Chem Differential Eq HW Solutions Fall 2011 145

Chem Differential Eq HW Solutions Fall 2011 145 - Section...

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Section 8.2 Further Properties of The Laplace Transform 145 Using this and Exercise 52, we fnd L (erF( at )) ( s )= 1 a 1 s a e s 2 4 a 2 erFc ± s 2 a ² = 1 s e s 2 4 a 2 erFc ± s 2 a ² . 57. Bessel’s equation oF order 0 is xy ±± + y ± + xy =0 . Applying the Laplace transForm, we obtain L ( xy ±± )+ L ( y ± L ( xy )=0 ; - d ds L ( y ±± L ( y ± ) - d ds L ( y - d ds ³ s 2 Y - sy (0) - y ± (0) ´ + sY - y (0) - Y ± ³ - 2 sY - s 2 Y ± + sy (0) ´ + sY - y (0) - Y ± - Y ± (1 + s 2 ) - sY Y ± + s 1+ s 2 Y . An integating Factor For this frst order linear differential equation is
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This note was uploaded on 12/22/2011 for the course MAP 3305 taught by Professor Stuartchalk during the Fall '11 term at UNF.

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