
differential equations
this seems like it should be simple but again I haven't taken diff. eq. in a while
how does one solve dP/dt = aP+b (a and b are constants)
also how would one analyze it as a populations model in the long run in 2 cases (b is  and a is +; b is  and a is )?
thanks :)

Separate the variables:
$\displaystyle \int \frac {dP} {aP+b} = \int dt$
The RHS is simply $\displaystyle t$ (plus a constant) while the LHS you substitute a variable for $\displaystyle aP+b$ and you should get something with a logarithm in in.