Question $3.$ Score:$\frac{0\mathrm{.}67}{1}$

Consider the following initial value problem

$x^2{y}^{\text{'}}=3xy+y^3,x>0$;$,y(1)=-1$

$(1)We$ introduce a new unknown $v.$ What $is$ the formula $ofvin$ terms $ofy?$

$v=$

$(2)$ What $is$ the standard form $of$ the linear equation with the new unknown $v?$ Fill $in$ the missing part

below.

$\frac{dv}{dx}+\frac{6}{x}v=$

$(3)$ Find the solution $yof$ the original equation. The answer must $be$ written $in$ the form $y=$cdots.