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Diff Eq 7.3

 

<== Differential Equations
Number Question Answer
See the work
1. Find the inverse Laplace Transform of
rac{8 s - 105}{s^2-12 s+57}

y(t)= .

The work
2. Use the Laplace transform to solve the following initial value problem:
y'' +8 y' + 16 y= 0 \hspace{0.5in} y(0)=-6, \; y'(0)=2

First, using Y for the Laplace transform of y(t), i.e., Y = \mathcal{L} \lbrace y(t) 
brace,
find the equation you get by taking the Laplace transform of the differential equation
=0

Now solve for Y(s) =
and write the above answer in its partial fraction decomposition, Y(s) = rac{A}{s+a}+rac{B}{(s+a)^2}
Y(s) = +

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

Y(s) =
Y(s) =        
y(t)=
The work
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