The general solution of the differential equation $xdy + ydx + 2x^3 dx = 0$, is

$xy+\frac{1}{2} x^4=C$

We have,

$d y+y d x+2 x^3 d x =0$

$\Rightarrow d(x y)+2 x^3 d x=0 \Rightarrow d(x y)+\frac{1}{2} d\left(x^4\right)=0$

On integration, we get $x y+\frac{1}{2} x^4=C$, which is the required solution of the given differential equation.