- #1
jborcher
- 1
- 0
Homework Statement
x d2y(x)/dx2 + dy(x)/dx + 1/4 y(x)
Show that the solution can be obtained in terms of Bessel functions J0.
Homework Equations
Hint: set u = xa where a is not necessarily an integer. Judiciously select a to get y(u).
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.