I am so confused.. i need to factor out $e^t$ from the following equation $2{e^2}^ty''-6e^ty'+8y=2e^t+2{e^2}^tt$ i know in fact that the answer is $y''-4y'+4y=t{e^2}^t+e^t$ but i always end up with something different. Here's my try
(1) -> $2e^t(e^ty''-3y')+8y=2e^t(1+e^tt)$ (2) -> $e^ty''-3y'+8y=1+e^tt$ I am doing something wrong... please help.