2. Consider the Mathieu equation x" +(8+&cost)x = 0 (a) Using the small parameter approximation () = 8 +8+82 +... derive the right boundary arising from So= 1/4 and both boundaries arising from 80 = 1 up to second order. Plot your results in the (d, )-plane together with the left curve arising from do = 1/4 and the curve arising from do = 0. (b) Divide the period into 100 small time intervals and on each interval approximate the time-varying matrix of the Mathieu equation with its average. Create a 100-by-100 mesh on the parameter domain = [-1,4], & = [0,5] and for each mesh-point calculate the numerical approximation of the monodromy matrix. Calculate the Floquet multipliers numerically and mark the points on the (d, )-plane where the system is unstable. (c) Repeat part (b) for the damped Mathieu equation x" + Kx'+(8+&COST)x=0 when considering