Question

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

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

Added by Melissa S.

Calculus: Early Transcendentals
Calculus: Early Transcendentals
James Stewart 8th Edition
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Without actually solving the differential equation (cos x)y'' + y' + 5y = 0, find a lower bound for the radius of convergence of power series solutions about x = 0 and x = 1.
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Transcript

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00:01 X y double dash plus y dash plus y -dash plus y -dice plus y -y equals zero given equation if x equal x -not is an ordinary point of the differential equation then the corresponding power series power series has the minimum radius of convergence convergence given by r and it is defined as mod of x minus x not less than r where r is the distance from x not to the closest singular point then evaluating the coefficient of y double dash to find the singular points where cos x equal zero then x will be equals to pi by two or minus pi by 2...
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