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## Homework Statement

Find a particular solution using variation of parameters.

y'' + 3y' + 2y = 4e^x

## Homework Equations

y

_{p}= -y

_{1}* INT (y

_{2}f(x)/W[y1,y2]) dx + y

_{2}* INT (y

_{1}f(x)/W[y1,y2]) dx

## The Attempt at a Solution

So, first I find the homogeneous solution, correct?

r

^{2}+ 3r + 2 = 0, so the roots are - 1 and -2, so

y

_{h}= c

_{1}* e

^{-x}+ c

_{2}* e

^{-2x}

Then, I use the variation of parameters formula:

y

_{p1}= -y

_{1}* INT (y

_{2}f(x)/W[y1,y2]) dx

= 2/3e

^{x}

y

_{p1}= y

_{2}* INT (y

_{1}f(x)/W[y1,y2]) dx

= -4e

^{x}

Adding them together, y

_{p}= y

_{p1}+ y

_{p2}= -10/3e

^{x}.

However, the answer is just 2/3e

^{x}, what I got for y

_{p1}.