Laplace Transform of a Bessel Equation

1. Mar 6, 2012

wtmoore

Hi guys, I have this question on Laplace transforms, but am not sure how to start it.

The zero order Bessel function Jo(t) satisfies the ordinary differential equation:
tJ''o(t) + J'o(t) + tJo(t) = 0

Take the Laplace transform of this equation and use the properties
of the transform to find the Laplace transform of J0(at) where a is a constant.

Now I can do laplace transforms, but I haven't been given it in this form before, and am not too sure on Bessel functions. I have googled, and am having trouble finding out exactly what J(t) is. I am going to have 3 seperate integrals right? Do you know what Jo(t) is?

Thanks

Last edited: Mar 6, 2012