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**Maccaman** I really need help solving these coupled differential equations

$\displaystyle \frac{dZ}{dt} = -aZ $

$\displaystyle \frac{dY}{dt} = cZ - gY $

where a = b+c+g and a,b,c,g are all constants.

The initial conditions are

$\displaystyle Z(0) = Z_0 $, and $\displaystyle Y(0) = Y_0 $,

I know that $\displaystyle Z(t) = e^{-at} $ , but im having trouble with finding Y(t)

This is a past exam question so I have the answer already, but I need to know exactly how to do it for a homework question I have.

Here is the solution

$\displaystyle Y(t) = Y_0 e^{-gt} + \frac{c*Z_0*(e^{-gt} - e^{-at}) }{a - g}$