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.
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
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)
1 answer