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Solved: PROBLEM 28ELet y1(t) = t2 and y2(t) = 2t
Chapter 4, Problem 28E(choose chapter or problem)
PROBLEM 28ELet y1(t) = t2 and y2(t) = 2t|t|. Are y1 and y2 linearly independent on the interval:(a) (b) (c) (d) Compute the Wronskian W[y1,y2](t) on the interval
Questions & Answers
QUESTION:
PROBLEM 28ELet y1(t) = t2 and y2(t) = 2t|t|. Are y1 and y2 linearly independent on the interval:(a) (b) (c) (d) Compute the Wronskian W[y1,y2](t) on the interval
ANSWER:Solution Step 1To check whether two functions are linearly independent or not we use the following definition :Definition : Two functions y1(t) and y2(t) are defined in the interval I. If there exist constants a and b , not both zero such that ay1(t) + by2(t) = 0 for every t I then y1(t) and y2(t) are linearly dependent , otherwise they are linearly independent.In the given problem y1(t) =t2 and y2(t) =t|t|