Science:Math Exam Resources/Courses/MATH215/December 2011/Question 03 (c)/Solution 1

From (a) we know that the fixed points are given by $\ y_{0}=-1,1,2$.

In part (b) we calculated that y is increases in $(-\infty ,-1)\cup (1,\infty )$ and decreases in (-1,1).

This means, that starting at $\ y(0)=1.5$, the solution increases towards the critical point $\ y_{0}=2$. Hence $\ \lim _{t\rightarrow \infty }y(t)=2$.

Starting at $\ y(0)=-3$, the solution increases towards the critical point $\ y_{0}=-1$. Hence $\ \lim _{t\rightarrow \infty }y(t)=-1$.

Starting at $\ y(0)=4$, the solution increases. Since there is no larger critical point, the solution increases indefinitely. Hence $\ \lim _{t\rightarrow \infty }y(t)=\infty$.