Solution 2.9.5.6 Applying the Laplace transform yields s 2 Y (s); sy(0); y [1] (0);4[sY (s); y(0)]+ 5Y (s)=0: Rearranging yields (s 2 ;4s +5)Y (s)=sy(0); 4y(0)+ y [1] (0);; or Y (s)= sy(0); 4y(0)+ y [1] (0) (s; 2; j)(s;2+j) : For the given initial conditions we then have Y (s) = s; 1 (s;2; j)(s;2+j) = M s; 2;j + M  (s;2+j) : M = (s;2+j)Y (s) j s=2+j =  s;1 (s ;2+j)  s=2+j = 1+j j2 = 0:5;j0:5 = q (2)=2 6 ; 45  = p 2=2 6 ;=4r. y(t)=[ p 2e 2t cos(t;=4)]1(t) 1