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(Solved): Problem 3: Consider the system x^()=4x-y,y^()=2x+y. (a) Write the system as x^()=Ax. Show that ...
Problem 3: Consider the system x^(?)=4x-y,y^(?)=2x+y.
(a) Write the system as x^(?)=Ax. Show that the characteristic polynomial is \lambda -5\lambda +6, and find the
eigenvalues and eigenvectors of A.
(b) Find the general solution of the system.
(c) Classify the fixed point at the origin.
(d) Solve the system subject to the initial condition (x_(0),y_(0))=(3,4).