Transform the differential equation

$6$y$^(\text{'}\text{'}\text{'})+50$y$^(\text{'}\text{'})-54$y$^(\text{'})-450$y$=8$e$^(-7$t$)$

y$(0)=0$

y$^(\text{'})(0)=0$

y$^(\text{'}\text{'})(0)=1$

into an algebraic equation by taking the Laplace transform of each side. Use Y for the Laplace transform of

Y$=$

$=,(1)/($s$-3)+-(1)/($s$+3)+-(1)/($s$+7)$

Taking the inverse Laplace transform we get

y$=$

Note: You can earn partial credit on this

problem.