Hello. I have been trying to solve this ODE, but not able to get an answer. Please take a look. Any help is appreciated. Thank you in advance,

It is found that the birth rate of the population is a linearly decreasing function of the population size that is proportional to the population, P, such that birth rate is equal to (beta1− beta2)P, where beta1 and beta2 are positive constants. Further, it is found that the bacterial cells do not live indefinitely, and die at a constant rate proportional to the population size of sigma1(P), where sigma1 is a positive constant. a. Using the birth and death rates of the bacterial population discovered in the study, write down the model differential equation. (Hint: the model will be in the form dp/dt=f(P,beta1,beta2,sigma1), meaning, the rate of population growth with respect to time will be expressed in terms of the population itself and the constants found from the study. The solution is a quadratic function of population.)

[Geoff Hayes]

Refat - please describe what you have attempted (rather than copying and pasting your homework assignment) and tell us what problems you are experiencing. If you are observing an error (with your code), then please copy the full error message to this question.

[Refat Chowdhury]

dP/dt =rP. r= birth rate-death rate. The birth rate=(beta1-beta2)P. I am not able to come up with sth for the death rate. The death rate is proportional to sigma1(P). So I cannot understand what death rate is equal to.

[Torsten]

dP/dt = (beta1-beta2-sigma1)*P

although I don't understand what the "beta2" stands for.

Best wishes

Torsten.