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## Homework Statement

Let xy''-y'=0. Try a solution of the form y=x

^{r}. Is this a solution for some r? If so, find all such r.

## Homework Equations

xy''-y'=0

y=x

^{r}

## The Attempt at a Solution

The answer I came up with was: r*x-r*x=0, for all r.

But in the solutions it says, "y = x

^{r}is a solution for r = 0 and r = 2."

Is there some reason it would only work for r=0 and r=2?