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."

Answer 1

dy/dx = k / (y^4) where k is a constant

Separate the variables

(y^4) dy = k dx

Integrate both sides

(y^5) / 5 = kx + c where c is also a constant