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MEM33
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Homework Statement
Solve the differential equation using laplace transforms. Assume zero intial conditions and that the forcing functions are zero prior to t=0
x''(t) + 6x'(t) +8x(t)=sin3t
Homework Equations
The Attempt at a Solution
I took the laplace transform which I found to be after simplyfing
X(s)=-8s^2-57/(s^2+3^2)(s^2+6s)
after partial fraction decompistion and comparing coeffcients I found these equations
0=a+b+c+d
-8=6a+6b+6c
0= 9c
-57=54c+9d
When I plug that into Ax=b it gives me free variables. i am not sure if my logic is wrong or I just made some mistakes along the way. Any help would be gratly appreciated.
MEM33