au fferential equations and+p(x)v=g(x), dx espectively. If u(x₁) > v(x₁) for some x, and f(x) > g(x) for all >x₁, prove that any point (x, y), where x>x₁, does not satisfy e equations y= u(x) and y = v(x) simultaneously. - dx + p(x) u=f(x)
au fferential equations and+p(x)v=g(x), dx espectively. If u(x₁) > v(x₁) for some x, and f(x) > g(x) for all >x₁, prove that any point (x, y), where x>x₁, does not satisfy e equations y= u(x) and y = v(x) simultaneously. - dx + p(x) u=f(x)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![du
dv
dx
Let u(x) and v(x) be two continuous functions satisfying the
differential equations + p(x) u = f(x) and -+p(x)v=g(x),
dx
respectively. If u(x₁) > v(x₁) for some x, and f(x) > g(x) for all
x>x₁, prove that any point (x, y), where x>x₁, does not satisfy
the equations y= u(x) and y = v(x) simultaneously.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8b59af76-c5b0-48d4-bf84-71f3767e5f47%2F4a0d2e5e-491f-4e08-8eda-f7547ff36be3%2F97iayyr_processed.jpeg&w=3840&q=75)
Transcribed Image Text:du
dv
dx
Let u(x) and v(x) be two continuous functions satisfying the
differential equations + p(x) u = f(x) and -+p(x)v=g(x),
dx
respectively. If u(x₁) > v(x₁) for some x, and f(x) > g(x) for all
x>x₁, prove that any point (x, y), where x>x₁, does not satisfy
the equations y= u(x) and y = v(x) simultaneously.
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