Task $37$: Consider a first$-$order reaction $in$ which $Ais$ converted $toBat$ rate $k$ and $Bis$ converted

$toAat$ rate $k^{\text{'}}.If$ the initial concentration $ofAis[A]0$ and $noBis$ initially present $in$ the mixture,

then

$\frac{d[A]}{dt}=-k[A]+k\text{'}([A{]}_0-[A])=-(k+k\text{'})[A]+k^{\text{'}}[A{]}_0.$

What solution results from this differential equation for $A?$