In Problems 23-28 show by computing the Wronskian that the given functions are linearly independent on the indicated interval. SECTION 4.1 Preliminary Theory13125. sinx, csc x; (0, π)26. tan x, cot x; (0, π/2)27. e, ex, ex,(-∞0,00)28. x, x ln x, x² In x; (0, ∞)29. Observe that for the functions f₁(x) = 2 and f₂(x) = e*,1. fi(0)-2f₂(0) = 0.Does this imply that f₁ and f₂ are linearly dependent on any intervalcontaining x = 0?

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Answered: 25. sinx, csc x; (0, π)

Math

Advanced Math

25. sinx, csc x; (0, π)

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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Question

In Problems 23-28 show by computing the Wronskian that the given functions are linearly independent on the indicated interval.

SECTION 4.1 Preliminary Theory
131
25. sinx, csc x; (0, π)
26. tan x, cot x; (0, π/2)
27. e, ex, ex,
(-∞0,00)
28. x, x ln x, x² In x; (0, ∞)
29. Observe that for the functions f₁(x) = 2 and f₂(x) = e*,
1. fi(0)-2f₂(0) = 0.
Does this imply that f₁ and f₂ are linearly dependent on any interval
containing x = 0?

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