We have the ODE y' = -ky + R for a population y(t) where death rate exceeds birth rate, counteracted by a constant restocking rate.
I'm assuming k is the decay constant and R is the restocking rate
The population at time t0 = 0 is y0, and I have to find a formula for y(t)
Also, interpret the solution in terms of the long term behavior (0< y0 < R/k, y0 = R/k, and y0 > R/k).
y' = -ky + R
The Attempt at a Solution
I solved the DE and got y = R/k + Ce^(-kt)
But how do I know what this does in those given intervals of y0?
Also if k = .5, R = 2, how would I graph the solutions?