How to solve this system of differential equations?

Question

anonymous · Answer

$$dx _{1}/dt = k_{21}x_{2}+D-k_{12}x_{1}-mu$$
$$d(x_{2})/dt = k_{12}x_{1}+k_{32}x_{3}-k_{21}x_{2}-k_{23}x_{2}-S$$
$$d(x_{3})/dt=k_{23}x_{2}-k_{32}x_{3}$$

where x1 x2 and x3 are concentrations in a compartmental model, and the k's representing rate of flow between the different compartments (k21 = flow from x2 to x1) and mu and S are constants.

all ks are constant, so this is a constant coefficient problem - however I'm not too sure how to set up this system of equations

anonymous · Answer

Sooo I tried to just integrate each term separately with respect to t, and got something like each x term raised to the 2nd power and divided by 2 and each constant mutliplied by t.

This doesn't make sense, but is the only solution i can offer.