In this problem you will solve the non-homogeneous differential equation y" + 4y = sec²(2x) Let Cj and C2 be arbitrary constants. The general solution to the related homogeneous differential equation y" + 4y = 0 is the function Yn (x) = C1 y1 (x) + C2 y2(x) = C1 -2cos^2 (2x) +C2 -2sin^2 (2x) help (formulas) Note: The order in which you enter the answers is important; that is, C1f(x) + C29(x) # C19(x) + C2f(x). Therfore put sine before cosine. The particular solution y,(x) to the differential equation y" + 4y = sec²(2x) is of the form y,(x) = y1 (x) u1(x) + Y2(x) u2(x) where u; (x) and u, (x) = help (formulas) It follows that u1 (x) = and u2(x) = help (formulas) Thus y,(x) help (formulas) The most general solution to the non-homogeneous differential equation y" + 4y = sec2(2x) is y = C, +C2 + help (formulas)