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

$y^{\text{'}\text{'}}+5y^{\text{'}}-14y=0,y(0)=-2,y^{\text{'}}(0)=-3$

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

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$=0$

Now solve for $Y$ and write the above answer in its partial fraction decomposition, $Y(s)=\frac{A}{s+a}+\frac{B}{s+b}$ where $Y(s)=y(t)=aY(s)=(1)$

$$

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