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Suppose that u(x, y) = x³ — kxy² + 12xy - 12x for some constant k € R. Find all values (b) of k for which u is the real part of an analytic function f : C → C.

Suppose that u(x, y) = x³ — kxy² + 12xy - 12x for some constant k € R. Find all values (b) of k for which u is the real part of an analytic function f : C → C.

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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help me with part b and c

(a) x5 (b) Suppose that u(x, y) of k for which u is the real part of an analytic function f: C → C. (c) = Suppose f(z) = u(x, y) + iv(x, y) is entire. Suppose we know that u(x, y) 10x³y² + 5xy¹. Using the Cauchy-Riemann equations, find v(x, y). = x³ — kxy² + 12xy - 12x for some constant k = R. Find all values Show that the only analytic function ƒ : C → C of the form f(x + iy) = u(x) + iv(y) is given by ƒ(z) = Az + a for some À E R and a ≤ C.
Transcribed Image Text:(a) x5 (b) Suppose that u(x, y) of k for which u is the real part of an analytic function f: C → C. (c) = Suppose f(z) = u(x, y) + iv(x, y) is entire. Suppose we know that u(x, y) 10x³y² + 5xy¹. Using the Cauchy-Riemann equations, find v(x, y). = x³ — kxy² + 12xy - 12x for some constant k = R. Find all values Show that the only analytic function ƒ : C → C of the form f(x + iy) = u(x) + iv(y) is given by ƒ(z) = Az + a for some À E R and a ≤ C.
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