af Ꭷf f(x, y) — f(y, x) = (x − y) — (x, y) + (y − x) — (x², y") ду or some point (x*, y*) € R² b) Evaluate the general solution of partial differential equat (x−y)ux+(y−x−u)uy
af Ꭷf f(x, y) — f(y, x) = (x − y) — (x, y) + (y − x) — (x², y") ду or some point (x*, y*) € R² b) Evaluate the general solution of partial differential equat (x−y)ux+(y−x−u)uy
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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Question
Transcribed Image Text:(a) Let f be a function of R2 such that
af
af
(x, y) = (x, y); for all (x, y) = R²
Əy
Əx
then prove that
af
af
-
f(x, y) - f(y,x) = (x −y) — (x*,y*) + (y − x) — (x*, y*)
əx
ду
for some point (x*, y*) € R²
(b) Evaluate the general solution of partial differential equation
(x−y)ux+(y−x−u)uy = u
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