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Solved: In 45 through 48, a differential equation and a
Chapter 4, Problem 46E(choose chapter or problem)
In Problems 45 through 48 , a differential equation and a non-trivial solution are given. Find a second linearly independent solution using reduction of order.
\(t^{2} y^{\prime \prime}+6 t y^{\prime}+6 y=0\) , \(t>0\) ; \(f(t)=t^{-2}\)
Equation Transcription:
Text Transcription:
t^2y''+6ty'+6y=0
t>0
f(t)=^{-2}
Questions & Answers
QUESTION:
In Problems 45 through 48 , a differential equation and a non-trivial solution are given. Find a second linearly independent solution using reduction of order.
\(t^{2} y^{\prime \prime}+6 t y^{\prime}+6 y=0\) , \(t>0\) ; \(f(t)=t^{-2}\)
Equation Transcription:
Text Transcription:
t^2y''+6ty'+6y=0
t>0
f(t)=^{-2}
ANSWER:
Solution:
Step 1:
In this problem we need to find a second linearly independent solution by using reduction of order.