Solve the differential equation:

Step-by-step explanation:

Considering ordinary point we could use Frobenius method assuming

and consider the series representation given by the method to solve the equation. I think this way is harder.

In your case, It seems to have something to do with Bessel differential equation

that will have the same representation as the Frobenius method. To get the form as we have in the given equation we can substitute and take

Thus,

The solution will have the format

such that

and are constants

And the order of the Bessel equation is

In our case, we can just write