(a) Seek power series solutions of the given differential equation about the given point \(x_0\), find the recurrence relation.

(b) Find the first tour terms in each of two solutions \(\displaystyle{y}_{{{1}}}{\quad\text{and}\quad}{y}_{{{2}}}\) (unless the series terminates sooner).

(c) By evaluating the Wronskian \(\displaystyle{W}{\left({y}_{{{1}}}{y}_{{{2}}}\right)}{\left({x}_{{{0}}}\right)}\), show that \(\displaystyle{y}_{{{1}}}{\quad\text{and}\quad}{y}_{{{2}}}\) form a fundamental set of solutions.

(d) It possible, find the general term in each solution \(\displaystyle{\left({1}+{x}^{{{2}}}\right)}{y}\text{}{4}{x}{y}'+{6}{y}={0},{x}_{{{0}}}={0}\)