I need to not only find a general solution for the given DE (using the method of finding the integrating factor) but also find an interval on which the general solution is defined.
For the first part I found the integrating factor to be $e^x$. Then,
$$ My = e^x $$
$$ Nx = e^x + xe^x $$
Am I to come to the conclusion that there is no general solution to this DE because $My$ does not equal $Nx$?
Edit - The method used MUST BE by finding the integrating factor (it says so in the homework).