My attempt: I tried to find the Integrating Factor but couldn't find it by the standard methods. Also this is a non-linear differential equation which is non-homogeneous. I couldn't find any substitution as well which would simplify the equation.
$y(3y+10x^2)dx-2x(y+3x^2)dy=0$
$M= y(3y+10x^2) \,\, and \,\,N=2x(y+3x^2) $
$\therefore \, \dfrac{\partial M}{\partial y}=6y+10x^2 \,\,\,\, and\,\,\,\, \dfrac{\partial N}{\partial x}=-2y-18x^2 $
How do I proceed from here to find the Integrating Factor?
$$y(3y+10x^2)2xdx-4x^2(y+3x^2)dy=0$$ $X=x^2$ $$y(3y+10X)dX-4X(y+3X)dy=0$$ HINT : Now, the equation is homogeneous.