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P5: nts) Assume that f is a function such that fæy and fy exist and are continuous. Assume additionally that f(tx, ty) = t™ f(x, y). for all numbers x, y, and t. Show that x202f ?x2 8² f əxəy 20² f дуг Hint: Differentiate twice with respect to t. Then take t = 1. + 2xy- +y²5 - m(m − 1)f(x, y)

P5: nts) Assume that f is a function such that fæy and fy exist and are continuous. Assume additionally that f(tx, ty) = t™ f(x, y). for all numbers x, y, and t. Show that x202f ?x2 8² f əxəy 20² f дуг Hint: Differentiate twice with respect to t. Then take t = 1. + 2xy- +y²5 - m(m − 1)f(x, y)

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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P5: nts) Assume that f is a function such that fay and fyr exist and are continuous. Assume additionally that tm f(x, y). f(tx, ty) for all numbers x, y, and t. Show that 20² f ?x2 a² f + 2xy- + əxəy 28² f 320 = m(m — 1) ƒ (x, y) дуг Hint: Differentiate twice with respect to t. Then take t = 1.
Transcribed Image Text:P5: nts) Assume that f is a function such that fay and fyr exist and are continuous. Assume additionally that tm f(x, y). f(tx, ty) for all numbers x, y, and t. Show that 20² f ?x2 a² f + 2xy- + əxəy 28² f 320 = m(m — 1) ƒ (x, y) дуг Hint: Differentiate twice with respect to t. Then take t = 1.
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