lecture07

lecture07 - Section 2.5 Feb 5 2009 Exact Equations Special...

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Section 2.5 Feb 5, 2009 Exact Equations: Special Integrating Factors
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Reminders WebAssign 2 is online. Please start working on it. I will be available by email and through WebAssign next week if you have any questions about the homework. Remember, Prof. Indik is covering class next week. A Summary of This Session: How to transform a non-exact equation, into an exact one. Exact Equations: Special Integrating Factors
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Today’s session Still solving M ( x , y ) dx + N ( x , y ) dy = 0 (First order DFQ) This equation is exact if: M y = N x Question: What to do when the DFQ is not exact? Answer: Find a (magical) function μ = μ ( x , y ) so that μ M ( x , y ) dx + μ N ( x , y ) dy = 0 is exact. This means: ( μ M ) y = ( μ N ) x Then work it out as in Section 2.4. Note: μ is called an “integrating factor”. Exact Equations: Special Integrating Factors
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This means (in a diferent notation): y ( μ M ) = x ( μ N ) Example 1: (a) Show that the DFQ (2 y 6 x ) dx + (3 x 4 x 2 y 1 ) dy = 0 is not exact. (b) Use the “integrating ±actor” μ ( x , y ) = xy 2 to solve this DFQ. Make sure to check that the trans±ormed equation is exact. (c) Does the integrating ±actor (or multiplier) introduce solutions we do not want? Do the interpretation on a phase plane. Exact Equations: Special Integrating Factors
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This note was uploaded on 04/07/2009 for the course MATH taught by Professor Lotfi during the Spring '09 term at Arizona.

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lecture07 - Section 2.5 Feb 5 2009 Exact Equations Special...

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