Differential Equation population question.

[scarlets99]

Hi could someone please explain how this can be done please

1.
The population P satisfies the differential equation
dP
dt = X(P) − Y(P) , where X(P) is the birth rate and Y(P) is the death rate. Find the general solution P(t) to this differential equation for the case that X(P) = k1(sqrt)P and Y(P) = k(sqrt)P , where k1 and k2 are positive constants. In the case k2 > k1, determine the time t0 at
which the population has died out if the population at time t = 0 was P0.

Thanks

 

[Dick]

Well, it looks like your ODE is dP/dt=k1*sqrt(P)-k2*sqrt(P)=(k1-k2)*sqrt(P). You usually start to solve something like that by separating the variables. Can you get started?