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If a differential equation of the form
becomes exact by multiplication with a function then is called an integrating factor of the differential equation.
Note that it follows that
In general integrating factors are not easy to find. Sometimes it is possible to find an integrating factor which depends only on (or only on ).
The condition on an integrating factor depending only on is
This can be solved, if the right hand side is only a function of In this case it follows that
Similarly integrating factors depending only on may be determined if they exist.
|automatically generated 7/ 5/2005