Consider the initial value problem 2ty' = 8y, y(-1) = 2. a. Find the value of...

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Consider the initial value problem 2ty' = 8y, y(-1) = 2. a. Find the value of the constant C and the exponent r so that y Ct" is %3D the solution of this initial value problem. y =t' help (formulas) 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. help (inequalities) c. What is the actual interval of existence for the solution (from part a)? help (inequalities) Consider the initial value problem 2ty' = 8y, y(-1) = 2. a. Find the value of the constant C and the exponent r so that y Ct" is %3D the solution of this initial value problem. y =t' help (formulas) 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. help (inequalities) c. What is the actual interval of existence for the solution (from part a)? help (inequalities)