(Solved): Given the autonomous equation \( y^{\prime}=-y(y-1)(y-2) \). 1. Determine all constant solutions. ...

Given the autonomous equation \( y^{\prime}=-y(y-1)(y-2) \). 1. Determine all constant solutions. These are also called critical points or equilibrium solutions of the differential equation. 2. Determine regions when \( y^{\prime}>0 \) and when \( y,<0 \). 3. Sketch the slope field and solutions in the different regions found in (b). 4. Compute the solutions for the initial conditions \( y(0)=-1, y(0)=1 / 2, y(0) \) \( =3 / 2 \), and \( \mathrm{y}(0)=3 \). Plot the solutions on one graph together with the constant solutions found in part (a). 5. Classify each critical point found in part (a) as either an attractor, a repeller, or a semi-stable critical point.