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
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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1. Q7
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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.
=](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F46e25b63-ec76-4540-acbf-018e1222ac73%2F403135fc-8404-4f3e-a6e4-a25ec0b8d34b%2Fgm6h1dj_processed.jpeg&w=3840&q=75)
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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