Originally Posted by

**Maccaman** Hi all,

Earlier I started a thread with a past exam question that I wanted to understand before I attempted a homework question. It is similar to the question I posted earlier, but Im still having trouble with it.

Here it is:

"find the equation of R(t) when

$\displaystyle \frac{dE}{dt}= -\gamma_{b}E$ where $\displaystyle E(0) = E_0 $ and $\displaystyle \gamma_b = \gamma_{b_1} + \gamma_{b_2} + \lambda_p $,

$\displaystyle \frac{dS}{dt}= -\gamma_{s}S$ where $\displaystyle S(0) = S_0 $ and $\displaystyle \gamma_s = \gamma_{s_1} + \gamma_{s_2} + \lambda_p $

and

$\displaystyle \frac{dR}{dt} = \gamma_{b_1} E + \gamma_{s_1} MS $

where $\displaystyle M, \gamma_{b_1}, \gamma_{b_2}, \gamma_{b}, \gamma_{s_1}, \gamma_{s_2}, \gamma_{s}, \lambda_p $ are all constants.

Now I know that

$\displaystyle S(t) = S_0 e^{-\gamma_{s} t} $

$\displaystyle E(t) = E_0 e^{-\gamma_{b} t} $

and then by substituting these values into $\displaystyle \frac{dR}{dt} $ we obtain

$\displaystyle \frac{dR}{dt} = \gamma_{b_1} E_0 e^{-\gamma_b t} + \gamma_{s_1} M S_0 e^{-\gamma_s t} $

this is where I get lost. How do I continue from here? What type of differential equation is this? Thanks