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Unformatted text preview: Algorithms for solving some differential equations Jonathan L.F. King University of Florida, Gainesville FL 32611-2082, USA firstname.lastname@example.org 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 irst-o 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 + ( x ) y = g ( x ) . 1 : Pick ( i.e, compute ) an antiderivative of , ( x ) := Z ( x )d x. 2 : Finally, we store for later use the following two func- tions: e ( x ) = ... and 1 e ( x ) = ... . 3 : Step F2. Now define B ( x ) := e ( x ) g ( x ). Then compute an antiderivative, A ( x ) := Z B ( x )d x. Step F3. Now, for = anyconstant, the following definition of y will satisfy eq(1). y ( x ) := 1 e ( 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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