This is what I see - I don't know if it'll help
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Working with Tenenbaum's ODE page 91, problem 17, , can't figure it out. Here are some pieces of information that could be useful, given the methods of finding an integrating factor discussed in the chapter:
(a)
(b)
Now I need to take or it times or , and divide it by (a) or (b) so that the result is a function of , or . But none of it seems to work. The book says that the integrating factor necessary is , but I don't see how you could possibly obtain that with the methods discussed in the chapter.
If I understand you, the variables are separated and then next step is to just straight-up integrate like a boss. If that's correct then I doubt it's the intended solution since that uses (1) a cleverness beyond my current capacity, (2) basic principles of the preceding chapter, and (3) none of the techniques discussed in the concurrent chapter.\footnote{Yeah, that's definitely not the right use of that word, but whatev.} But it is good for me to see such a technique for future problems. Thank you!