What Is the Role of u in This Laplace Transform Problem?

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SUMMARY

The discussion centers on the application of the unit step function, denoted as u(t-2), in solving the Laplace transform problem involving the differential equation y'' + 4y' + 4y = (t-2)u(t-2)e^{-(t-2)}. The user has derived the Laplace transform of the left side, resulting in (s+2)^2L(y)(s) = 5s - 1, but seeks guidance on handling the right side. The relevant formula for transforming functions multiplied by the Heaviside step function is L[f(t-a)H(t-a)] = e^{-as}F(s), which is crucial for solving the problem.

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drew1435
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Laplace inital value help!

Homework Statement


y''+4y'+4y=(t-2)u(t-2)exp-(t-2)
y(0)=1 y'(0)=-1

what is the use of this u i have worked the problem to the following


The Attempt at a Solution



(s+2)^2*L(y)(s)= 5s-1 ...

i have no idea how to approach the laplace ot the right side of the equation. some help please.
 
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L[f(t-a)H(t-a)]=e-atF(s).

That will help you.
 

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