Talk:First Order ODE/y' - f (y) phi' (x) over f' (y) = phi (x) phi' (x) over f' (y)

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This example was got from the Internet some time back (Quora, probably), cited as an example of a differential equation from the book of Edwards (cited). The Primitive of $x e^{a x}$ has not been calculated correctly -- it was given as $e^A e^v \paren {v - 1} + C'$. This changes everything. The answer was given as $\map f y = e^{2 \, \map \phi x} \paren {\map \phi x - 1} + C$. It is the intention of raising this as a question in StackExchange (to raise my rep) and then to publish a mistake page on $\mathsf{Pr} \infty \mathsf{fWiki}$. I'll also see if I can get a copy of the book, if it can be found. --prime.mover

Here: https://archive.org/details/integralcalculus00edwarich/page/220/mode/2up The problem in question is 18(4) on page 220. The answer given in page 302 is equivalent to mine. -- Random Undergrad

That clears up a lot of stuff. My guess is that someone did the exercise in Quora and got it wrong. Or maybe it was wrong in the 1890 edition and got corrected for 1894. I'll just put it to bed. Thanks for resolving it. --prime mover (talk) 21:23, 28 August 2020 (UTC)