Using an integrating factor in a differential equation

Using an integrating factor in a differential equation -...

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Using an integrating factor in a differential equation http://www.ucl.ac.uk/mathematics/geomath/level2/deqn/de8.html 1 of 2 4/2/08 6:19 AM Finding and using an integrating factor Suppose you have this equation to solve: In this case we cannot separate the variables and introducing a new variable doesn't help either. In this case we need to use a different method entirely, as follows. First I'll tell you the steps to follow, for the general equation of this form, apparently pulling them from thin air, then we'll go through the example of the equation above, and then whne it's a bt more familiar to you I'll show you why the procedure works! Here's the typical equation for which we can use this method: Here the functions P(x) and Q(x) can be any functions of x, in the example above they were 1 and x respectively. Step One: calculate the integral of the function P(x). Step Two: the integrating factor , which we'll call IF, is defined as the exponential of this, i.e. it's defined by:

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