Help with solving differential equation

I got stuck solving this differential equation using substitution:


(x+y)*dx+x*dy=0

(x+y)*dx+x*dy=0

or dy/dx= -(x+y)/x
or dy/dx= -1 -y/x

let y/x=r
so
y= rx
dy/dx=r+x*dr/dx

substituting with r in the equation
r+xdr/dx= -1 -r
or x*dr/dx+(2r+1)=0
xdr = -(2r+1)dx

dr/(2r+1)= -dx/x
integrating
(1/2)*ln(2r+1)= -ln(x)+c
gives
sqrt(2r+1)*x= constant
or
(2r+1)x^2=constant
(2*(y/x)+1)x^2=A
2xy+x^2=A
which is the solution: simplification leads to pretty answer
y=(A-x^2)/(2x)
y=(1/2) { (A/x)-x}

Try multiplying by the mass of the sun.