Question $3$: Differentiation

$($a$)y(x)$ satisfies the equation $2x^3+3x{y}^2=y^3.$ Use implicit differentiation to find an expression for $\frac{dy}{dx}$ in terms of $x$ and $y.$

$($b$)$ A spherical ice block melts so that its volume decreases at $k$ times its surface area. Show that the rate of change of radius is constant and find the time taken for a block of radius $a$ to melt completely.