solve (x^3*y^3+x^2*y^2+xy+1)ydx + (x^3*y^3-x^2*y^2-xy+1)xdy=0

Question

solve (x^3*y^3+x^2*y^2+xy+1)ydx + (x^3*y^3-x^2*y^2-xy+1)xdy=0

Answer 1

Make the substitution v=xy defining further that dy/dx=(dv/dx-y)/x ... After simplifying you will find that the equation is separable and thus, may be directly integrated to find the solution x-.5xy+ln(xy)-.5/xy=constant