1. The problem statement, all variables and given/known data One model for the spread of rumor is 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. i) Write a differential equation that is satisfied by y ii) Solve the differential equation. 2. Relevant equations 3. The attempt at a solution i) dy/dt = ky(1-y) ii) I was having trouble solving this equation When I took the integral I got ln| (y^2)/(y - y^2) | + c = kt I checked that ln| (y^2)/(y - y^2) | + c was the correct integral of 1/(y-y^2) with wolfram alpha and it was I than began to solve for y and got a quadratic equation but than stopped solving because I checked the answer key... "Logistic Eqn dp/dt = kp(1-p/k) so k=1, P=y Now the solution to (i) is y(t) = k/(1 + A e^(-kt)) y(t) = 1/(1+Ae^(-kt)) At t = 0 y_0 = 1/(1+A) => 1+ A = 1/y_0 A = 1/y_0 - 1 y = 1/(1+(1/y_0 - 1)e^(-kt) ) = y_0/(y_0 + (1-y_0)e^(-kt))" I don't understand what this equation is y(t) = k/(1 + A e^(-kt)) and have never seen it before and don't think that if I solved the equation ln| (y^2)/(y - y^2) | + c = kt I would of gotten this... I don't understand... also y_0 is y sub zero or y at time equals zero... thanks for any help!