Consider the differential equation $\frac{dy}{dt}=2\sqrt[\phantom{2}]{|y|}$

$($a$)$ State all equilibrium solutions to the DE$.$

Checking the requirements of the Uniqueness Theorem.

$($b$)$ For $f(t,y)=2\sqrt[\phantom{2}]{|y|},$ state the region$($s$)$ in the ty$-$plase where $f$ is continuous.

$($c$)$ For $y>0,|y|=y.$ This means $f(t,y)=2\sqrt[\phantom{2}]{y}.$ Find $ty.$

$($d$)$ For This means $f(t,y)=2\sqrt[\phantom{2}]{-y}.$ Find $\frac{\text{d}\text{e}\text{l}\text{f}}{\text{d}\text{e}\text{l}\text{y}}.$