THIS IS THE ONLINE TOOL: https://www.bluffton.edu/homepages/facstaff/nesterd/java/slopefields.html
1. The population of Hoffmanistan is modeled by the differential equation dy dt=2y . (1-y) where y is measured in thousands of people and t is in years since 2010 (a) Find the general solution to the differential equation, showing each step (partial fractions) and (b) Find the specific solution satisfying y(0-2. Take the limit as t â oo and explain what it means for the (c) Find another specific solution satisfying y(0)- Take the limit as t â oo and explain what it means (d) What happens when y(0) 1? Find a specific solution for y(0 1 and explain what it means for the (e) What happens when y(0) is negative? Find a specific solution for y(0) =-1. Take the limit as t-+ oo (f) Use technology (such as this online tool) to create a slope field for this differential equation over the 2t simplifying the final answer until it has the form y(t-Te population. for the population. population (even if it seems unrealistic) and explain what it means for the population (even if it seems unrealistic) intervals -1t
