Separate the variables:
The RHS is simply (plus a constant) while the LHS you substitute a variable for and you should get something with a logarithm in in.
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 -)?