icefall5
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Homework Statement
Determine the values of r for which the given differential equation has solutions of the form y=t^r for t > 0.
Homework Equations
t^2 y'' - 13ty' + 48y = 0
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 y=t^r, which are (r-1)*(r)*(t^{r-2}) and rt^{r-1}, respectively. It then tells me to plug those into the original equation, which gives me (t^2)(r-1)(r)(t^{r-2}) - (13)(t)(r)(t^{r-1}) + (48)(t^r). I can apparently simplify that to r^2 - 14r + 48 = 0, but I have no idea how that works. I have not continued with the problem.
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