Euler's Method Question, can't get the right answer?

Question

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Use Euler's method with step size 0.2 to estimate y(1), where y(x) is the solution of the initial-value problem below. Give your answer correct to 4 decimal places.
y' = 1 - xy
y(0) = 0

So, my work is:
y(0) = 0
y(.2) = y(0) + f(0)*.2 = 0 + (1 - .2 * y(0))*.2 = (1 - .2*0)*.2 = .2
y(.4) = y(.2) + f(.2)*.2 = .2 + (1 - .2 * .2) * .2 = .392
y(.6) = y(.4) + f(.4)*.2 = .392 + (1 - .2 * .392) * .2 = .57632
y(.8) = y(.6) + f(.6)*.2 = .57632 + (1 - .2 * .57632) * .2 = .7532672
y(1) = y(.8) + f(.8) *.2 = .7532672  + (1 - .2 * .7532672) * .2 = .923136

But .9231 is not the answer. What have I done wrong?

Thanks a bunch!

O(n) · Accepted Answer

y' = f(x,y(x)) , in this case f(x,y) = 1 - xy

y(0) = 0 => y'(0) = f(0,0) = 1 - 0 = 1

y(0.2) = y(0) + 0.2 * y'(0) = 0 + 0.2 * 1 = 0.2
=> y'(0.2) = 1 - 0.2*0.2 =  0.96

y(0.4) = y(0.2) + 0.2 * y'(0.2) = 0.2 + 0.2 * 0.96 = 0.392
=> y'(0.4) = 1 - 0.4*0.392 = 0.8432

y(0.6) = y(0.4) + 0.2 * y'(0.4) = 0.392 + 0.2 * 0.8432 = 0.56064
=> y'(0.6) = 1 - 0.6*0.56064 = 0.663616

y(0.8) = y(0.6) + 0.2 * y'(0.6) = 0.56064 + 0.2 * 0.663616 = 0.6933632
=> y'(0.8) = 1 - 0.8*0.6933632 = 0.44530944

y(1.0) = y(0.8) + 0.2 * y'(0.8) = 0.6933632 + 0.2 * 0.44530944 = 0.782425088

So, to 4 digits precision, y(1) = 0.7824

Euler's Method Question, can't get the right answer?

1 Answer