How to solve

Problem $13$: A minimum parts count Colpitts Oscillator is shown below. Assume the Sil$555$DL$\_$N can be modeled as having $V_1=1\mathrm{.}1V$ and $(1\mathrm{.}2)k^{\text{'}\text{'}}(WIL)=2\frac{A}{V^2},C_p=0\mathrm{.}1nF,C_v=0\mathrm{.}01nF,$ and is otherwise ideal.

$($a$)$ Find the DC drain current and drain voltage.

$($b$)$ Ignoring the transistor capacitances, what is the ideal small$-$signal oscillation frequency?

$($c$)$ Taking into account the transistor capacitances, estimate the small$-$signal oscillation frequency.