Solve the given initial value problem.

y double prime plus $2$ y prime plus yequals$0$;

$$

$$y$(0)$equals$3,$

$$

y prime left parenthesis $0$ right parenthesisequalsnegative $2$

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Part $1$

What is the auxiliary equation associated with the given differential$$ equation?

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$($Type an equation using r as the$$ variable.$)$