Determine for which values of m the function ∅(x) = xm is a solution to the given equation
a) 3x2y" + 11xy' -3y = 0
b) x2 y" - xy' - 5y = 0
The Attempt at a Solution
I tried approaching this problem by substituting ∅(x) into the question.
a) 3x2(xm)'' + 11x(xm)' - 3(xm) = 0
xm(3x2m2 + 11xm - 3) = 0
I don't know what to do after this step and I'm not sure this is the correct way to do this problem. I just tried doing this because I looked at a similar question and this is how it was approached in the solutions manual.