- #1
Ithryndil
- 142
- 0
Homework Statement
The problem is this:
[tex]y'' - 4y = e^{-t} , y(0) = 1, y'(0) = 0 [/tex]
Homework Equations
L{y(t)} = Y(s)
L{y'(t)} = sY(s) - y(0)
L{y''(t)} = s^2Y(s) - sy(0) - y(0)
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.