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?

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Nice Laplace Transform

**Physics Forums | Science Articles, Homework Help, Discussion**