Second order DE, reduction of order method?

[ProPatto16]

Homework Statement

find general solution of x²y''-xy'-3y=0

Homework Equations

two solutions are given, y1=1/x and y2=x³

The Attempt at a Solution

i think this is a reduction of order question? the only theory i can find in my text for second order DE relates to constant coefficients, and obvioulsy these ones arent. anyone have some method for reduction of order? or am i going about this the wrong way?

thanks

 

[ProPatto16]

hold up... by superposition of homogeneous equations...

with y1 and y2 solutions, then a general solution would just be y=c1(1/x)+c2(x^3) ??

but that seems too easy...