1. (6 pts) Given a system of differential equations x = (-) x X' 6 a)...
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1. (6 pts) Given a system of differential equations x² = (²-³) x X' 6 a) Use Python to find the eigenvalues and the corresponding eigenvectors. Type your eigenvalues and the eigenvectors in the report. Then, type the general solution of the system. Make sure to state what principle you use for this. Also, state the stability and the type of fixed point. b) Draw the vector field of the system. Superimpose the eigenvector lines and four solution curves from different initial conditions and different regions. Make sure to have different colors for them and include a legend. c) Plot the four solutions on the t-domain (i.e. graph the solutions as x(t) and y(t)). Note that for each plot, you will have the solutions x(t) and y(t). It will be really crowded if you plot all (8 solutions) on the same plot. You should split them up. d) Analyze your results in parts b) and c): stability of the fixed point, type of the fixed point, the behavior of the graph x(t) and y(t), and if the pictures match with the calculation in part a). 1. (6 pts) Given a system of differential equations x² = (²-³) x X' 6 a) Use Python to find the eigenvalues and the corresponding eigenvectors. Type your eigenvalues and the eigenvectors in the report. Then, type the general solution of the system. Make sure to state what principle you use for this. Also, state the stability and the type of fixed point. b) Draw the vector field of the system. Superimpose the eigenvector lines and four solution curves from different initial conditions and different regions. Make sure to have different colors for them and include a legend. c) Plot the four solutions on the t-domain (i.e. graph the solutions as x(t) and y(t)). Note that for each plot, you will have the solutions x(t) and y(t). It will be really crowded if you plot all (8 solutions) on the same plot. You should split them up. d) Analyze your results in parts b) and c): stability of the fixed point, type of the fixed point, the behavior of the graph x(t) and y(t), and if the pictures match with the calculation in part a).
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