You have the Bessel function of the first kind

The first derivative is

Analogously, the second derivative is

Plugging those in in the equation you will get

All you need to do now is multiply out the x^2-1 on the third series, equate the summing ranges for all three series (you will have to take out the first 2 terms of the first two series) and then you should get some cancellation and eventually 0.