# Use six decimal digits with rounding in calculations. : Solve the following problem with the fourth-order RK method: d²y dy 2 + 3 + 3.125y

Use six decimal digits with rounding in calculations. : Solve the following problem with the fourth-order RK method:
d²y
dy
2
+ 3
+ 3.125y = sin x
dx?
dx
where y(0) = 5 and y'(0) = 3. Solve from x = 0 to 5 with h = 0.5.
Find the error considering the exact solution is
y(x) = e
075* (5.292237 cos x+ 6.859589 sin x)-0.292237 cos x+0.109589 sin x
%3D
Display the analytical and numerical results on the same graph.

(550 words)

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