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Consider the initial value problem 2ty' = 6y, y(1) = 2. a. Find the value of the constant C and the exponent r so that y = Ct" is the solution of this initial value problem. Y 2³ 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. 0 help (inequalities) c. What is the actual interval of existence for the solution (from part a)? 23 help (inequalities)
Consider the first order differential equation a. y(-6)= -3.14. help (inequalities) For each of the initial conditions below, determine the largest interval a < t < b on which the existence and uniqueness theorem for first order linear differential equations guarantees the existence of a unique solution. b. y(-3.5) = -4. help (inequalities) c. y(0) = 0. help (inequalities) d. y(5.5) -3.14. help (inequalities) e. y(14) = -4. t² help (inequalities) t et y = 16 t-7