BCLet z(t) be the solution of z"+a(t)z'+b(t)z=0, where a(t) b(t) are continuous functions on I. ShoW that y(t)=u(t)z (t) solves the ODE y"+a(t)y'+b(t)y=f(t) = for some function f- when u(t) zu"+(2z'+az)u'=f. and is a solution of
BCLet z(t) be the solution of z"+a(t)z'+b(t)z=0, where a(t) b(t) are continuous functions on I. ShoW that y(t)=u(t)z (t) solves the ODE y"+a(t)y'+b(t)y=f(t) = for some function f- when u(t) zu"+(2z'+az)u'=f. and is a solution of
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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Transcribed Image Text:3. BCLet z(t) be the solution of
z"+a(t)z'+b(t)z=0, where a(t) and
b(t) are continuous functions on I. Show
that y(t)=u(t)z(t) solves the ODE
y"+a(t)y'+b(t)y=f (t)
function f – when u(t) is a solution of
zu"+(2 z'+az)u'=f
Z
for some
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