Given the differential equation

$y^{\text{'}\text{'}}+9y=7e^{-7t},y(0)=0,y^{\text{'}}(0)=0$

Apply the Laplace Transform and solve for $Y(s)=L\{y\}$

$Y(s)=$

Now solve the IVP $by$ using the inverse Laplace Transform $y(t)=L^{-1}\{Y(s)\}$

$y(t)=$