= Solution
Because the <hazard functions> are constant, normalization gives $\Lambda_1=2\alpha$ and $\Lambda_2=3\alpha$. The population <characteristic polynomial> factors as
$$
s^2+5\alpha s-6\alpha^2=(s-\alpha)(s+6\alpha).
$$
Thus
$$
\boxed{\mu=\alpha,\qquad f_1(\tau)=3\alpha e^{-3\alpha\tau},\qquad f_2(\tau)=4\alpha e^{-4\alpha\tau}.}
$$
These <exponential distributions> describe ages among currently present <biological cells>. Their rates differ from the phase-exit rates because <exponential growth> overrepresents younger entrants. The stable phase ratio is $N_2/N_1=1/2$, so the <G1 phase> and <G2 phase> fractions approach $2/3$ and $1/3$.
Increasing $\alpha$ rescales all times by $1/\alpha$: the population undergoes faster <exponential growth>, its <doubling time> is $\boxed{(\log2)/\alpha}$, and the profile <means> $1/(3\alpha)$ and $1/(4\alpha)$ decrease. The phase fractions do not depend on $\alpha$. The population <matrix> has exact solution
$$
\begin{pmatrix}N_1\\N_2\end{pmatrix}
=C e^{\alpha t}\begin{pmatrix}2\\1\end{pmatrix}
+E e^{-6\alpha t}\begin{pmatrix}-3\\2\end{pmatrix},
$$
so population-ratio transients decay relative to the growing term at rate $7\alpha$. This exact population formula does not require initially stationary <cell-cycle age densities>.
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