second order homogenous ode with non-constant coefficients

How do I solve this differential equation?
y''(x)-A*exp(-B*x)*y(x)=0
How to solve it? Not easily, I think. Wolfram Alpha returns this:

. . . . .\(\displaystyle y(x)\, =\, c_1 \, I_0\, \left(\dfrac{2\, \sqrt{A\, e^{-Bx}\,}}{B}\right)\, +\, c_2\, K_0\, \left(\dfrac{2\, \sqrt{A\, e^{-Bx}\,}}{B}\right)\)

. . . . .\(\displaystyle I_n (z)\) is the modified Bessel function of the first kind.
. . . . .\(\displaystyle K_n (z)\) is the modified Bessel function of the second kind.


What generated the original equation? Thank you! ;)
 
Hej!

Thank you for your reply! Yes I also noted Wolframs answer, but I didnt know what I0 etc was. Does this preclude a more 'clean' solution?
I also looked into this method:
http://mathworld.wolfram.com/Second-OrderOrdinaryDifferentialEquation.html
But Im not sure if it is applicable or not....

This differential equation describes the steady-state diffusion equation with an exponentially decaying (in terms of distance) sink.
 
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