Verify that the given differential equation is exact; then solve it$.$

$(\frac{16x}{y}-\frac{3y^2}{x^4})dx+(\frac{2y}{x^3}-\frac{8x^2}{y^2}+\frac{6}{\sqrt[\phantom{2}]{y}})dy=0$

Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

A$.$ The equation is exact and an implicit solution in the form $F(x,y)=C$ is $=C,$ where C is an arbitrary constant.

$($Type an expression using $x$ and $y$ as the variables.$)$

B$.$ The equation is not exact.