Science:Math Exam Resources/Courses/MATH215/December 2013/Question 06 (c)/Solution 1

The only stable equilibrium solution is (1,2), which is a stable spiral. Saddle points and sources are unstable. While little can be done rigorously, our prediction is that with $x(0)=y(0)=1$ that $(x(t),y(t))\rightarrow (1,2)$ as $t\rightarrow \infty$.