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Should I just assume that any problems that involve integrating factor will always result in a perfect integral pair? That's probably not the right terminology but for instance if I have a differential equation which has had an integrating factor multiplied to both sides, then the left hand side most likely becomes a 'perfect integral' as an arbitrary example, a left hand side is y' e^2t + 2y e^2t which if I integrate this as a whole, I would say well that is y e^2t.

Can I assume that this will always be the case in terms of an entry level differential equations class? What happens if the left hand side is not easy to differentiate ?

Can I assume that this will always be the case in terms of an entry level differential equations class? What happens if the left hand side is not easy to differentiate ?

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