Can someone answer this exact equation of differential equation.. (2xy-y)dx + (x²+x)dy=0?

This is a separable equation:

(2xy-y)dx + (x^2 + x)dy

y(1-2x)dx = (x^2+x)dy

(1-2x)/(x^2 + x) dx = dy/y

Expand the left hand side using partial fractions:

(1/x - 3/(x+1)) dx = dy/y

ln(x) - 3*ln(x+1) = ln(y/c)

where c is a constant of integration.

ln(x/(x+1)^3) = ln(y/c)

y = c*x/(x+1)^3

M=(2xy-y)

dM/dy=(2x-1)

N=(x^2+x)

dN/dx=(2x+1)

This is not an exact differential equation as given because dM/dy does not equal dN/dx.

I think it is the derivation of

(x^2y-xy)+(x^2y+xy)=0

2x^2y=0

x^2y=0