$($a$)$ Show that $y^{6}x-5=0$ is an implicit solution to $\frac{dy}{dx}=-\frac{1}{6y^5}$ on the interval $(-,5)$

$($b$)$ Show that $x{y}^7-x{y}^{7}sinx=1$ is an implicit solution to the differential equation $\frac{dy}{dx}=\frac{(xcosxsinx-1)y}{7(x-xsinx)}$ on the interval $(0,\frac{}{2}).$

$($a$)$ To verify the solution and the interval, convert $y^{6}x-5=0$ to explicit function$($s$).$