b) (b) Verify that the following function is harmonicu(x, y) = -ey sin x - 2e-siny.Find a harmonic conjugate v of u, namely a function v such that the functionu(x, y) + iv(x, y) is an analytic function, such that v(0, 0) = 4. Justify all of your steps.

Here we have to verify that the function is harmonic and then find the harmonic conjugate.

Answered: (b) Verify that the following function…

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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(b) Verify that the following function is harmonic u(x, y) = −e sin x - 2e-siny. Find a harmonic conjugate v of u, namely a function v such that the function u(x, y) + iv(x, y) is an analytic function, such that v(0,0) = 4. Justify all of your steps.