Answer Happy

1. (50+ points) The function y(t) = (Int+21 is a solution to the Initial Value Problem (IVP) ✓=1+ y(1) = 2 on the interval (0,00). (a.) (10 points) Is there a unique solution to the IVP on [1,2]? Justify your answer. Rocall that a correct answer without supporting work may not receive full credit. (6.) (15 points) What is the largest open interval on which there is a unique solution to the IVP? Justify your answer. Recall that a correct answer without supporting work may not receive full credit. (c.) (5 points) Run RKA with h=0.1. What are the first three terms (starting with the coefficient of ") of the Newton polynomial that passes through all points generated via RKA? (d.) (5 points) Plot the polynomial you obtained in the previous item and y(t) = { Inc +2 in the same graph. (e) (5 points) Approximate y(1.2) using Euler's Method with h = 0.1. (.) (5 points) What is the relative error in the previous item? (9) (5 points) Approximate y(1.2) using Euler's Method with h not fixed (your solution is written in terms of h). (h.) (5 points) What is the relative error in the previous item? (6.) (10 points) Give an example of h and n we can choose so that the relative error from the previous item is smaller than 0.01 (which means <1%).