2. Consider an ODE of the form: x2y′′+axy′+by=0 with given constants a and b and unknown solution y(x). Assuming that y(x) follows the form y=xm For each solution listed below, determine the corresponding roots of the characteristic equation and derive the respective Cauchy-Euler ODE: a.) y = x2+1 b.) y = (1+lnx)x−2/3 c.) y = x[cos(2lnx)+sin(2lnx)]

2. Consider an ODE of the form: x2y′′+axy′+by=0 with given constants a and b and unknown solution y(x). Assuming that y(x) follows the form y=xm For each solution listed below, determine the corresponding roots of the characteristic equation and derive the respective Cauchy-Euler ODE: a.) y = x2+1 b.) y = (1+lnx)x−2/3 c.) y = x[cos(2lnx)+sin(2lnx)]

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 12CR

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