This problem is split into several steps. All refer to the differential equation

$\frac{dy}{dx}=\frac{8}{x^3}\frac{1}{y^3}$

Step $1$: Separate the equation

A separable equation can be rewritten in the form

$g(y)\frac{dy}{dx}=f(x)$

Find the functions $f(x)$ and $g(y).$ If the equation is not separable, enter "DNE" for both functions.

$g(y)=$

$\frac{8}{x^3}$

Step $2$: Integrate both sides

Integrate both sides of your answer above:

Step $3$: Solve for y

Solve for $y$ from your answer above. This should be a general solution. Use $C$ for the constant of integration.

$y(x)=$

$$