$($d$)(6$ points$)$ Fig. $1$ below shows the slope field for a differential equation with $x$ as the independent variable and $y$ as the dependent variable.

Figure $1$: Slope field for a differential equation.

According to the figure, indicate whether the following statements are true $(T)$ or false $(F).$

$($i$)$ The solution with initial condition $y(0)=2$ is a decreasing function of $x.$

$($ii$)$ All solutions are asymptotic to either $y=-2$ or $y=4.$

$($iii$)$ All solutions remain bounded.

$($iv$)$ Among all solutions, there are two constant solutions.

$($v$)$ Solutions with initial conditions are increasing functions of $x.$

$($iv$)y=0$ solves the differential equation.