Two roots of a cubic auxiliary equation with real

Chapter 4, Problem 60E

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QUESTION:

Find the general solution of \(2 y^{\prime \prime \prime}+7 y^{\prime \prime}+4 y^{\prime}-4 y=0\) if \(m_{1}=\frac{1}{2}\).

Text Transcription:

2 y^{\prime \prime \prime}+7 y^{\prime \prime}+4 y^{\prime}-4 y=0

m_{1}=\frac{1}{2}

Questions & Answers

QUESTION:

Find the general solution of \(2 y^{\prime \prime \prime}+7 y^{\prime \prime}+4 y^{\prime}-4 y=0\) if \(m_{1}=\frac{1}{2}\).

Text Transcription:

2 y^{\prime \prime \prime}+7 y^{\prime \prime}+4 y^{\prime}-4 y=0

m_{1}=\frac{1}{2}

ANSWER:

Step 1 of 4

We have the third order differential equation  with the root , and we have to obtain its general solution as the following technique :

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