x² y + 10 x y" + 14 y = 0 in (0, +∞). Compute the wronskian of the solutions ₁ Yr Ys W(x) = * € (0, +∞0)

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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-1
-6
You can verify that y₁ = x¹, y₂ = x²
and y₁ = = 6 are all solutions of the differential equation
x² y + 10 x y" + 14 y' = 0
in (0,+∞), Compute the wronskian of the solutions ₁, ₂, Yz
W(x) =
x € (0, +∞0)
I
Yes 1. Is {y1, 92, 93} a fundamental set for x²y" + 10 x y" + 14 y' = 0 in (0, +∞0)?
Transcribed Image Text:-1 -6 You can verify that y₁ = x¹, y₂ = x² and y₁ = = 6 are all solutions of the differential equation x² y + 10 x y" + 14 y' = 0 in (0,+∞), Compute the wronskian of the solutions ₁, ₂, Yz W(x) = x € (0, +∞0) I Yes 1. Is {y1, 92, 93} a fundamental set for x²y" + 10 x y" + 14 y' = 0 in (0, +∞0)?
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