The notation $y^{\text{'}}(t)=\frac{dy}{dt}=\frac{d}{dt}y$ was devised $to$ suggest that the derivative $of$ a function $yis$ the result $of$ operating $on$ the function $y$ with the

differentiation operator $\frac{d}{dt}.$ Indeed, second derivatives are formed $by$ iterating the operation: $y^{\text{'}\text{'}}(t)=\frac{d^{2}y}{d{t}^2}=\frac{d}{dt}\frac{d}{dt}y.$ Commonly, the symbol $Dis$

used instead $of\frac{d}{dt},$ and the second$-$order differential equation $y^{\text{'}\text{'}}+4y^{\text{'}}+3=0is$ represented $by$

$D^{2}y+4Dy+3y=(D^2+4D+3)[y]=0$

Question: $is(D+8t)D$ the same $asD(D+8t)?$ Please show your work $to$ support your conclusion.

You may write your solutions $on$ a scrap paper and then take a picture $ofit$ and then upload $it.Or$ you may insert Math equation directly when you

reply $to$ the thread.