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## Homework Statement

Differential equation:

[tex] \frac{d^2x}{dt^2}+4\frac{dx}{dt}+4x=6e^{-2t} [/tex]

with initial conditions [tex] x(0)=-2 and \frac{dx}{dt}(0)=8 [/tex]

Use the laplace transform to solve for x(t)

## Homework Equations

http://www.atp.ruhr-uni-bochum.de/rt1/syscontrol/node9.html

Laplace transform theorems

## The Attempt at a Solution

Taking Laplace transform results:

[tex] {s^2X(s)-sx(0-)-f(0-)}+4{sX(s)-f(0-)}+{4X(s)}=6X(s+2) [/tex]

I am not sure about this but I *think* its right, the e term worries me a bit?????

Normally I would just throw the initial conditions in here but I have a differential initial condition - not sure what to do with it?

This is for an intro control systems course so I may be missing something very easy??

Thanks