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Start by deriving a recurrence relation giving ?? for ? ≥ 2 in terms of ?0...

Start by deriving a recurrence relation giving ?? for ? ≥ 2 in terms of ?0 and ?1 (or both). Then apply the given initial conditions to find the values of ?0 and ?1. Next, determine ?? (in terms of n) and, finally, identify the particular solution in terms of familiar elementary functions.

?′′ − 2?′ + ? = 0; ?(0) = 0, ? ′(0) = 2

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