How can I solve this differental equation? \(\displaystyle{b}{e}{g}\in{\left\lbrace{a}{l}{i}{g}{n}\right\rbrace}{\left({\frac{{{1}}}{{{x}}}}-{y}^{{2}}{\frac{{{1}}}{{{\left({x}-{y}\right)}^{{2}}}}}\right)}{\left.{d}{x}\right.}&+{\left({x}^{{2}}{\frac{{{1}}}{{{\left({x}-{y}\right)}^{{2}}}}}-{\frac{{{1}}}{{{y}}}}\right)}{\left.{d}{y}\right.}={0}\quad?\backslash{e}{n}{d}{\left\lbrace{a}{l}{i}{g}{n}\right\rbrace}\) I



Answered question


How can I solve this differental equation?
(1xy21(xy)2)dx+(x21(xy)21y)dy=0 ?
I have this as a part of my homework, and there were like 20 other differential equations that I easily solved, but this one stood out.
This is not linear, not separable. I don't know how to approach this problem. If you could tell me to what class this kind of equation belongs, and some methods to solve them, I would be very very glad.

Answer & Explanation

Alannah Campos

Alannah Campos

Beginner2022-03-28Added 10 answers

Step 1
The equation can be rewritten as
Step 2
Here, I would suggest the substitution xw=y. Hence














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