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## Homework Statement

Use Laplace transform to the system:

[itex] \frac{dy}{dt} + 6y = \frac{dx}{dt}3x - \frac{dx}{dt} = 2\frac{dy}{dt} [/itex]

[itex] x(0) = 2 ; y(0) = 3 [/itex]

## The Attempt at a Solution

I've tried everything on this one. I first solved [itex] \frac{dy}{dt} + 6y = 2\frac{dy}{dt} [/itex] and I got [itex] y = 3e^{6t} [/itex].

Next I tried writing it:

[itex] 36e^{6t} = 3 \frac{d}{dt}(\frac{x^2}{2}) - \frac{dx}{dt} [/itex] so that I could use the identity of the laplace transform of derivatives. That still leaves me with trying to find the transform of x

^{2}(t)...

So then I tried

[itex] 36e^{6t} dt = 3x - 1 dx [/itex]

and integrating, but this brings me to the same problem.

I can't either figure out how to solve it without using laplace transform, so I'm really stuck. What am I doing wrong???

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