Consider a two$-$dimensional flow field given by:

$V_{?}=3x^2$yhat$()-3x{y}^2$hat$(),=xy.$

$($a$)$ Is the flow physically possible?

$($b$)$ Is the flow compressible?

$($c$)$ Is the flow irrotational?

$($d$)$ Find the pressure gradient necessary to drive the flow field assuming an inviscid flow with no body forces.