Extra problem to Section 2.5

Uranium in radioactive decay generates radon, whic also decays radiactively (it is a bit more complicated because there are several isotopes of radon). In this simplified model quantity of uran is $y(t)$ is described by \begin{equation} y'=-\alpha y, \qquad y(0)=y_0 \label{eq-1} \end{equation} and quantity of radon is $z(t)$ is described by \begin{equation} z'=\beta y-\gamma z, \qquad z(0)=z_0 \label{eq-2} \end{equation} where $y_0,z_0$ are initial quantity, $\alpha,\beta,\gamma$ are positive coefficients.