Calculate the Wronskian of y = 3, y2 = 6x and y3 = -18 +6 W(z) b) Are the functions y₁ = 3, y2 = 6x, and y3 = -18x + 6 linearly independent or dependent? O Dependent ◇ Independent c) If the functions are linearly dependent, there exist non-zero coefficients c₁ and c₂ such that c₁y+C1y2+ c3y3 = 0 Which of the following would satisfy this? O c₁-1, c-3, and c3=-2 O C₁=-2, C₂=3, C3 = 1 Oc₁-3, C2-1 and c3=-2 O The functions are linearly independent.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Calculate the Wronskian of y = 3, y2 = 6x and y3 = -18 +6
W(z)
b) Are the functions y₁ = 3, y2 = 6x, and y3 = -18x + 6 linearly independent or
dependent?
O Dependent
◇ Independent
c) If the functions are linearly dependent, there exist non-zero coefficients c₁ and c₂
such that c₁y+C1y2+ c3y3 = 0
Which of the following would satisfy this?
O c₁-1, c-3, and c3=-2
O C₁=-2, C₂=3, C3 = 1
Oc₁-3, C2-1 and c3=-2
O The functions are linearly independent.
Transcribed Image Text:Calculate the Wronskian of y = 3, y2 = 6x and y3 = -18 +6 W(z) b) Are the functions y₁ = 3, y2 = 6x, and y3 = -18x + 6 linearly independent or dependent? O Dependent ◇ Independent c) If the functions are linearly dependent, there exist non-zero coefficients c₁ and c₂ such that c₁y+C1y2+ c3y3 = 0 Which of the following would satisfy this? O c₁-1, c-3, and c3=-2 O C₁=-2, C₂=3, C3 = 1 Oc₁-3, C2-1 and c3=-2 O The functions are linearly independent.
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