I hope somebody's up tonight, this is due in the morning and I'm so close.(adsbygoogle = window.adsbygoogle || []).push({});

So I was assigned to solve this differential equation using laplace transforms and although I (think I) can solve it, I'm not getting the same answer that Maple spits out.

The DE is:

[tex]x'' + 2x' + 5x = 3e^{-t}cos(2t); x(0) = x'(0) = 1[/tex]

Let L(x) = Laplace(x)

So here's my work:

Take the Laplace of everything

[tex]L(x'')+2L(x')+5L(x) = 3L(e^{-t}cos(2t))[/tex]

Becomes:

[tex]s^2L(x)-s(1)-(1)+2sL(x)+2(1)+5L(x)=3L(e^{-t}cos(2t))[/tex]

Let L(x) = X

[tex]X(s^2+2s+5)-s+1=\frac{3(s+1)}{(s+1)^2+4}[/tex]

I solved for X, simplified and broke it into partial fractions to figure out the Inverse Laplase but got the wrong answer. Is there anywhere I messed up in what you can see?

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# Nice Laplace Transform

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