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2. Consider the function u(x, y) = (B − 3)x³ + 2x +(3+1)xy², where 3 € R. For which value(s) of 3 is u(x, y) harmonic? For the same value(s) of 3 found in part (a), find an analytic function f(z) using u(x, y). Write f(z) explicitly as a function of z.

2. Consider the function u(x, y) = (B − 3)x³ + 2x +(3+1)xy², where 3 € R. For which value(s) of 3 is u(x, y) harmonic? For the same value(s) of 3 found in part (a), find an analytic function f(z) using u(x, y). Write f(z) explicitly as a function of z.

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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2. Consider the function u(x, y) = (ß − 3)x³ + 2x + (6 +1)xy², where 3 € R. For which value(s) of ß is u(x, y) harmonic? For the same value(s) of 3 found in part (a), find an analytic function f(z) using u(x, y). Write ƒ(z) explicitly as a function of z.
Transcribed Image Text:2. Consider the function u(x, y) = (ß − 3)x³ + 2x + (6 +1)xy², where 3 € R. For which value(s) of ß is u(x, y) harmonic? For the same value(s) of 3 found in part (a), find an analytic function f(z) using u(x, y). Write ƒ(z) explicitly as a function of z.
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