Continuous dynamic systems27In each of the first three examples there is only one variable other than time,namelyx. They are therefore referred to asordinary differential equations. Whenfunctions of several variables are involved, such asuandvin example (iv), suchequations are referred to aspartial differential equations. In this book we shallbe concerned only with ordinary differential equations.Ordinary differential equations are classified according to their order. Theorderof a differential equation is the order of the highest derivative to appear in theequation. In the examples above (i) and (iii) are first-order differential equations,while (ii) is a second-order differential equation. Of particular interest is thelineardifferential equation, whose general form isa0(t)dnxdtn+a1(t)dn−1xdtn−1+. . .+an(t)x=g(t)(2.2)Ifa0(t),a1(t),. . .,an(t) are absolute constants, and so independent oft, thenequation (2.2) is aconstant-coefficientnth-order differential equation. Anydifferential equation not conforming to equation (2.2) is referred to as a
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