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