Extraordinary Differential Equations #12

Calculus Level 4

Consider the differential equation on a series of cosine functions involving \(y=y(x)\): \[\frac{dy}{dx}=\sum_{k=1}^{2017} k\cos{((2k-1)y)}\] where \(y(0)=\dfrac{\pi}{2}\). Determine the value of \(\dfrac{y(2017)}{\pi}\).


This problem is part of the set Extraordinary Differential Equations.
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