notexact_steps - GE 207K Exact Equations Integrating...

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GE 207K Exact Equations – Integrating Factors September 14, 2010 This page aims to recap our mini-lecture on differential equations which have been classified as not exact. A differential equation which can be written in the form M ( x,y ) + N ( x,y ) y 0 = 0 . is not exact if M y ( x,y ) 6 = N x ( x,y ) The following steps may be taken to find the general solution to the differential equation: Steps: 1. Write the given differential equation in the STANDARD FORM M ( x,y ) + N ( x,y ) y 0 = 0 . 2. Is the integrating factor function of x or y ? On exams, most likely you will be given this information. If you haven’t been given this information, assume μ = μ ( x ) , and if it did not work, try μ ( y ) . Example 1 shows how having a wrong μ might not work. If μ is only a function of x , i.e., μ = μ ( x ) , then, μ ( x ) = e R My - Nx N dx . (1) If μ is only a function of y , i.e., μ = μ ( y ) , then, μ ( y ) = e R Nx - My M dx . (2) NOTE : Some professors won’t give you credit for using above two equations, and
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notexact_steps - GE 207K Exact Equations Integrating...

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