homework set 18 - a y 000-y 00-y y = 2 e-x 3 b y 000 4 y =...

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B ˙ ILKENT UNIVERSITY Department of Mathematics MATH 225, LINEAR ALGEBRA and DIFFERENTIAL EQUATIONS, Homework set # 18 U.Mu˘gan July 16, 2008 METHOD OF UNDETERMINED COEFFICIENTS 1) Find the general solution of the following D.E’s a) y 00 - 2 y 0 - 3 y = 3 e 2 x . b) y 00 + 2 y 0 = 3 + 4 sin2 x . c) y 00 + 2 y 0 + y = 2 e - x . d) y 00 + y = 3 sin2 x + x cos2 x . e) y 00 + y 0 + 4 y = 2 sinh x , Hint: sinh x = ( e x - e - x ) / 2. 2) Solve the following I.V.P. a) y 00 + y 0 - 2 y = 2 x, y (0) = 0 , y 0 (0) = 1 . b) y 00 - 2 y 0 - 3 y = 3 xe 2 x , y (0) = 1 , y 0 (0) = 0 . 3) Determine a suitable form for the particular solution y p ( x ) if the method of undetermined coefficients (M.U.C) is to be used. Do not evaluate the coefficients . a) y 00 + 3 y 0 = 2 x 4 + x 2 e - 3 x + sin3 x . b) y 00 + 2 y 0 + 2 y = 3 e - x + 2 e - x cos x + 4 e - x x 2 sin x. c) y 00 + 2 y 0 + 5 y = 3 xe - x cos2 x - 2 xe - 2 x cos x . METHOD OF UNDETERMINED COEFFICIENTS, HIGHER ORDER D.E. 4) Determine the general solution of the given D.E.
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Unformatted text preview: a) y 000-y 00-y + y = 2 e-x + 3. b) y 000 + 4 y = x, y (0) = y (0) = 0 , y 00 (0) = 1. 5) Determine a suitable form for the particular solution y p ( x ) if the method of undetermined coefficients (M.U.C) is to be used. Do not evaluate the coefficients . a) y 000-2 y 00 + y = x 3 + 2 e x b) y (4)-y 000-y 00 + y = x 2 + 4 + x sin x . c) y (4) + 4 y 00 = sin 2 x + xe x + 4. 6) For each of the equations in exercise #5, obtain the differential operator g ( D ) such that g ( D ) R ( x ) = 0 and then find the form of the particular solution y p ( x ) from g ( D ) f ( D ) y = g ( D ) R ( x ) = 0 ....
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This note was uploaded on 06/18/2010 for the course COMPUTER S Math 225 taught by Professor Yosumhoca during the Spring '10 term at Bilkent University.

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