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2. Let y' (9:) = an, y}, with a S r S b and Me) = yo be a given rst order dilferential equation. Divide b a the interval [(1,3)] into n subintervals [rt-0,31], [rt-1,32], ..., [rc_1,:c,,] of length h = each. It is assumed that a = so and b = on. An approximate solution of the differential equation is a table, like the one below, consisting of approximate values of y at the selected points are. $0 501 $2 "' xi 3H1 "' 3n 9'0 9'1 9'2 ' " 3;.- MM. ' ' ' yn Euler's method uses the straight line segment through (32;, m) with slope f(s:,:, m) to approximate the graph of y between $1 and 3,-4.1. (a) Derive the equation ye+1 = 3!\" + hf(33e:yel called the Euler formula with step size h. (b) You are given the differential equation y'(m) = E + 21 y(2] = 1 on the interval [2, 3]. Determine 331 an approximate solution of the equation using the Euler formula with step size )1 = 0.2. You are required to write down the details leading to your approximate values