Elements of Numerical Mathematical Economics with Excel

4.5. Systems of linear differential equations

A first-order, nonhomogenous system of autonomous linear differential equations can be expressed formally in the following matrix notation:

[\begin{matrix} {\dot{y}}_{1} (t) \\ ⋮ \\ {\dot{y}}_{n} (t) \end{matrix}] = A [\begin{matrix} y_{1} (t) \\ ⋮ \\ y_{n} (t) \end{matrix}] + [\begin{matrix} b_{1} \\ ⋮ \\ b_{n} \end{matrix}]

(4.5-1)

where A is a (m, n) matrix of constant coefficients.

The system is autonomous because it does not depend explicitly on the variable t, namely the coefficients a _ij and b _i are constant.

We will only deal with systems of two differential equations represented as follows: ...

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