$(a)(4pts)$ Show that $(0,0)isan$ isolated critical point $of$ the nonlinear autonomous system

$x^{\text{'}}=x^4-2x{y}^3$

$y^{\text{'}}=2x^{3}y-y^4$

but that linearization $of$ the system gives $no$ useful information about the nature $of$ this critical point.

$(b)(10pts)$ Show that solutions are made $upof$ the curves $x^3+y^3=3cxy,$ Hint: The differential $inx$ and $yis$ homogeneous; use the substitution $y=ux$ when integrating.

$(c)$ Use graphing software $or$ pplane $to$ graph solution curves. Based $on$ your graphs, would you classify the critical point $as$ stable $or$ unstable? Would you classify the critical point $as$ a node, saddle point, center, $or$ spiral? Explain.

Please show steps $to$ every part