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View Full Document Right Arrow Icon Module 1 Introduction and First Definitions 1. A differential equation is an equation involving an unknown function and its derivatives. 2. The order of the differential equation is the order of the highest derivative of the unknown function involved in the equation. 3. A linear differential equation of order n is a differential equation written in the following form: where is not the zero function. Note that some may use the notation for the derivatives. A linear equation obliges the unknown function y to have some restrictions. Indeed, the only operations which are accepted for the variable y are: (i) Differentiating y ; (ii) Multiplying y and its derivatives by a function of the variable x (iii) Adding what you obtained in (ii) and let it be equal to a function of x . 4. Existence : Does a differential equation have a solution? 5. Uniqueness : Does a differential equation have more than one solution? If yes, how can we find a solution which satisfies particular conditions?
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This note was uploaded on 03/16/2012 for the course FENS 101 taught by Professor Selçukerdem during the Fall '12 term at Sabancı University.

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Module 1 - http:/ Module...

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