# differential equation solved by Laplace transform

Submitted by Structure on Sun, 10/19/2008 - 21:19.We solve the differential equation

with initial condition

where

We have

We have

We have from convolution theorem

# Linear trigonometric equation

Submitted by Structure on Wed, 09/24/2008 - 06:18.We solve the equation

where and .

Then we can write

There is a unique such as

and

.

so we can write

or

Now, if

we have a countable set of solutions