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I'm just reading ahead for my DE class, and there isn't really an answer for when the integrating factor can't be found in terms of purely $x$ or purely $y$:

http://www.sosmath.com/diffeq/first/intfactor/intfactor.html

What sort of techniques are there to handle this? Please suggest edits if the question is too broad rather than voting to close (I am new to DE so not sure how to ask the question)

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  • $\begingroup$ There is no general method. $\endgroup$
    – Markoff Chainz
    May 20, 2018 at 16:14
  • $\begingroup$ You should try making susbstitutions or manipulate the expression somehow to make it a total differential $\endgroup$
    – Markoff Chainz
    May 20, 2018 at 16:20
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    $\begingroup$ Unfortunately, if that happens, you'll need to find another method to solve the equation. It'd help if you could provide a specific example equation. However, the new method will depend on the equation. $\endgroup$
    – Dylan
    May 21, 2018 at 6:35
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    $\begingroup$ i found this question, maybe will help you with the problem that you want to solve, or if was curiosity only math.stackexchange.com/q/428216/546265 You can try Numerically, with any CAS. $\endgroup$
    – MR ASSASSINS117
    May 21, 2018 at 11:04

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