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?
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!