Delermine whether the given relation is an implicit solution to the given differential equation. Assume that the relationalip does define y implically as a function of x and use implicit differentiation.

$siny2xy-x^3=2,y^{\text{'}\text{'}}=\frac{6xy(y^{\text{'}}{)}^{3}siny-4(y^{\text{'}}{)}^2}{3x^2-2y}$

Applying implicit differentiation to the equation gives $,$ which $$ equivalent to $y^{\text{'}\text{'}}=\frac{6x{y}^{\text{'}}(y{)}^{3}siny-4(y{)}^2}{3x^2-2y}$

Therefore sin $y2xy-x^3=2$ a solution to the differential equation.

$($Type an equation$)$