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Unformatted text preview: Differential Equations 2 Answers to Question 4 In this question, the main aim is to identify the type of d.e., and hence, to identify the method of solution. Can the d.e. be rearranged so as to resemble ( 29 ( 29 y g x f dx dy =- the separable equation, which can be solved by separating the variables? Or can the d.e. be rearranged so as to resemble ( 29 ( 29 x Q y x P dx dy = +- the general first order linear equation, which can be solved by use of an integrating factor? 4a. The equation can be rearranged to the form 2 + =- x x y dx dy- a linear equation, where the function, ( 29 x x P 1- = The integrating factor is 1 ln ln 1 1--- = = = = - x e e e e x x dx Pdx x After following the usual procedure, the general solution is found to be ( 29 c x x x y + + = ln 2 where c is an arbitrary constant 4b. After rearranging the d.e. into the form ( 29 2 2 2 1 xy dx dy x- = + it is clear that the variables can be separated The general solution is ( 29 ( 29 2 2 1 2 1 1 2 x c x y +...
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- Spring '10