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Name________________________ Student I.D.___________________ Math 2250-4 Quiz 11 Solutions April 13, 2012 1a) Use the methods we've been discussing to find the general solution to the system of differential equations x# t = y# t 0 1 x K6 K5 y . (8 points) 0Kl K6 1 K5 K l 2 = l lC5 C6 = l C5 lC6 = lC3 l =K3 the homogeneous system is 3 1 0 K6 K2 0 l =K2 the homogeneous system is 2 1 0 K6 K3 0 / / 3 1 0 0 0 0 2 1 0 0 0 0 0v= 0v= lC2 1 K3 1 . K2 Thus the general solution is x t y t = c1 eK2 t 1 K2 C c2 eK3 t 1 K3 . 1b) For any solution x t , y t T to the first order system of DEs above, what is the second order differential equation satisfied by x t ? (2 points) The first order system reads x# t = y y# t =K6 x K 5 y . Thus x##= y#=K6 x K 5 y =K6 x K 5 x# . We can also write this DE in the usual form for an unforced undamped mechanical or electrical system x##C 5 x#C 6 x = 0 .