Integrating Factor
المؤلف:
Adams, R. A
المصدر:
_A Complete Course, 4th ed. Reading, MA_ Addison Wesley, 1999
الجزء والصفحة:
...
13-6-2018
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Integrating Factor
An integrating factor is a function by which an ordinary differential equation can be multiplied in order to make it integrable. For example, a linear first-order ordinary differential equation of type
 |
(1)
|
where 
and 
are given continuous functions, can be made integrable by letting 
be a function such that
 |
(2)
|
and
 |
(3)
|
Then 
would be the integrating factor such that multiplying by 
gives the expression
using the product rule. Integrating both sides with respect to 
then gives the solution
 |
(6)
|
REFERENCES:
Adams, R. A. Calculus: A Complete Course, 4th ed. Reading, MA: Addison Wesley, 1999.
Morse, P. M. and Feshbach, H. Methods of Theoretical Physics, Part I. New York: McGraw-Hill, pp. 526-529, 1953.
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