Answered: y+3y+28y=0.

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Question

what is the characteristic equation for the following

Expert Solution

Step 1: Given data

The given equation is $y apostrophe apostrophe plus 3 y apostrophe plus 28 y equals 0$ .

This is a second order differential equation, since the highest order derivative in this equation is 2, i.e, the co-efficients of higher order derivatives (above 2) is zero.

Also, the co-efficient of the highest order derivative (y'') is 1. Hence, it is a linear differential equation.

The general form of a second order linear differential equation is $bold italic y bold apostrophe bold apostrophe bold plus bold italic P bold left parenthesis bold italic x bold right parenthesis bold italic y bold apostrophe bold plus bold italic Q bold left parenthesis bold italic x bold right parenthesis bold italic y bold equals bold italic f bold left parenthesis bold italic x bold right parenthesis$ . Since the function $f left parenthesis x right parenthesis equals 0$ in the given equation, it is also a homogeneous equation.

Finally, it can be seen that the functions P(x) and Q(x) are constants.

Thus, the given equation is a second order, linear, homogeneous differential equation with constant co-efficients.

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