4x^2 y′′ + 8 x y′ − 3 y = 0 , x > 0

y(4) = 8, y′ (4) = 0

So far I've only seen characteristic solutions being solved via reduction of order but I'm not so sure about equations that include variable coefficients and in which Y1 and Y2 subsets of the general solution Y are not given.....a quick clarification on this would be much appreciated! Thanks!