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

$(1-2xlny)dx-(\frac{x^2}{y}-2y)dy=0,y>0$

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

$2(1+xy)dx+(\frac{4x}{y}+3x^2)dy=0,y>0$

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 $($b$)$ with initial condition $y(1)=1.$