$1.($a$)(4$ points$)$ Find the general solution of the differential equation

$(12$x ln y$)$ dx $$

x$2$

y $2$y

dy $=0,$ y $>0.$

$($b$)(4$ points$)$ Show that the differential equation

$2(1+$ xy$)$ dx $+$

$4$x

y $+3$x$2$

dy $=0,$ y $>0,$

is not exact, but can be made exact using the integrating factor $($x$,$ y$)=$ y$2.$ Find the

general solution $($you may leave it in implicit form$).$