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ind a differential equation that relates the output voltage, vo$($t$),$ to the input voltage vi$($t$).$

$($b$)$ Find vo$($t$)$ for t $>0$ when Vi$($t$)=$ e$3$tu$($t$),$ and the initial voltage across the capacitor and

initial current through the inductor are vo$(0)=1$ V and i$(0)=1$ A$,$ respectively