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## Homework Statement

Find the solution to :y''+2y'+y=t

## Homework Equations

Suppose y(t)=B1t

^{2}+B2t+B3

And I believe, Y(t)=Yh+Yp. That is the solution is equal to the solution to the homogenous equation, plus the particular solution.

## The Attempt at a Solution

First Solve the homogeneous equation:

y(t)=B1t

^{2}+B2t+B3

y'(t)=2B1t+B2

y''(t)=2B1

Substitute this back into the homogenous problem(y''+2y'+y=0) gives:

2B1+2(2B1t+B2)+B1t

^{2}+B2t+B3=0

Rearrange:

B1(t

^{2}+4t+2) +B2(t+2)+B3=0

Solution is t=-2 or B1,B2,B3=0

Now I'm unsure of what to do?

As for the particular solution say Yp:

Yp=ct, where c is a constant so,

Y'p=c

Y''p=0

Substitute this into :y''+2y'+y=t

0+2c+ct=t

c=?

Thanks for any help.