Consider the initial value problem given below. 1 y'= -3y, Y0)=4 h Show that when Euler's method is used to approximate the solution to this initial value problem at x =7, then the approximation with step size h is 4[1 - 3] Apply one iteration of Euler's method in order to write the next term y,, , 4 in terms of x,,, y,,, and h, as needed. v yn+1 = 1 Substitute in f(x,,y,)= = 3n into the previous form. yn+1 = Use this recursive relationship to write a term k steps in the future y,, . in terms of x;,, y,,, h, and k, as needed. Yn+k = For the approximation in question, write the number of steps that are needed in terms of the step size h. k= |~ h Thus, the approximation k = steps after y, = is 4[1 - 5} |~ Apply one iteration of Euler's method in order to write the next term y + ; in terms of X,, y, , and h, as needed. Yn+1= Substitu the previous form. Yn+1= Yo + h Use this write a term k steps in the future y + k in terms of *. y, . h, and k, as needed. In +f (*n. yn ) Yn+ k = For the Yn * hf (*n. Yn) write the number of steps that are needed in terms of the step size h. k= hf (*n )n) Yn + hf (X . )n) Thus, th ps after yo = is 4 1- Yn "(* Yn )