Question

hi, i already got the fourier series for f(x) = x where -pi/2 =< x =< pi/2
which is f(x) = sigma, n=1 to infinity ( (-1)^n+1*sin (2nx) / n )

in order to find particular solution for y'' + 4y = f(x)
i have to equate with with y(x)_p = A0 + sigma, n=1 to infinity (An*cos(2nx) + Bn*sin(2nx))

and i get y(x)_p = sigma, n=1 to infinity ( (-1)^n+1 (sin(2nx) ) / 4n(1-n^2) ) which is the correct answer. but this is not valid if n = 1.

so is anyone can show me how to get particular solution for n = 1. i already equate with
y_p = axcos 2x + bxsin x but i didnt get the answer

the correct answer for n=