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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
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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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.
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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