One model for the spread of rumors is one where it is assumed that the rate of spread is proportional to the product of the fraction y of the population who have heard the rumor and the fraction who have not heard the rumor. Here y= y(t) is a function of time satisfying

Question

0≤ y(t) ≤ 1 for all times t.

1. Write a differential equation that
is satisfied by y(t). Hint:what does it mean for a quantity to be proportional to another quantity?

*Would it be something like:
dy/dt = k(a/y)(b/y)
k being a proportion constant and a and b are real numbers???*

2.Solve the differential equation from the last part to get a general solution for y(t)

Answer 1

since y is a fraction, I'd go with
dy/dt = ky(1-y)
since the two fractions have to add up to 1
Use partial fractions to do the integral.