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How to get a step by step solution of an ODE in Wolfram Alpha pro?

Posted 11 years ago
Dear members,
I would like to solve the following differential equation with the help of WolframAlpha Pro, it gives me the final solution but it could not give me the step by step solution.
Would you please help me how can I access to the step by step solution for this equation:

y''(x)+y'(x)/b-a*exp(-x/b)*y(x)=0

Note: a and b are constant parameters

Thanks in advance,
Saeid
POSTED BY: Saeid nik
Covering the method of solving this is probably well beyond what could be presented in a small step-by-step solutions window.

You mean to derive both of these are independant solutions:
-Sqrt[a] b Sqrt[E^(-(x/b))] BesselI[1, 2 Sqrt[a] b Sqrt[E^(-(x/b))]]
Sqrt[a] b Sqrt[E^(-(x/b))]BesselK[1, 2 Sqrt[a] b Sqrt[E^(-(x/b))]]

Are you familiar with BesselI and BesselK? Understanding the differential equations behind these special functions would be where I start. 
POSTED BY: Sean Clarke
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