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
y(1) = ____ ?
... help, this is what i've done but got the wrong answer..
h = 0.2
x0 = 0
y0 = 0
F(x,y) = 1-xy
y1 = y0 + hF(x0,y0)
= 0 + 0.2(1-(0)(0)) = 0.2
y2 = y1 + hF(x1,y1)
= 0.2 + 0.2(1-(0.2)(0.2)) = 0.392
y3 = y2 + hF(x2,y2)
= 0.392 + 0.2(1-(0.4)(0.392)) = 0.5606
y4 = y3 + hF(x3,y3)
= 0.5606 + 0.2(1-(0.6)(0.5606)) = 0.6934
y5 = y4 + hF(x4,y4)
= 0.6934 + 0.2(1-(0.8)(0.6934)) = 0.7824
y6 = y5 + hF(x5,y5)
= 0.7824 + 0.2(1-(1.0)(0.7824)) = 0.8259
...my answer was 0.8259, which was wrong. please show me what i'm doing wrong? thanks!
y5 is the estimate for y(1), not y6:
y5 = 1528174/1953125 = 0.782425088
The exact answer involves the error function of imaginary argument and is to 30 significant figures:
0.724778459007076331818227967606
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