I don't know how to solve the following problem!!

Prove that the general solution of,

is given by

Use this result to solve

Where do I start?? what substitution do I make to make it look like a bessel equation???? Any suggestion?

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- April 29th 2009, 08:30 PMynn6871Bessel Equation
I don't know how to solve the following problem!!

Prove that the general solution of,

is given by

Use this result to solve

Where do I start?? what substitution do I make to make it look like a bessel equation???? Any suggestion? - May 10th 2009, 07:03 AMthe_doc
Firstly I'm assuming you meant a - inplace of the equals sign in the brackets. Also, naturally, I'll assume that , and are all constants.

To do this you simply use the substitution where to transform the equation in terms of , the function and its derivatives wrt . So to start you off you should find that

and, using Leibniz's differentiation of products rule),

.

Further to this you only need to substitute for the derivatives of wrt using:

and .

Assuming your original equation was correct this should do the trick transforming it into the Bessel equation. Hope that helped!