Question

Write and then solve for y = f(x) the differential equation for the statement: "The rate of change of y with respect to x is inversely proportional to y^4"

So dy/dx=k/y^4

(y^4)dy=(k)dx

Integrate

y^5/5=kx+C

Is this the final answer or is there more?

Answer 1

looks good to me.
or, you could say
y = 5kx+c
using a different c.