# Homework Help: Laplace much?

1. Jul 21, 2008

### silvrstring

Hello everyone.

I think Pierre-Simon Laplace is alive and well and he is trying to kill me, or drive me mad. I am trying to solve the attached problem. It is a differential equation---D2x+Dx-2*x=5*e^(-t)*sin(t). I have repeatedly tried to solve this problem. I don't like asking for help with homework, but I desperately want to know what I am doing wrong. I would like to think that the book has the wrong answer (it has happened before). Unfortunately, I don't have access to my MATLab, right now---I don't know why. So, I can't check it.

The problem, and one of my several attempts at the solution, are attached. I hope you can help me see my error(s).

#### Attached Files:

• ###### Laplace5.jpg
File size:
24.5 KB
Views:
104
Last edited: Jul 21, 2008
2. Jul 22, 2008

### CompuChip

Unfortunately I can't see the attachment yet. But generally one would first solve the homogeneous problem and try to find a particular solution.
The homogeneous problem is
$$x''(t) + x'(t) - 2 x(t) = 0$$
so the standard approach is plugging in $x = e^{\lambda t}$ as a trial solution.
For the inhomogeneous problem, you have something with trig functions, so I'd try plugging in $x = \left[ A cos(t) + B sin(t) \right] e^{-t}$ and try to solve for A and B to find a particular solution.

Otherwise, I'm waiting for the attachment to be approved :)

3. Jul 22, 2008

### Defennder

I got the same answer you did. Seems like there's something wrong with the book's answer. By the way, being lazy, I used the online calculators at wims:
http://wims.unice.fr/wims/

4. Jul 22, 2008

### silvrstring

Welp, the book was wrong. The written answer is correct. Thanks for responding, though.
I'll check out the wims calculator Defennder. Thanks for the tip.

Share this great discussion with others via Reddit, Google+, Twitter, or Facebook