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

priya19

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.

HallsofIvy

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.

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priya19	Lower bound for radius of convergence of series solutions about a given point Tweet 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.

HallsofIvy Recognitions: Gold Member Science Advisor 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.