$1.($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$).($c$)(2$ points$)$ Find the solution of the initial value problem for the DE of part $($a$)$ with initial condition y$(1)=1$