- #1

phantom lancer

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## Homework Statement

Using the method of undetermined coefficients, determine the general solution of the following second-order, linear, non-homogenous equations.

y'' - 4y' + 4y = 2e^(2x+3)

## Homework Equations

I'm not sure what to do from here...

Also, I'm new here. How do I use the superscript for exponents?

## The Attempt at a Solution

r^2 - 4r + 4 = 0

r = 2, so y = C1e^(2x) + C2xe^(2x)

I assume Yp = Ax^(2)e^(2x+3)

so, Yp' = 2Ax^(2)e^(2x+3)

Yp'' = 4Ax^(2)e^(2x+3)

plugging them in the equation: 4Ax^(2)e^(2x+3) - 4(2Ax^(2)e^(2x+3) + 4(Ax^(2)e^(2x+3) = Ax^(2)e^(2x+3)

I get 0 = Ax^(2)e^(2x+3)

From here, I don't know what to do. Please Help.