Solve the ODE $\cot (x^2+y^2)dy+xdx+ydy=0$ Solve the ODE $\cot (x^2+y^2)dy+xdx+ydy=0$
i am trying to solving integrating combination
since given that 
$\cot (x^2+y^2)dy+xdx+ydy=0$
then $\cot (x^2+y^2)dy+d(xy)=0$ is it correct way ? and we can apply integration from here? can any one help me this problem

$$2\cot(x^2+y^2)dy+2xdx+2ydy=0$$
$$2\cot(x^2+y^2)dy+d(x^2+y^2)=0$$
$$\dfrac{d(x^2+y^2)}{\cot(x^2+y^2)}=-2dy$$
$$-\ln\cos(x^2+y^2)=-2y+C$$
