General solution of $y''-2xy'+2y=0$ I have to find the general solution of the differential equation $$y''-2xy'+2y=0.$$ An obvious solution is $y(x)=ax$ but I am unable to find another solution. Any hint as to how to proceed or which kind of method to apply is greatly appreciated.

Making $z = x y$ we obtain
$$
z''-\frac{2(x^2-1)}{x}z' = 0
$$
now making $v = z'$
$$
v'-\frac{2(x^2-1)}{x}v = 0
$$
which is separable.
