$M(x,y)dx + N(x,y)dy=0$ is said to be a perfect differential when
$$\frac{\partial (M(x,y))}{\partial y}=\frac{\partial (N(x,y))}{\partial x}$$
Let $M_y=\frac{\partial (M(x,y))}{\partial y}$ and $N_x=\frac{\partial (N(x,y))}{\partial x}$.
In case if:
$\frac{M_y-N_x}{N(x,y)}$ is only a function of x only (say $f(x)$) then it has a integrating factor $e^{\int f(x)dx}$.
But if $\frac{M_y-N_x}{N(x,y)}$ is a constant then what will be the integrating factor?
Say for this problem: $(axy^2+by)dx+(bx^2y+ax)dy=0$
Is there any other method to solve this differential equation?