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)]
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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)]
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