- #1

- 73

- 0

y'' + y' -2y = 3e

^{-2x}+ 5cosx

y = y

_{c}+ y

_{p}

I found

y

_{c}= Ae

^{-2x}+ Be

^{x}

for A, B arb. Const.

Then when selecting a trial function to find the particular integral, y

_{p}I came up with:

y

_{p}= ae

^{-2x}+ bcosx + csinx

However the correct trial function to choose is:

y

_{p}= axe

^{-2x}+ bcosx + csinx

Where the ae

^{-2x}has been multiplied by x. I was wondering in what instance I would have to multiply the term in the y

_{p}equation by x or x

^{2}.