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Integrating factor 
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#1
Sep2505, 12:59 AM

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 


#2
Sep2505, 01:57 AM

P: 109

(2x^2)+y+((x^2)*y)x)dy/dx=0
(2x^2+y)dx + [(x^2)*yx]dy=0 Now you just need reread your textbook about how to solve Pdx+Qdy=0, after checking some conditions on P&Q if such an equation has roots or none. 


#3
Sep2505, 03:10 AM

Sci Advisor
HW Helper
P: 1,593

Or can approach it this way:
[tex](2x^2+y)dx+(x^2yx)dy=0[/tex] 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: [tex]2x^2dx+ydx+x^2ydyxdy=0[/tex] Well, the ydxxdy can be grouped as: [tex]y^2\left(\frac{ydxxdy}{y^2}\right)[/tex] This leaves us with: [tex]2x^2dx+x^2ydy+y^2 d\left(\frac{x}{y}\right)[/tex] Can you rearrange this now to obtain exact differentials which can be integrated? 


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