# Bessel Function as Solutions of ODE

I have encountered Bessel functions in the context of Partial Differential Equations. It is supposed that Bessel functions are also the solutions of the Ordinary differential Equation: $$x^2y''+xy'+(x^2-\alpha^2)y=0$$ But I don't know how to deduce from this equation the Bessel functions. Of course I could just prove that they satisfy the equation therefore they are solutions, but I'm interested in seeing how they can be obtained by solving de ODE.

Thanks a lot