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## Homework Statement

Determine the values of

*r*for which the given differential equation has solutions of the form [itex]y=t^r[/itex] for [itex]t > 0[/itex].

## Homework Equations

[itex]t^2 y'' - 13ty' + 48y = 0[/itex]

## The Attempt at a Solution

The program (online) has a thing that walks me through the question. It first had me find the second and first derivatives of [itex]y=t^r[/itex], which are [itex](r-1)*(r)*(t^{r-2})[/itex] and [itex]rt^{r-1}[/itex], respectively. It then tells me to plug those into the original equation, which gives me [itex](t^2)(r-1)(r)(t^{r-2}) - (13)(t)(r)(t^{r-1}) + (48)(t^r)[/itex]. I can apparently simplify that to [itex]r^2 - 14r + 48 = 0[/itex], but I have no idea how that works. I have not continued with the problem.

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