$(40$ points$)$ Solve the following DE$,$ using Exact method:

$[e^{2y}-ycos(xy)]dx+[2x{e}^{2y}-xcos(xy)+2y]dy=0$

Possible answers

a$.$

$y{e}^{2x}-sin(xy)+x^2=c$

b$.$

$x{e}^{2y}-sin(xy)+y^2=c$

c$.,x{e}^{2y}-sin(xy)+x^2=c$

d$.$ None of the above