Consider the following first order differential equation. Let $y={\displaystyle \underset{n=0}{\overset{}{}}}{a}_n{x}^n$ be a power series solution in $x$ to the equation.

$y^{\text{'}}-3y=0,y(0)=4$

a$)$ Find the general coefficient $a_n$ of the power series of the solution $y$ in terms of $n.$

$a_n=$

b$)$ Calculate the radius of convergence $($use oo if the radius is infinite$).$

$R=$

c$)$ Express the solution in terms of familiar elementary functions.

$y(x)=$

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