How do you solve a differential equation using undetermined coefficients?

[s7b]

How do I go about solving a DE using the method of undetermined coeficients in a question like for example;

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

I tried assuming the yp to be Ae^2x but when I plugged it into the DE I ended up with 0=2e^2x


??

 

[rock.freak667]

Since '2' double root of your aux. eq'n.

the yp should be Ax^2e^2x

 

[s7b]

Once you substitute back into the original DE
Do you get:

8Ax^2e^2x + 2Ae^2x = 2e^2x