Question: Question 6. Find a solution of thy (t ) + ty' (t) + y(t) = f(t) with y(1) = 1 and y'(1) = 2. Question

Question 6. Find a solution of thy" (t ) + ty' (t) + y(t) = f(t) with y(1) = 1 and y'(1) = 2. Question 7. Let f(x) be smooth and suppose f(0) = 0 and Df (0) = A is 'negative definite' in the sense that there is some o > 0 such that (Ar) . r S o for all ax = 1. (i). Show for small & > 0 that Be := {x e R" : (x| 0 such that (g(x)| 0 (small) such that if To 0 as t -> co.\f

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