We are tasked with finding the general solution to the differential equation:

$y + \frac{1}{y^3} = (y^5 + 2x)y'$

and expressing the solution in the form:

$F(x, y) = C$

where $C$ is an arbitrary constant.

Step 1: Rewrite the equation in differential form

First, let's separate the terms involving $y$ on one side and $x$ on the other. To do this, we start by expressing the equation in differential form. Using $y' = \frac{dy}{dx}$, the given equation can be rewritten as:

$y + \frac{1}{y^3} = (y^5 + 2x) \frac{dy}{dx}$

Multiply both sides by $dx$:

[ \left(y + \frac{1}{y^3}\