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**sfgiants13** Err meant integrating factor not constant. My book is terrible and is confusing the heck out of me. The equation is y'-2y=3e^t and I'm supposed to find a general solution and draw a direction field as well as describe how solutions behave for large t. For the solution I've taken the integrating factor m to be e^-2t and the equation to be my'-2my=m3e^t

That yields y'e^-2t-2ye^-2t=e^-2t 3e^t Mr F says: The whole point of getting the integrating factor is to write the left hand side of this equation as $\displaystyle {\color{red} \frac{d}{dt} [y e^{-2t}]}$ ....

or y'e^-2t-2ye^-2t=3e^-t

I'm stumped at this point. Can someone help me out?