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## Homework Statement

Determine for which values of m the function ∅(x) = x

^{m}is a solution to the given equation

a) 3x

^{2}y" + 11xy' -3y = 0

b) x

^{2}y" - xy' - 5y = 0

## The Attempt at a Solution

I tried approaching this problem by substituting ∅(x) into the question.

a) 3x

^{2}(x

^{m})'' + 11x(x

^{m})' - 3(x

^{m}) = 0

x

^{m}(3x

^{2}m

^{2}+ 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.