# integrating factor

by roryhand
Tags: factor, integrating
 P: 2 Howdy, I've read this forum for some time, however this is my first post. I am attempting to solve this ODE. I am looking to find an integrating factor, then solve. I have attached the link to the problem set if my input here is ambiguous. Number 4d. Thank you kindly for any help you might lend. (2x^2)+y+((x^2)*y)-x)dy/dx=0 My reasoning takes me as far as the integrating factor being exp(int( ? )dx) https://people.creighton.edu/%7Elwn7...%202%20PDF.pdf
 P: 112 (2x^2)+y+((x^2)*y)-x)dy/dx=0 (2x^2+y)dx + [(x^2)*y-x]dy=0 Now you just need re-read your text-book about how to solve Pdx+Qdy=0, after checking some conditions on P&Q if such an equation has roots or none.
 HW Helper Sci Advisor P: 1,593 Or can approach it this way: $$(2x^2+y)dx+(x^2y-x)dy=0$$ So, after a quick check for homogeneous, exact, and explicit calc. of an integrating factor via partials, we expand the differentials and attempt to group them together to form exact differentials: $$2x^2dx+ydx+x^2ydy-xdy=0$$ Well, the ydx-xdy can be grouped as: $$y^2\left(\frac{ydx-xdy}{y^2}\right)$$ This leaves us with: $$2x^2dx+x^2ydy+y^2 d\left(\frac{x}{y}\right)$$ Can you re-arrange this now to obtain exact differentials which can be integrated?

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