# Lower bound for radius of convergence of series solutions about a given point

1. ### priya19

1
without solving the differential equation(cosx)y''+y'+5y =0, find a lower bound for the radius of convergence of power series solutions about x = 0. about x = 1.

2. ### HallsofIvy

40,957
Staff Emeritus
Any solution to that equation will be analytic (and so its Taylor series will converge) as long as the coefficient of y'' is not 0. Find the least distance from 0 (and then 1) to a point where cos(x) is 0.