Hi,
One way you could do this is as follows.
Starting with the original equation:
dy/dx=-(x^2+y^2)/(x^2-x*y)
Expand the right side using partial fractions in x:
dy/dx=-2*y/(x-y)+y/x-1
Divide both the top and bottom of the first term on the right by x:
dy/dx=-2*(y/x)/((x/x)-(y/x))+y/x-1
Simplify and group occurrences of y/x:
dy/dx=-2*(y/x)/(1-(y/x))+(y/x)-1
If desired, change into this form:
dy/dx=((y/x)^2+1)/((y/x)-1)
This is now in the form:
dy/dx=F(y/x)
You could also start with the original and divide top and bottom of right hand side by x^2.
Either way once you subtract y/x you end up with:
(y/x+1)/(y/x-1)