Question: Let f(t) = sgn(t)t , t E [-n, x], have period 2n. (a) Find its Fourier series f(t) = c+ Zn= (an cos(nt) + bn

Let f(t) = sgn(t)t , t E [-n, x], have period
2n. (a) Find its Fourier series f(t) = c+ Zn= (an cos(nt)

Let f(t) = sgn(t)t , t E [-n, x], have period 2n. (a) Find its Fourier series f(t) = c+ Zn= (an cos(nt) + bn sin(nt)) , giving your answer for the coefficients (b) Hence find the particular solution yo of the ordinary differential equation dy dt - y = f(t) Give your answer in the form yp = a+ Z(Bn cos(nt) + yn sin(nt))

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