Lesson 9a - Integrating Factors

x i x x i x i x x dx dx i x dx ln i

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Unformatted text preview: ( x, y ) Qx ( x, y )) Q ( x, y ) If we integrate: ( Py ( x, y ) Qx ( x, y )) Q ( x, y ) ( Py ( x, y ) Qx ( x, y )) Q ( x, y ) I x ( x) I x ( x) I ( x) I x ( x) dx dx I ( x) dx ln | I ( x) | Integrating Factor Continued This means if we can get: e ( Py ( x , y ) Qx ( x , y )) Q( x, y ) dx I ( x) To only have x in it, then this will be our integrating factor that will make the equation exact! ( Qx ( x , y ) Py ( x , y )) dy Similarly, we could prove that if only has y in it, e I ( y) then this would be our integrating factor that would make the equation exact. P ( x, y ) If neither of these integrating factors work, we will not go any further. We will simply say that we cannot (with our current techniques) find an integrating factor for the differential equation. The Integrating Factor Strategy f xy ( x, y ) Py x, y Qx x, y f yx ( x, y ) Step 1: Determine if , if this works, the equation is exact and we follow the exact method. f xy ( x, y ) Py x, y Qx x, y f yx ( x, y ) Step 2: If then we try one of the following Integrating factors: e ( Py ( x , y ) Qx ( x , y )) Q( x, y ) dx I ( x) e ( Qx ( x...
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This note was uploaded on 02/07/2014 for the course MATH 1004 taught by Professor Mark during the Summer '00 term at Carleton CA.

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