You have a decaying isotope $\displaystyle x=x_0e^{-kt}$ which decays in isotope $\displaystyle y$. Now $\displaystyle y$ decays in $\displaystyle z$ which is stable. Is the following correct

$\displaystyle \dfrac{dy}{dt}=kx-cy$

Also what is the equation of $\displaystyle z$?

Edit

I think $\displaystyle z=z_0+y_0-y+x_0-x$ which means $\displaystyle \dfrac{dz}{dt}=cy$ what you would expect