Why does the integrating factor method work

# Why does the integrating factor method work - Multiply...

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Why does the integrating factor method work? http://www.ucl.ac.uk/mathematics/geomath/level2/deqn/de81.html 1 of 2 4/2/08 6:20 AM Return Why does the integrating factor method work? Let's look back at that first example: Remember the integrating factor was e x in that case. Now look what we get if we multiply the whole equation through by the integrating factor: Now this is the crux of the method: the left-hand side is the derivative of a product (this is a result of the definition of the integrating factor and will always be the case): Now we can integrate both sides of the equation: and by dividing both sides by x to get y on its own, we retrieve the result we found with the formula: We can see now where the formula came from if we follow that same procedure with the general equation:

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Unformatted text preview: Multiply through by the integrating factor: Write the left-hand side as the derivative of a product (it's rather more complicated this time but try differentiating what's inside the square brackets and you'll see it does give the previous left-hand side. ...): We'll write the integrating factor as just IF instead of that exponential to make it clearer: Then integrate both sides: Finally divide both sides by IF to get y on its own and there we are, we have found the formula: Why does the integrating factor method work? http://www.ucl.ac.uk/mathematics/geomath/level2/deqn/de81.html 2 of 2 4/2/08 6:20 AM Return...
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Why does the integrating factor method work - Multiply...

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