Question

 x^3dx+(y+1)^2dy=0

Answer 1

Let us solve the differential equation

$x^3dx+(y+1)^2dy=0.$

It follows that

$\int x^3dx+\int(y+1)^2dy=C,$ and we conclude that the general solution of this differential equation is

$\frac{x^4}4+\frac{(y+1)^3}3=C.$