Question Number 100184 by bobhans last updated on 25/Jun/20

((ydx + xdy)/(1−x^2 y^2 )) + xdx = 0

Answered by maths mind last updated on 26/Jun/20

u=xy⇒du=ydx+xdy  ⇔(du/(1−u^2 ))+xdx=0  ⇒((ln(((1+u)/(1−u))))/2)=−(x^2 /2)+c  ⇒((1+u)/(1−u))=ke^(−x^2 )   ⇒u=((ke^(−x^2 ) −1)/(1+ke^(−x^2 ) ))  y=(1/x)(((ke^(−x^2 ) −1)/(1+ke^(−x^2 ) )))