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Integrating Factors for ODEs (Question from Boas)
Find an integrating factor by inspection to make the below differential equation exact.
(y^2-xy)dx+(x^2+xy)dy=0
I've been inspecting, but I'm not seeing it! Is there a way to analyze this in my head that will lead me more easily to the integrating factor? I tried dividing by xy and (xy)^2 and a bunch of other things, but they didn't really get me anywhere.
Note this isn't actually for coursework, the original question is from Boas (2nd Edition, Ch 8.4, Problem 10), and asks to actually solve the differential equation, but I just want to practice finding integrating factors by inspection, so I modified the problem slightly.
Find an integrating factor by inspection to make the below differential equation exact.
(y^2-xy)dx+(x^2+xy)dy=0
I've been inspecting, but I'm not seeing it! Is there a way to analyze this in my head that will lead me more easily to the integrating factor? I tried dividing by xy and (xy)^2 and a bunch of other things, but they didn't really get me anywhere.
Note this isn't actually for coursework, the original question is from Boas (2nd Edition, Ch 8.4, Problem 10), and asks to actually solve the differential equation, but I just want to practice finding integrating factors by inspection, so I modified the problem slightly.
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