From the existence theorems for power series solutions, we know that the initial value problem (x-4)y' +y=0, y(0)=3, has a solution of the form 00 y=ak xk on an open interval (-R,R) of length equal to twice the radius of convergence. Fill in the answers below. k=0 Write the recursion formula for ak+1 = Find the value of ao = Find the radius of convergence R= Express y as an elementary function of x: y= , k≥ 1.

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