Problem $4(10$ pts$)$: Suppose a $200$L tank contains $100$L of brine with $10$ kg of dissolved salt. Brine with a concentration of $\backslash (0\mathrm{.}1\backslash$mathrm$\{$~kg$\}/\backslash$mathrm$\{$L$\}\backslash )$ enters the tank at a rate of $\backslash (10\backslash$mathrm$\{$~L$\}/\backslash$mathrm$\{$min$\}\backslash )$ and the $($thoroughly mixed$)$ brine is drained from the tank at a rate of $\backslash (5\backslash$mathrm$\{$~L$\}/\backslash$mathrm$\{$min$\}\backslash ).($a$)$ Find a differential equation for $\backslash ($ y$($t$)\backslash ),$ the amount of salt in the tank after $\backslash ($ t $\backslash )$ minutes. Be sure to include an initial condition. $($You do not need to solve the differential equation.$)($b$)$ Is your differential equation in part $($a$)$ separable, first$-$order linear, both, or neither? $($c$)$ How long will it take for the tank to overflow? Note: You do not need to solve your differential equation in order to do this part.