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Assume that p and q are continuous, and that the functions y₁ and 32 are solutions of the differential equation y" + p(x)y' + q(x)y = 0 on an open interval I. Show that if y₁ and y2 have an extremum at the same r-value, then they cannot form a linearly independent set of solutions on that interval.

Assume that p and q are continuous, and that the functions y₁ and 32 are solutions of the differential equation y" + p(x)y' + q(x)y = 0 on an open interval I. Show that if y₁ and y2 have an extremum at the same r-value, then they cannot form a linearly independent set of solutions on that interval.

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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1. Q7 Please help me out with this question ? Differential Equations
7. Assume that p and q are continuous, and that the functions y₁ and 32 are solutions of the differential equation y" + p(x)y' + q(x)y 0 on an open interval I. Show that if y₁ and y2 have an extremum at the same r-value, then they cannot form a linearly independent set of solutions on that interval. =
Transcribed Image Text:7. Assume that p and q are continuous, and that the functions y₁ and 32 are solutions of the differential equation y" + p(x)y' + q(x)y 0 on an open interval I. Show that if y₁ and y2 have an extremum at the same r-value, then they cannot form a linearly independent set of solutions on that interval. =
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