I start with the equation:

(-xysinx +2ycosx)dx +(2xcosx)dy with the integrating factor given u(x,y)=xy

after multiplying by u I get:

(-x^2 * y^2 * sinx +2xy^2 * cosx) +(2x^2 * ycosx)y'=0

then taking partial derivatives for M and N

Msuby= -2x^2*y*sinx +4xycosx

Nsubx= -4xysinx

I get Msuby does not equal Nsubx

Do I have to find another integrating factor for this equation or is there some calculus/algebra rule I'm not seeing where Msuby does equal Nsubx?