389_pdfsam_math 54 differential equation solutions odd

389_pdfsam_math 54 differential equation solutions odd -...

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Review Problems its degree, unless it’s the zero polynomial, we conclude that the linear combination (6.27) vanishes identically on ( −∞ , ) if and only if c 1 = c 2 = c 3 = c 4 = 0. This means that the given functions are linearly independent on ( −∞ , ). 5. (a) Solving the auxiliary equation yields ( r +5) 2 ( r 2) 3 ( r 2 +1) 2 =0 ( r 2 =0 or ( r 2) 3 ( r 2 2 . Thus, the roots of the auxiliary equation are r = 5 of multiplicity 2 , r = 2 of multiplicity 3 , r = ± i of multiplicity 2 . According to (22) on page 329 and (28) on page 330 of the text, the set of functions (assuming that x is the independent variable) e 5 x ,x e 5 x ,e 2 x e 2 x 2 e 2 x , cos x, x cos
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This note was uploaded on 03/29/2010 for the course MATH 54257 taught by Professor Hald,oh during the Spring '10 term at University of California, Berkeley.

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