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Chapter 6: Q26E (page 337)

use the annihilator method to determinethe form of a particular solution for the given equation.

y''+2y'+y=x2-x+1

Short Answer

Expert verified

yp(x)=c3+c4x+c5x2

Step by step solution

01

Solve the homogeneous of the given equation

The homogeneous of the given equation is

(D2+2D+1)[y]=0

The solution of the homogeneous is

yh(x)=c1e-x+c2xe-x (1)

Now x2-x+1is annihilated byD3

Then, every solution to the given nonhomogeneous equation also satisfies

.D3(D2+2D+1)[y]=0

Then

y(x)=c1e-x+c2xe-x+c3+c4x+c5x2 (2)

is the general solution to this homogeneous equation

We knowu(x)=uh+up

Comparing (1) & (2)

yp(x)=c3+c4x+c5x2

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