(Solved): The point x=0 is a regular singular point of the given differential equation. Find the recursive re ...

The point $x=0$ is a regular singular point of the given differential equation. Find the recursive relation for the series solution of the DE below. Show the substitution and all the steps to obtain the recursive relation. Do not solve the equation for $y=y(x)$ $2x^2{y}^{??}?x{y}^{?}+(1+x)y=0$ a. $C_k=\frac{1}{((r+k?1)(2k+2r?1)}{C}_{k?1},k?1$ b. $C_k=?\frac{1}{(k+r)(2k+2r?1)}{C}_{k?2},k?2$ c. $C_k=\frac{1}{k+r}{C}_{k?1},k?1$ d. $C_k=?\frac{k+r}{(k+r{)}^2+5(k+r)}{C}_{k?1},k?1$ e. $C_k=?\frac{1}{(k+r{)}^2?2(k+r)?8}{C}_{k?2},k?2$