The roots of a cubic auxiliary equation are m1 = 4 and m2=

Chapter 4, Problem 59E

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QUESTION:

Two roots of a cubic auxiliary equation with real coefficients are \(m_{1}=-\frac{1}{2} \text { and } m_{2}=3+i\) and What is the corresponding homogeneous linear differential equation? Discuss: Is your answer unique?

Text Transcription:

m_{1}=-\frac{1}{2} \text { and } m_{2}=3+i

Questions & Answers

QUESTION:

Two roots of a cubic auxiliary equation with real coefficients are \(m_{1}=-\frac{1}{2} \text { and } m_{2}=3+i\) and What is the corresponding homogeneous linear differential equation? Discuss: Is your answer unique?

Text Transcription:

m_{1}=-\frac{1}{2} \text { and } m_{2}=3+i

ANSWER:

Step 1 of 3

We know that if an equation has a complex root, then it also has another complex conjugate root. Hence, the cubic auxiliary equation has three roots,  and .

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