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Identify the auxiliary equation of the following differential equation along with its roots and the two fundamental solutions. yII+6yI+8y=0

Identify the auxiliary equation of the following differential equation along with its roots and the two fundamental solutions. yII+6yI+8y=0

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question

Identify the auxiliary equation of the following differential equation along with its roots and the two fundamental solutions.

yII+6yI+8y=0

Expert Solution
Step 1

Given differential equation is second order linear homogeneous differential equation: y''+6y'+8y=0

To find auxiliary equation for any second order differential equation, replace:

y'' as m2

y' as m

y as 1

Now, replacing these terms the differential equation turns to: m2+6m+8=0

which is called as Auxiliary equation for the given differential equation.

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