Please help with this question only the last part

Find the solution to the initial value problem: x" + 4x = (u+2)cos ut x(0) = 0 x'(0) = 0 x(t) = Write x(t) as a product of two sines, one with the beat (slow) frequency (u - 2)/2 , and the other with the carrier (fast) frequency (u+ 2)/2 . x(t) = The solution x(t) is really a function of two variables t and u . Compute the limit of x(t,#) as u approaches 2 (your answer should be a function of t). lim x(t,") = 4 - 2 Define y(t) = lim x(t,() Now let u approach 2 in the differential equation satisfied by x(t) to find a differential equation that y(t) satisfies. H - 2 y