Show that if f(t) is a periodic function of period 2 and Show also that, when

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Show that if f(t) is a periodic function of period 2π and

then f(1) = [t [(2n-1) (0

Show also that, when ω is not an integer,

1 202 (1-cost) y = 4 10 cos(2n +1)t - cos cot (2n +1)[w (2n + 1)]

satisfies the differential equation

dy dr + wy = f(t)

subject to the initial conditions y = dy/dt = 0 at t = 0.

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