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**Quiz-7 / Q7 TUT 0301**

« **on:**November 30, 2018, 04:06:33 PM »

**(a)**Determine all critical points of the given system of equations.

(b) Find the corresponding linear system near each critical point.

**(c)**Find the eigenvalues of each linear system. What conclusions can you then draw about the nonlinear system?

**(d)**Draw a phase portrait of the nonlinear system to confirm your conclusions, or to extend them in those cases where the linear system does not provide definite information about the nonlinear system.

$$\left\{\begin{aligned}

&\frac{dx}{dt} = (1 + x) \sin (y), \\

&\frac{dy}{dt} = 1 - x - \cos (y).

\end{aligned}\right.$$

**Bonus:**Computer generated picture