Technique #$5$: Phase line analysis for autonomous equations

$($a$)$ Apply the technique to this problem: $y^{\text{'}}(t)=2y(1-y_0)-0\mathrm{.}5y.$ That is$,$ sloetch a well$-$labeled phase line to determine the equilibrium solutions. Clearly state all equilibrium solutions. Then, determine the stability of the equilibrium solutions. Finally, next to your phase line, sketch the graph of solutions passing through the given points $y(0)=-50,y(0)=50$ and if $y(0)=100.$ Determine the long term behavior of each of these solution curves. As you apply the teclanique, do not skip any steps, and explain your steps in words alongside your math work.

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