Oscillations

Abstract

Matrices are useful for solving systems of linear differential equations. Let x ₁, x ₂ . . . x _n be unknown functions of a single independent variable (t) and connected by simultaneous differential equations with constant coefficients:

$$ \eqalign{& d{x_1}/dt = {a_{11}}{x_1} + {a_{12}}{x_2} + \ldots + {a_{1n}}{x_n} \cr& d{x_2}/dt = {a_{21}}{x_1} + {a_{22}}{x_2} + \ldots + {a_{2n}}{x_n} \cr& \vdots \quad \quad \,\quad \quad \vdots \,\quad \quad \quad \vdots \quad \quad \quad \quad \vdots \cr& d{x_n}/dt = {a_{n1}}{x_1} + {a_{n2}}{x_2} + \ldots + {a_{nn}}{x_n} \cr} $$

(28.1)