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Integration and Differential Equations

2 Integration and Differential EquationsOften, when attempting to solve a Differential equation, weare naturally led to computing one ormore integrals after all, Integration is the inverse of differentiation. Indeed, we have alreadysolved one simple second-order Differential equation by repeated Integration (the one arising inthe simplest falling object model , starting on page 10). Letus now briefly consider the generalcase where Integration is immediately applicable, and alsoconsider some practical aspects ofusing both the indefinite integral and the definite Directly-Integrable EquationsWe will say that a given first-order Differential equation isdirectly integrableif (and only if) itcan be (re)written asdydx=f(x)( )wheref(x)is some known function of justx(noy s ).

more integrals — after all, integration is the inverse of differentiation. Indeed, we have already solved one simple second-order differential equation by repeated integration (the one arising in the simplest falling object model, starting on page 10). Let us now briefly consider the general

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