Problem $3$: $(20$ pts $)$ Determine which of the following equations are exact. Provide solutions to the equations that are exact:

$(2x+y)dx+(x-6y)dy=0$

$[1-ysin(x)]dx+cos(x)dy=0$

$(1+\frac{y}{x})dx-\frac{1}{x}dy=0$

$\frac{dr}{ds}=\frac{lns}{\frac{r}{s}-2s}$

$(2r+lny)dr+rydy=0$