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Unformatted text preview: M ( t, y ) dt = x N ( x, y ) y M ( x, y ) = 0 due to (5). Thus ( g ) /x 0 which implies that g does not depend on x (a consequence of mean value theorem). EXERCISES 2.5: Special Integrating Factors, page 71 1. Here M ( x, y ) = 2 y 3 + 2 y 2 and N ( x, y ) = 3 y 2 x + 2 xy . Computing M y = 6 y 2 + 4 y and N x = 3 y 2 + 2 y , we conclude that this equation is not exact. Note that these functions, as well as M itself, depend on y only. Then, clearly, so does the expression ( N/x M/y ) /M , and the 72...
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 Spring '10
 Hald,OH
 Math, Differential Equations, Linear Algebra, Algebra, Equations

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