Integration-II

[Hoda]

Please, can you help in solving this problem as i solved it by substitution but no use. it is;
(x+y)+(x-y)y' = 0
could you integrate it?? please.

 

[Deleted member 4993]

Please, can you help in solving this problem as i solved it by substitution but no use. it is;
(x+y)+(x-y)y' = 0
could you integrate it?? please.

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Please share your work/thoughts about this assignment.

 

[MarkFL]

I would arrange the ODE as:

[MATH]\d{y}{x}=\frac{y+x}{y-x}=\frac{\dfrac{y}{x}+1}{\dfrac{y}{x}-1}[/MATH]
Now, use the substitution:

[MATH]v=\frac{y}{x}\implies \d{y}{x}=v+x\d{v}{x}[/MATH]