(Solution) - a Show that for arbitrary a 0 y -(2025 Original AI-Free Solution)

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Academic Level: Undergrad. (yrs 3-4)

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(a) Show that for arbitrary a ? 0, y' = y has infinitely many solutions that can be written
y(t) = e(t-a)
(b) Show that for arbitrary a ? 0, the IVP s' = 2?S, s(0) = 0, has infinitely many solutions

(c) Sketch the similar graphs of the two families in (a) and (b). Explain in terms of uniqueness where and why they differ.