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Chapter 6: Q14E (page 332)

Find a general solution for the differential equation with x as the independent variable:

y(4)+2y'''+10y''+18y'+9y=0

Short Answer

Expert verified

The general solution for the differential equation with x as the independent variable is y(x)=c1e鈭�x+c2xe鈭�x+c3cos3x+c4sin3x

Step by step solution

01

Auxiliary equation:

Consider the equation .y(4)+2y'''+10y''+18y'+9y=0

The associated auxiliary equation is r4+2r3+10r2+18r+9=(r+1)2(r2+9)=0 which hasr=鈭�1 as a double solution andr=鈭�3i andr=3i as a simple solutions.

02

General solution:

The general solution to the given equation is given by

y(x)=c1e鈭�x+c2xe鈭�x+c3cos3x+c4sin3x

Hence the final solution is y(x)=c1e鈭�x+c2xe鈭�x+c3cos3x+c4sin3x

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Most popular questions from this chapter

find a general solution to the given equation.

y'''-3y''+3y'-y=ex

Find a general solution for the differential equation with x as the independent variable:

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

In Problems 1-6, use the method of variation of parameters to determine a particular solution to the given equation.

y'''-2y''+y'=x

use the annihilator method to determinethe form of a particular solution for the given equation. y''-6y'+10y=e3x-x

In Problems 1-6, use the method of variation of parameters to determine a particular solution to the given equation.

y'''-3y''+4y=e2x
See all solutions

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