Hi, I need help on this problem
Suppose that a certain population has a growth rate that varies with time and that this population satisfies the differential equation
dy/dt = (0.5 + sin t)y/5
If y(0)=1, find or estimate the time at which the population has doubled.
I think that this can be done with separation of variables. If we cross multiply then we get 5 dy (1/y) = dt (0.5 + sint)
5 ln|y| = 0.5t - cost
Does this seem correct?