Bessel Differential Equation: General Solution and Derivation of the Neumann Function for Integer Orders

We derive the general solution of the Bessel equation for all orders via the Frobenius method. In particular, for integer orders, we obtain the Bessel function of the second kind (Neumann function), which serves as the second linearly independent solution alongside the Bessel function of the first kind. Finally, it is concluded that the universal general solution is given by the linear combination of both functions.