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
- 2 3! I a! - (2k: I
(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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