Use the Laplace transform to solve the following initial value problem:

$y^{\text{'}\text{'}}5y^{\text{'}}-6y=0,y(0)=-2,y^{\text{'}}(0)=-2$

a$.$ First, using $Y$ for the Laplace transform of $y(t),$ i$.$e$.,Y=L\{y(t)\},$ find the equation you get by taking the Laplace transform of the differential equation

$=0$

b$.$ Now solve for

$Y(s)=\frac{-2s-12}{s^{2}5s-6}$

c$.$ Write the above answer in its partial fraction decomposition,

$y(t)=Y(s)=\frac{A}{sa}\frac{B}{sb}$ where $a$

$d.$ Now $by$ inverting the transform, find $y(t)=$