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--- title: "SU-MATH53 JAN292024" source: https://www.jemoka.com/posts/kbhsu_math53_jan292024/ date: 2024-01-29 --- Review For Linear Constant-Coefficient Equation that are homogeneous, we can solve it generally in terms of some matrix \(A\) as: \begin{equation} x’ = Ax \end{equation} if \(A\) has enough eigenvectors, we can just write out \(y(t) = c_1 e^{\lambda_{1}t} v_1 + … + c_{n}e^{\lambda_{n}t} v_{2}\) But, if we don’t, we can use matrix exponentiation Content eigensolutions