(2) Consider the IVP y' : 2:592 , 34(0) : 1 Your task is to approximate the value y(0,5) of the solution at .r : 0.5 using several methods. Starting at ($0, yo) : (0,1), compute the next few steps necessary to get from 17 : 0 to m : 0.5. (a) First, use the classical Euler method (Sec 2.4) with step size 11 : 0.25. (b) Next, use the classical Euler method (Sec 2.4) again but using a smaller step size [1 : 0.1, (c) Finally7 perform the Runge -Kutte method (Sec 2.6) using the same big step size h : 0.25, (d) Since we are learning these numerical methods for the rst time, I purposely picked an IVP whose exact solution we are able to compute using Chapter 1 techniques, and this exact solution is 1 y($) 15:;2' What is the value of the exact solution at a: = 0.5? (e) Rank the four approximations above (from best to worst). What observations can you make