Hello PF, maybe you can help with this one! I need to show that the Laplace transform of J0(at) is (s^2 + a^2)^-1/2. My prof told me to start with the form: x2y'' + x y' + (x2 + p2)y = 0, where p = 0 ITC. What have I got so far?.... Doing the Laplace transform on both sides, where Y stands for L[y]: x2(s2Y - sy(0) - y'(0)) + x(sY - y(0)) + x2Y = 0, ...then 3 lines of algebra... Y = y(0)* (1 + xs)/(xs2 + s + x) + y'(0)* x/(xs2 + s + x). Do I convolve these two terms on the RHS now? Do I factor the denominator first? Or do I use some recurrence relns for Bessel functions, which is what y(x) is? Your help would be much appreciated!!