$($a$)$ A radioactive material has a decay rate proportional to the amount of radioactive material present at that time, with a proportionality factor of $33$ per unit time.Write a differential equation of the form P$=$F$($P$)$P$=$F$($P$),$ which models this situation, where PP is the amount of radioactive material micrograms as function of time.P$=$P$=$

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Note: Write the differential equation, but you do not need to solve it$.$

$($b$)$ Suppose we have the same radioactive material as in part $($a$),$ but now we add radioactive material at the constant rate of $66$ micrograms per unit time.That is$,$ the material decays but we also add material at the rate mentioned before.Write the differential equation P$=$F$($P$)$P$=$F$($P$)$ in this case.P$=$