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3. Consider the function u(x, y) = f(3x +4y) + e2(3x-4y) + 3x - 4y and let s = 3x +4y and t = 3x - 4y. Given that f(s) is a twice differentiable function prove that 4 ди дх 3 ди ду 82u дудх = = 12 (f" (s) + 2).

3. Consider the function u(x, y) = f(3x +4y) + e2(3x-4y) + 3x - 4y and let s = 3x +4y and t = 3x - 4y. Given that f(s) is a twice differentiable function prove that 4 ди дх 3 ди ду 82u дудх = = 12 (f" (s) + 2).

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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3. Consider the function u(x, y) = f(3x + 4y) + e2(3x-4y) + 3x - 4y and let s = 3x +4y and t = 3x - 4y. Given that f(s) is a twice differentiable function prove that ди дх ди ду 02 u дудх = = 12 (ƒ"(s) + 2).
Transcribed Image Text:3. Consider the function u(x, y) = f(3x + 4y) + e2(3x-4y) + 3x - 4y and let s = 3x +4y and t = 3x - 4y. Given that f(s) is a twice differentiable function prove that ди дх ди ду 02 u дудх = = 12 (ƒ"(s) + 2).
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