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

$x^{\text{'}\text{'}}+9x^{\text{'}}=0,x(0)=5,x^{\text{'}}(0)=6$

Using $x$ for the Laplace transform $ofx(t),i.e.,x=L\{x(t)\},$ find the equation you get $by$ taking

the Laplace transform $of$ the differential equation

$=0$

Solve for $x(s)=$

Write the answer $in$ its partial fraction decomposition, $x(s)=\frac{A}{s+a}+\frac{B}{s+b},$ where $x(s)=,+x(t)=a$

$x(s)=,+$

$By$ inverting the transform, find $x(t)=$