Consider the initial value problem y?= 8x-y+9;y(0) =2. (you should have found th

Question

Consider the initial value problem y?= 8x-y+9;y(0) =2. (you should have found the exact solution to this in problem 1, but you don?t need that to answer this problem.) Use Euler?s method to find approximate values for y at each of the points x = 0.1, 02, 0.3, and 0.4. Use a step size of h = 0.1. Fill in the values you obtain in the following table (calculate your values at each step to at least eight figures, and then record your answers rounded to four decimal places): Now find approximate values for y at each of the points x = 0.1, 0.2, 0.3, and 0.4 with the smaller step size of h = 0.05 (again, calculate your values at each step to at least eight figures, and then record your answers rounded to four decimal places): Stop and write down your answers in the two tables above; you will need them for the next problem.

Explanation / Answer

Here, x? = 0, y?=-1, and f(x,y) = (x/y). So,
-Yn+1 = yn + hf(xn,yn) = yn + 0.1 (xn/yn), n = 0,1,2,

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