Suppose y 1 , y 2 , . . . , y k are k linearly independent
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Suppose y1, y2, . . . , yk are k linearly independent solutions on (‑∞, ∞) of a homogeneous linear nth-order differential equation with constant coefficients. By Theorem 4.1.2 it follows that yk+1 = 0 is also a solution of the differential equation. Is the set of solutions y1, y2, . . . , yk, yk+1 linearly dependent or linearly independent on (‑∞, ∞)? Discuss.
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A First Course in Differential Equations with Modeling Applications
ISBN: 978-1305965720
11th edition
Authors: Dennis G. Zill
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