Consider the initial value problem $$2 t y^{\,\prime} = 4 y, \ \ \ y(1) = -2.$$

1. Find the value of the constant $C$ and the exponent $r$ so that $y = C t^r$ is the solution of this initial value problem.
   $y =$ help (formulas)
   
   
2. 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)
   
   
3. What is the actual interval of existence for the solution (from part a)?
   help (inequalities)