1. The problem statement, all variables and given/known data x d2y(x)/dx2 + dy(x)/dx + 1/4 y(x) Show that the solution can be obtained in terms of Bessel functions J0. 2. Relevant equations Hint: set u = xa where a is not necessarily an integer. Judiciously select a to get y(u). 3. The attempt at a solution I tried just straight pluggin in x=u1/a and ended up with the following form for the diff eq: u2 d2y(u)/du2 + (1-a)/a u1-a-1 dy(u)/du + (1-a)/4a2 y(u) = 0 I've hit a wall here, this doesn't match the Bessel Equation (though I am pretty sure it is not supposed to). I am unsure how to select a in order to get a solution with J0. I tried another approach where I followed the various differentiation rules for Bessel functions and obtained the following: -x J0(x) + 1/4 J0(x) = 0 Again I have hit a wall and am not sure how I should proceed.