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Question: a x tx1 x1 2 a ftx...

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For which initial value problems can the Fundamental Existence and Uniqueness Theorem 1.1 be applied and for which can it not be applied? Explain your answer. In each case, what do you conclude about the initial value problem?(a) x' = (t-x)-1 , x(-1) = 2

For which to and zo does the Fundamental Existence and Uniqueness Theorem 1.1 apply to the initial value problem -f(t, x), a(to)-, with the four functions f(t, x) below? Explain your answer. What do you conclude from this theorem for such initial points? What do you conclude from this theorem for other initial points?(a) f(t,x) = (9-x2-t2)1/2

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