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

The statement "The rate of change of y with respect to x is inversely proportional to y^4" can be written mathematically as dy/dx = k/y^4

To solve the differential equation, we use variable saparable method.
y^4 dy = kdx
Integrating both sides gives,
y^5 / 5 = kx + A
y^5 = 5kx + 5A = Bx + C; where B = 5k and C = 5A
$y= \sqrt[5]{Bx+C}$