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Unformatted text preview: Algorithms for solving some differential equations Jonathan L.F. King University of Florida, Gainesville FL 326112082, USA [email protected] Webpage http://www.math.ufl.edu/ ∼ squash/ 11 February, 2009 (at 12:49 ) Abstract: Gives a general method for writing the solution to a f irsto rder l inear d ifferential e quation in terms of definite integrals. Step F1 of The FOLDE algorithm Write the DE in the form d y d x + β ( x ) · y = g ( x ) . 1 : Pick ( i.e, compute ) an antiderivative α of β , α ( x ) := Z β ( x )d x. 2 : Finally, we store for later use the following two func tions: e α ( x ) = ... and 1 e α ( x ) = ... . 3 : Step F2. Now define B ( x ) := e α ( x ) · g ( x ). Then compute an antiderivative, A ( x ) := Z B ( x )d x. Step F3. Now, for κ = anyconstant, the following definition of y will satisfy eq(1). y ( x ) := 1 e α ( x ) · 4 : Step F4. From eq(4), compute y . Plug in to eq (1) to see if your formula for y satisfies it. ( It is at this point that you will sometimes find that you have made a computa...
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This note was uploaded on 01/26/2012 for the course MAC 3472 taught by Professor Jury during the Fall '07 term at University of Florida.
 Fall '07
 JURY
 Calculus, Equations

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