Solve `(x+y(dy)/(dx))/(y-x(dy)/(dx))=x^2+2y^2+(y^4)/(x^2)`

Explanation

We have, `(xdx+ydy)/(ydx-xdy) = (x+y^(2)/x)^(2)`
`rArr (-1/2(d(x^(2))+d(y^(2)))/(x^(2)(xdy-ydx)/x^(2))=(x^(2)+y^(2))/(x))^(2)`
`rArr -1/2(d(x^(2)+y^(2))/(x^(2)+y^(2))^(2))= d(y/x)`
Integrating both sides, we get
`rArr 1/(2(x^(2)+y^(2)))=y/x+C`