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Differential Equations I

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Differential Equations IMATB44H3FVersion September 15, 2011-1949iiContents1 preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Sample Application of Differential Equations . . . . . . . . . . .22 First Order Ordinary Differential Separable Equations . . . . . . . . . . . . . . . . . . . . . . . . . Exact Differential Equations . . . . . . . . . . . . . . . . . . . . . Integrating Factors. . . . . . . . . . . . . . . . . . . . . . . . . . Linear First Order Equations . . . . . . . . . . . . . . . . . . . . Substitutions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . Bernoulli Equation. . . . . . . . . . . . . . . . . . . . . . Homogeneous Equations . . . . . . . . . . . . . . . . . . . Substitution to Reduce Second Order Equations to FirstOrder. . . . . . . . . . . . . . . . . . . . . . . . . . . . .203 Applications and Examples of First Orderode Orthogonal Trajectories. . . . . . . . . . . . . . . . . . . . . . . Exponential Growth and Decay.

Chapter 1 Introduction 1.1 Preliminaries Definition (Differential equation) A differential equation (de) is an equation involving a function and its deriva-

  Differential, Equations, Differential equations i, Preliminaries

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