homework set 19

# homework set 19 - BILKENT UNIVERSITY Department of...

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B ˙ ILKENT UNIVERSITY Department of Mathematics MATH 225, LINEAR ALGEBRA and DIFFERENTIAL EQUATIONS, Homework set # 19 U.Mu˘gan July 16, 2008 VARIATION OF PARAMETERS 1) Find a particular solution of the following D.E. by using the variation of parameters. Then check your answer by using the method of undermined coeﬃcients a) y 00 - y 0 - 2 y = 2 e - x . b) y 00 + 2 y 0 + y = 3 e - x . 2) Find the general solution of the following D.E’s. a) y 00 + y = tan x, 0 < x < π/ 2 . b) y 00 + 4 y 0 + 4 y = x - 2 e - 2 x , x > 0 . c) y 00 - 5 y 0 + 6 y = R ( x ) , R ( x ) is an arbitaray contionuous function. 3) Verify that the given y 1 and y 2 satisfy the corresponding homogenous equation and ﬁnd the particular solution. a) x 2 y 00 - x ( x + 2) y 0 + ( x + 2) y = 2 x 3 x > 0; y 1 = x, y 2 = xe x . b) x 2 y 00 + xy 0 + ( x 2 - 0 . 25) y = 3 x 3 / 2 sin x, x > 0; y 1 = x - 1 / 2 sin x, y 2 = x - 1 / 2 cos x. VARIATION OF PARAMETERS, HIGHER ORDER D.E. 4)

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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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homework set 19 - BILKENT UNIVERSITY Department of...

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