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Let y₁ and y2 be two solutions to ao(x)y"+a₁(x)y'+a₂(x)y = 0, where ao(x) ‡0, Vx € (a, b). Show that if y₁ and y2 are linearly independent on a ≤ x ≤ b and are such that y(xo) = y (xo) = 0 for some xo € (a, b), then a₁ (xo) = a₂(xo) = 0.

Let y₁ and y2 be two solutions to ao(x)y"+a₁(x)y'+a₂(x)y = 0, where ao(x) ‡0, Vx € (a, b). Show that if y₁ and y2 are linearly independent on a ≤ x ≤ b and are such that y(xo) = y (xo) = 0 for some xo € (a, b), then a₁ (xo) = a₂(xo) = 0.

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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6. Let y₁ and y2 be two solutions to ao(x)y"+a₁(x)y' + a₂(x)y = 0, where ao(x) ‡0, Vx = (a, b). Show that if y₁ and y2 are linearly independent on a ≤ x ≤ b and are such that y(xo) y (xo) = = 0 for some xo € (a, b), then a₁(xo) = a₂(x) = 0.
Transcribed Image Text:6. Let y₁ and y2 be two solutions to ao(x)y"+a₁(x)y' + a₂(x)y = 0, where ao(x) ‡0, Vx = (a, b). Show that if y₁ and y2 are linearly independent on a ≤ x ≤ b and are such that y(xo) y (xo) = = 0 for some xo € (a, b), then a₁(xo) = a₂(x) = 0.
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