Skip to content

Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6410 • ODE

2005 • Question 2

Question

Math 6410 • ODE 2005 • Question 2

Problem. Consider the nonlinear system \[ \begin {aligned} x' &= 2\sin y,\\ y' &= 3\sin x-\sin y. \end {aligned} \] Provide a complete phase plane analysis of this system and give justifications for your reasoning.

Raw LaTeX

\textbf{Problem.}
Consider the nonlinear system
\[
\begin{aligned}
  x' &= 2\sin y,\\
  y' &= 3\sin x-\sin y.
\end{aligned}
\]
Provide a complete phase plane analysis of this system and give justifications for your
reasoning.

Topic Tags

Contraction Mapping and Nonlinear Equations Linear Systems and Matrix Exponentials Phase Plane Analysis