Review Problemsits degree, unless it’s the zero polynomial, we conclude that the linear combination (6.27)vanishes identically on (−∞,∞) if and only ifc1=c2=c3=c4= 0. This means that thegiven functions are linearly independent on (−∞,∞).5. (a)Solving the auxiliary equation yields(r+5)2(r−2)3(r2+1)2=0⇒(r2=0 or(r−2)3(r22.Thus, the roots of the auxiliary equation arer=−5of multiplicity 2,r= 2of multiplicity 3,r=±iof multiplicity 2.According to (22) on page 329 and (28) on page 330 of the text, the set of functions(assuming thatxis the independent variable)e−5x,xe−5x,e2xe2x2e2x,cosx, xcos
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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.