Consider the initial value problem: 2tyâ²=8y, y(1)=â2. 2tyâ²=8y, y(1)=â2.

Required:
a. Find the value of the constant C and the exponent r so that y=Ct^r is the solution of this initial value problem.
b. Determine the largest interval of the form a < t < b on which the existence and uniqueness theorem for first order linear differential equations guarantees the existence of a unique solution.
c. What is the actual interval of existence for the solution (from part a)?