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Unformatted text preview: CHAPTER 1 Explicitly Solvable First Order Differential Equations In this chapter we will introduce the first order differential equations and several type of it that can be solved explicitly using integration methods covered in standard Calculus course. From Calculus, we know that the derivative df ( t ) dt of a function f ( t ) is the rate at which the quantity x = f ( t ) is changing with respect to the independent variable t . An equation relating an unknown function and one or more of its derivatives is called an differential equation. Particulary, an equation of the form x = f ( t,x ) is called a first order ordinary differential equation(ODE), more precisely a semi linear first order ordinary differential equation. In this chapter will will demonstrate how to find explicit solution(s) to a given ODE . In general one cant find explicit solution to a given ODE , but for special types of f ( t,x ), we will have luck to do that....
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- Spring '11