Consider the initial value problem for function $$y$,$

$10+21=45,(0)=0,(0)=0.$y$10$y$+21$y$=4$e$5$t$,$y$(0)=0,$y$(0)=0.$

$($a$)$ Find the Laplace Transform $()=[()]$F$($s$)=$L$[$f$($t$)],$ where $()$f$($t$)$ is the right$-$hand side of the differential equation.

$()=$F$($s$)=$

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$($b$)$ Find the Laplace Transform of the solution, $()=[()]$Y$($s$)=$L$[$y$($t$)].$

$()=$Y$($s$)=$

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Note: You do not need to solve for $()$y$($t$).$