The assumption is valid because the second order ODE is and its general solution has the form...
... where and are two particular independent solutions, and two 'arbitrary constants'...
I'm studying for power series solution for ODEs and I came over this example:
. And by assuming a power series centered at the ordinary point we're bound to get two equalities:
I went right ahead to continue working the solutions out but I accidently looked at the solution and it shows to sets of calculations: one assuming and another one supposing the opposite.
Can someone explain why is this assumption valid?