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

$\frac{dy}{dx}=8\frac{1}{x}+8\frac{1}{y^4}$

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.

$g(y)=,$ and $f(x)=$

$$

Step $2$: Integrate both sides

Integrate both sides of your answer above. $($Enter "DNE" if the equation is not separable.$)$

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}g(y)dy=,+C_1$ and ${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}f(x)dx=,+C_2$

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. $($Enter "DNE" if the equation is not separable. Note, however, that there may be a solution that could be found by another method.$)$

$y(x)=$

$$