Show that the Euler-Cauchy Equation ry" + ary + by = 0, r+0 can be transformed into the constant coefficient equation y" + (a – 1)y + by = 0 by making the substitution r = e'(t = Inr). Use this method to evaluate the r'y" + 7ry' + 5y = r %3D %3D equation

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Show that the Euler-Cauchy Equation
ry" + ary + by = 0, r+0
can be transformed into the constant coefficient equation
y" + (a – 1)y + by = 0
by making the substitution r = e'(t = Inr). Use this method to evaluate the
r'y" + 7ry' + 5y = r
%3D
%3D
equation
Transcribed Image Text:Show that the Euler-Cauchy Equation ry" + ary + by = 0, r+0 can be transformed into the constant coefficient equation y" + (a – 1)y + by = 0 by making the substitution r = e'(t = Inr). Use this method to evaluate the r'y" + 7ry' + 5y = r %3D %3D equation
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