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 y4."

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 y⁴."

Answer 1

Translation from English to math:

English: "The rate of change of y with respect to x"

math: dy/dx

English: "is"

math: =

English: "inversely proportional to y⁴"

math: 1/y⁴

Resulting equation:

dy/dx = 1/y⁴

To solve it, invert both sides, solve for x as a function of y, then solve for y as a function of x:

dx/dy = y⁴

x = y⁵/5

y = (5x)^1/5