Show that for given $P(x, y), Q(x, y)$ there is a function $F(x, y)$ such that, for any function $y(x)$,

$$P(x, y)+Q(x, y) \frac{d y}{d x}=\frac{d}{d x} F(x, y)$$

if and only if

$$\frac{\partial P}{\partial y}=\frac{\partial Q}{\partial x}$$

Now solve the equation

$$(2 y+3 x) \frac{d y}{d x}+4 x^{3}+3 y=0$$