Differential equation... please help?

Question

The weight of a fish, y(t), satisfies the equation:

dy/dx + y = 3y^(2/3)

If the initial weight y(0) = 0, find its weight at any subsequent time.

Thank you so much if you can help :)

Answer 1

This is a so-called Bernoulli differential equation. The substitution

w(x) = [y(x)]^(1/3)

will convert it to a first-order linear equation in w(x).

With the initial condition, I get

y = 27(1 - e^(-x/3))³