# differential equations

• Oct 4th 2009, 08:50 PM
morganfor
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 :)
• Oct 4th 2009, 09:29 PM
Matt Westwood
Separate the variables:

$\int \frac {dP} {aP+b} = \int dt$

The RHS is simply $t$ (plus a constant) while the LHS you substitute a variable for $aP+b$ and you should get something with a logarithm in in.