a$.$ To solve this problem, first obtain a slope field for the differential equation $y^{\text{'}}=1-\frac{1}{3}xy$ that shows the region The statements below refer $to$ the solution $to$ the initial value problem $y^{\text{'}}=1-\frac{1}{3}xy,y(0)=1.$ Sketch the integral curve corresponding $to$ the initial condition $y(0)=1on$ your slope field and then choose the responses below that best describe this solution.

$b.$

$A.$ The solution has $anx-$intercept $atx=0.$

$B.$ The solution has several $x-$intercepts $in$ the interval $(-5,5).$

$C.$ The solution has $nox-$intercepts $in$ the interval $(-5,5).$

$D.$ The solution has $anx-$intercept near $x=1.$

$E.$ The solution has $anx-$intercept near $x=-1.$

$c.A.$ The solution $is$ increasing $on$ the interval $[0,5).$

$B.$ The solution reaches a maximum value near $x=5.$

$C.$ The sollution $is$ decreasing $on$ the interval $[0,5).$

$D.$ The solution reaches a maximum value near $x=-2.$

$E.$ The solution reaches a maximum value near $x=1\mathrm{.}5.$

$d.A.If$ the solution has a critical point $atx=$a then $y(a)=-\frac{3}{a}.$

$B.If$ the solution has a critical point $atx=$a then $1-\frac{1}{3}ay(a)>0.$

$C.If$ the solution has a critical point $atx=$a then

$D.If$ the solution has a critical point $atx=$a then $y(a)=0.$

$E.If$ the solution has a critical point $atx=$a then $y(a)=\frac{3}{a}.$