MATLAB - Create systems of two linear differential equations with variables x and y with the following conditions...
Create systems of two linear differential equations with variables x and y with the following conditions: The matrix of the system has
1. two distinct positive eigenvalues
2. two distinct negative eigenvalues
3. two distinct eigenvalues, one positive and one negative
4. one double positive eigenvalue
5. one double negative eigenvalue
6. two complex eigenvalues with positive real part.
7. two complex eigenvalues with negative real part.
8. two complex eigenvalues with zero real part (pure imaginary).
You can either use the diagonal matrix with the eigenvalues you want as the elements (with the exception of the complex ones) or use a similarity transformation to find a similar matrix with the same eigenvalues.
For each of the above cases, create the phase plane as a separate plot in the same figure. Use square axes -10,10 and use initial conditions for both x and y of -3:3.