$($b$)$ Show that xy$^(3)-$xy$^(3)$sinx$=1$ is an implicit solution to the differential equation $($dy$)/($dx$)=(($xcosx$+$sinx$-1)$y$)/(3($x$-$xsinx$))$ on the interval $(0,(\backslash$pi $)/(2)).$

$($b$)$ Show that xy$^(3)-$xy$^(3)$sinx$=1$ is an implicit solution to the differential equation $($dy$)/($dx$)=(($xcosx$+$sinx$-1)$y$)/(3($x$-$xsinx$))$ on the interval $(0,(\backslash$pi $)/(2)).$