Consider the autonomous differential equation $y^{\text{'}}=\frac{e^{-y}}{y}.$

$($a$)(2$ points$)$ Does this equation have any equilibria? Explain.

$($b$)(2$ points$)$ For which values of $y$ are solutions decreasing functions?

$($c$)(10$ points$)$ Find the general solution to this differential equation $($You will not be able to solve explicitly for $y,$ in such cases we call the solutions implicit solutions. This is okay.$)$

$($d$)(2$ points$)$ Find the particular implicit solution which passes through the point $(0,2).$