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6. Find the general solution of the in homogeneous equation 's' Az+5, A G i) F ("). 7. Find the solution of the initial value problem A= (3 i). 5= ("). x(0)= () 8. You may have seen that many functions ran bie wrillen as infinite power series on cortain regions of their dornains, for examples DE - 2 3! I a! - (2k: I - and 20 22 (2k) & (a) Define sin(A) and where A is , square mal.ix. (b) Show that d cos(At) - - Asin(At) (c) Let J, i F R". Show that . is a solution to the differential equation -

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