Consider the differential equation x2y′′+x(1+2N +x)y′+N2y =0, (11.5.41) where N is a positive integer. x2y′′+x(1−x)y′+Nxy=0, (11.5.40) Q.)Show that the change of variables Y =xNy transforms Equation (11.5.41) into the Laguerre differential equation (11.5.40).
Consider the differential equation x2y′′+x(1+2N +x)y′+N2y =0, (11.5.41) where N is a positive integer. x2y′′+x(1−x)y′+Nxy=0, (11.5.40) Q.)Show that the change of variables Y =xNy transforms Equation (11.5.41) into the Laguerre differential equation (11.5.40).
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter11: Differential Equations
Section11.CR: Chapter 11 Review
Problem 16CR
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Consider the differential equation x2y′′+x(1+2N +x)y′+N2y =0, (11.5.41) where N is a positive integer.
x2y′′+x(1−x)y′+Nxy=0, (11.5.40)
Q.)Show that the change of variables Y =xNy transforms Equation (11.5.41) into the Laguerre differential equation (11.5.40).
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