Solve the initial value problem using the method of Laplace

Solve the initial value problem using the method of Laplace transforms. Show all work.

y\'\'\'+4y\'\'+y\'-6y=-12
y(0)=1
y\'(0)=4
y\'\'(0)=-2

s^3y+2s^2 -4s-1+4*s^2*y-16*s-4+sy-1-6y=-12/s y(s)=2/s +1/(s-1) +12/(s+2) -17/(s+3) y(t)=2+exp(t)+12*exp(-2t) -17*exp(-3t)

$Solve the initial value problem using the method of Laplace transforms. Show all work. y\'\'\'+4y\'\'+y\'-6y=-12 y(0)=1 y\'(0)=4 y\'\'(0)=-2Solution s^3y+2s^2 -$