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The differential equation t^(2)(d^(2y))/...

The differential equation `t^(2)(d^(2y))/(dt^(2))+alphat.(dy)/(dt)+betay=0` is known as Euler's equation. Show that `y=t^(r )` is a solution of Euler's equation if `r^(2)+(alpha-1)r+beta=0`.

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