(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

The problem is this:

[tex]y'' - 4y = e^{-t} , y(0) = 1, y'(0) = 0 [/tex]

2. Relevant equations

L{y(t)} = Y(s)

L{y'(t)} = sY(s) - y(0)

L{y''(t)} = s^2Y(s) - sy(0) - y(0)

3. The attempt at a solution

Ok, so I plugged the Laplace transforms for y'' and y into the equation as well as for e^(-t) and got:

[tex]Y(s) = \frac{1}{s(s-4)(s+1)} - \frac{1}{(s-4)} - \frac{4}{4(s+1)}[/tex]

From that point on I would need to perform a partial fraction decomposition on the first term and last term, the middle term is ok. Doing so I get:

[tex]Y(s) = \frac{-1}{4s} + \frac{-1}{20(s-4)} + \frac{1}{5(s+1)}- \frac{1}{(s-1)} + \frac{1}{s} - \frac{1}{(s-4)}[/tex]

However, the book is getting answers with e^(2t). I am not seeing how anything I have in that last line will yield that, so I assume I am doing something wrong.

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# Homework Help: Using Laplace Transforms to Solve DE

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