Find the critical points of y y2 y4 y sketch typical solu

Find the critical points of y\' = y(2 - y)(4 - y) sketch typical solution curves in the regions in the xy-plane determined by the graphs of the equilibrium solutions. Justify the behavior of the solution curves with proper reasoning.

Solution

Given y\'=y(2-y)(4-y)

critical points are given by y\'=0

so y(2-y)(4-y)=0

y=0 or 2-y=0 or 4-y=0

y=0,y=2,y=4 are the critical points