Using the method of undetermined coefficients, find a power series solution about $x_0 = 1$ of the equation; $$(4 − x^2)y''− 2xy' + 12y = 0,$$ satisfying the initial conditions: $y(1) = 7, y'(1) = 3.$
I am struggling once I find the ODE in terms of series for $y, y' and y''$ ($y=\Sigma_{n=0}^{\infty}a_r(x-1)^r, y'=...etc)$ to know what to do next to solve the ODE.