# Question: in math225 we learned that systems of linear ordinary homogeneous...

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In MATH225, we learned that systems of linear, ordinary, homogeneous, constant-coefficient differential equations can be solved by finding the eigenvalues and eigenvectors of the system’s coefficient matrix. As a reminder, consider the system: y 0 1 (t) = 3y1 − 2y2 y 0 2 (t) = −y1 + 4y2 The coefficient matrix for this system is A = 3 −2 −1 4 . The eigenvalues for this matrix are λ1 = 2 and λ2 = 5. The corresponding eigenvectors are v1 = −0.8944 −0.4472 and v2 = 0.7071 −0.7071 . The general solution ot the system is y(t) = c1 −0.8944 −0.4472 e 2t + c2 0.7071 −0.7071 e 5t What we learned in MATH225 about small linear systems generalizes to larger linear systems. Using Matlab to find the eigenvalues and eigenvectors, find the general solution of the following system of three differential equations: y 0 1 (t) = −2y1 − 4y2 + 2y y 0 2 (t) = −2y1 + y2 + 2y3 y 0 3 (t) = 4y1 + 2y2 + 5y3