and show that the Frobenius method leads to two independent solutions. What are the two indices? (c) use a Frobenius series expansion to find the two independent solutions, yı(x)=Σanxn n=0 and Y2(x) = bnxn Y2(x)=bnx" n=0 Write out the first four terms of each series in the general solution y(x) = Coy₁(x) + C₁y2(x). Bonus: [5 points] Show that the solution can be written in terms of Bessel functions of the first kind of order 3/2 and 3/2. Use the handouts on the generalized Bessel equation or see Equations 18 and 19 in section 5.3 of your text.