Consider the differential equation for which x0 is a singula

Consider the differential equation for which x0 is a singular point: 3xy\'\'+y\'-y=0

a.) Assuming a series solution of the form y=sum_n=0^infinitya_nx^r+n, find th indicial equation and its two roots r₁ and r₂.

b.) Find and simply th recurrance relation for r=r₁. Thrn determin a1, a2 and a3 in tems of a0 and write down the first four terms of the corresponding series solution.

Solution