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Question 1. Consider the nonhomogeneous system y' = A(t)y + g(t) where the coefficient matrix A(t) and the forcing vector g(t) are continuous and periodic in t of the same period ω > 0. Prove that this system has a periodic solution of period ω if and only if the homogeneous system y' = A(t)y has no periodic solution of period ω except the trivial solution y == 0.
Question 2. Determine if the zero solution of y'' + 2y' + y = 0 is stable, asymptotically stable or unstable. (Hint: Convert the DE into a first order system.)
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The questions were from differential equations. They had to be studied for stability using eigen value concept.
Please please help me get a good grade in that make it logically sand mathematically. Hint: Convert the DE into a first order system.) Prove that this system has a periodic solution of period
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