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Prove: The linear equation


ole.gif


has


             ole1.gif


as an integrating factor. The general solution is


             ole2.gif



Proof. If we multiply 1) through by the function


             ole3.gif


we obtain


ole4.gif  


Since


             ole5.gif



we see that 2) is equivalent to


ole6.gif


and is thus exact. Integrating 3) we get


ole7.gif




or


             ole8.gif


which is the general solution.


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