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et y (t) y' (t) : 1/₂ (1) y''2 (t) : (4) (1-3²1 (4) (1-4) ,(n-1) ... y', (t) y', (t) ⠀ (n-¹) (t)

et y (t) y' (t) : 1/₂ (1) y''2 (t) : (4) (1-3²1 (4) (1-4) ,(n-1) ... y', (t) y', (t) ⠀ (n-¹) (t)

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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by For a set of functions S= {y₁(t), y2(t), ..., yn(t)}. The Wronskian is defined W(t) = det y₁ (t) y₂ (t) y' (t) y'2 (t) : ⠀ (y(n-¹) (†) y(n-¹) (†) 1-1) ... ... yn, (t) y'n (t) : (n-1) (t) Prove that if W(t) = 0, then S is a linearly independent set.
Transcribed Image Text:by For a set of functions S= {y₁(t), y2(t), ..., yn(t)}. The Wronskian is defined W(t) = det y₁ (t) y₂ (t) y' (t) y'2 (t) : ⠀ (y(n-¹) (†) y(n-¹) (†) 1-1) ... ... yn, (t) y'n (t) : (n-1) (t) Prove that if W(t) = 0, then S is a linearly independent set.
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