III. Phase plane portraits [3 marks]For the following linear system of ODEs identify the nature and stability ofthe equilibrium point at (0,0) by analysing the coefficient matrix A. Sketchthe xy-phase plane portrait including arrows to show the behaviour of the1solution. If the eigenvectors are real then include them in the sketch else plotdirection fields to determine the orientation/direction.(dx)/(dt) = -2x 4y(dy)/(dt) = -3x 2y

Sketch phase portraits for the linear system\left[\begin{array}... | Filo

Construct a table of the possible linear systems as follows: (a) The first column contains the type of the system (sink, spiral sink, source, ...). if it has a rame. (b) The second column contains the condition on the eigenvalues that corresponds to this case. (c) The third column contains a small picture of two or more possible phase portraits for this system, and (d) 'The fourth column contains x(t) - and y(t)-graphs of typical solutions indicated in your phase portraits. | Numerade