Question

Please note that all the steps are meant to help solve the problem.

Question A1: We have yet to discover what happens when the matrix that defines our system has a repeated real eigenvalue. Let's start with the case of a system defined by a diagonal matrix, which has the twice repeated real eigenvalue A 3. Follow the steps below to analyze the shape of the trajectories and draw the phase plane portrait: 1. Write down the explicit solution to this decoupled system. (i.e. X(t) = , Y(t) = ) 2. Eliminate the exponential term by dividing the two equations by each other. (i.e., X(t)/Y(t) 3. Forget the t-dependence in X(t) and Y(t) for a moment-that is, erase the "(t)"s in the equation you just found, to get X/Y-.. 4. Solve for Y as a function of X. What familiar type of curve is this? 5. As this curve was derived directly from the solutions X(t), Y(t), you found in part (1), the trajectories must lie along these curves. With that (and the explicit solutions from part (1)) in mind, draw the phase portrait

Answer 1

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