Solution Found!
Verify that y1(x) = x is a solution of Use reduction of
Chapter 4, Problem 22E(choose chapter or problem)
Verify that \(y_{1}(x)=x\) is a solution of \(x y^{\prime \prime}-x y^{\prime}+y=0\). Use reduction of order to find a second solution \(y_{2}(x)=x\) in the form of an infinite series. Conjecture an interval of definition for y_{2}(x)=x.
Text Transcription:
y_{1}(x)=x
y_{2}(x)=x
x y^{\prime \prime}-x y^{\prime}+y=0
Questions & Answers
QUESTION:
Verify that \(y_{1}(x)=x\) is a solution of \(x y^{\prime \prime}-x y^{\prime}+y=0\). Use reduction of order to find a second solution \(y_{2}(x)=x\) in the form of an infinite series. Conjecture an interval of definition for y_{2}(x)=x.
Text Transcription:
y_{1}(x)=x
y_{2}(x)=x
x y^{\prime \prime}-x y^{\prime}+y=0
ANSWER:Step 1 of 3
Given differential equation is .
We have to verify that is a solution of given differential equation.
Also we have to find a second solution in the form of an infinite series.