Systems of First Order Linear Ordinary Differential Equations with Constant Coefficients
 Systems of First Order LinearODE with Constant Coefficients
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 Standard Form A system of first order linear ordinary differential equation can be expressed as the following form or in the matrix form where the matrix contains only constants and is function of . One way to solve these n coupled first order linear ODE is to diagonalize the coefficient matrix and thus decouple these equations. Suppose that and are distinct eigenvalues and associated eigenvectors of Let and the system of differential equations can be rewritten as Move to the right hand side of the equation, we have where and The general solution of this system of equations is Substituting back to , the original system of differential equations can be solved: