Verify that y1(x) = x is a solution of Use reduction of

Chapter 4, Problem 22E

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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

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.

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