Final answer:
To find the minimum radius of convergence R of power series solutions about the ordinary point x = 0 without solving the given differential equation, we can use the ratio test.
Step-by-step explanation:
To find the minimum radius of convergence R of power series solutions about the ordinary point x = 0 without solving the given differential equation, we can use the ratio test.
The ratio test states that if R is the radius of convergence of a power series, then the limit:
lim |an+1/an| as n approaches infinity, exists and is equal to L. The radius of convergence R is then given by R = 1/L.
By applying the ratio test to the given power series, we can determine the value of L, and hence the minimum radius of convergence R.