Hi all,

I have been trying to solve this problem for hours and have looked at many examples, but I still can't solve it. It is a past exam question, so I don't know if there was an error or if I am just doing it wrong.

The problem says:

"Consider the ordinary differential equation

$\displaystyle y''-2y'+y=te^t+4$

Using the Method of Undetermined Coefficients, find a particular solution $\displaystyle y_P(t)$ of the inhomogeneous problem."

So I have tried to solve it using $\displaystyle y_P=Ate^t+Be^t+C=e^t(At+B)+C$, but I can't get anything because the only result I get is $\displaystyle C=te^t+4$, and no values for $\displaystyle A$ or $\displaystyle B$. And $\displaystyle y_P=te^t+4$ would give $\displaystyle y''-2y'+y=4$ instead of $\displaystyle te^t+4$.

I would really appreciate it if someone could give me a hand. Thanks a lot!