The function is called a Bessel function of order 1. Show that it satisfies the differential equation I have tried differentiating the series and plugging in but I cannot get the right answer.
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We can check your computations. Fernando Revilla
May be that a more confortable way is to valuate what are the solution of the DE... (1)
... that can be expressed in the form... (2)
With a little of patience You find that is... (3)
Now You set in (3) and and Youn obtain ...
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