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Unformatted text preview: || . Exercise Consider the following two systems of dierential equations: x 1 =-x 1 + e t cos( x 1-x 2 ) x 2 =-x 2 + 15 sin( x 1-x 2 ) , x 1 =-x 1 + x 1 x 2 x 2 =-x 2 . (a) Do they satisfy a global Lipschitz condition? (b) For the second system, are solutions uniquely dened for all possible initial conditions? State Transition Matrix Exercise Let ( t, ) be the state transition matrix of x = A ( t ) x . (a) For nonsingular M ( t ) R n n , determine an expression for d dt M-1 ( t ). (b) Using this result, nd an expression for d d ( t, )....
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- Fall '10