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Chapter 6: Q30E (page 337)

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

y'''+2y''-y'-2y=ex-1

Short Answer

Expert verified

yp(x)=c1+c5xex

Step by step solution

01

Solve the homogeneous of the given equation

The homogeneous of the given equation is

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

The solution of the homogeneous is

yh(x)=c1e-2x+c2e-x+c3ex (1)

Now ex-1is annihilated byD2-D

Then, every solution to the given nonhomogeneous equation also satisfies

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

Then

y(x)=c1+c2e-2x+c3e-x+c4ex+c5xex (2)

is the general solution to this homogeneous equation

We knowu(x)=uh+up

Comparing (1) & (2)

yp(x)=c1+c5xex

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