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CalculusMultivariable Calculus11th Edition
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Finding a General Solution In exercises 19-28, find the general solution of the linear differential equation. y ( 4 ) + 6 y ' ' + 9 y = 0

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Multivariable Calculus

11th Edition
Ron Larson + 1 other
Publisher: Cengage Learning
ISBN: 9781337275378

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Multivariable Calculus

11th Edition
Ron Larson + 1 other
Publisher: Cengage Learning
ISBN: 9781337275378
Chapter 16, Problem 28RE
Textbook Problem
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Finding a General Solution In exercises 19-28, find the general solution of the linear differential equation.

y ( 4 ) + 6 y ' ' + 9 y = 0

To determine

To calculate:

The general solution of the given linear differential equation y(4)+6y''+9y=0.

Explanation of Solution

Given information:

The given linear differential equation is y(4)+6y''+9y=0.

Concept Used:

If m1=α+iβ,m2=α−iβ and m3=α+iβ,m4=α−iβ are equal complex zero of the characteristics equation, then the general solution is y=(C1eαxcosβx+C2eαxsinβx)+x(C3eαxcosβx+C4eαxsinβx).

Calculation:

The characteristics equation is m4+6m2+9=0.

First, we have to find the solution of the characteristics equation m4+6m2+9=0.

m4+6m2+9=0m4+3m2+3m2+9=0m2(m2+3)+3(m2+3)=0(m2+3)(m2+3)=0m=±3i,±3i

Here, m1=0+i3,m2=0−i3 and m3=0+i3,m4=0−i3 are equal complex zero of the characteristics equation

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