Show that u(x, y) is harmonic in some domain and find a harmonic conjugate v(x, y) when (a) u(x, y) = 2x(1 – y); (b) u(x, y) = 2x - x3 + 3xy2;

Q: Verify that u(x, y) = x4−6x2y2+y4 is harmonic everywhere and determine its harmonic conjugate

A:

Q: Consider the function w = √√x² +: dw b) Find əs 6z where x = sinp, y=p+3t-4s, z = and p = 1-2t.

A: I have explained everything with in the solution. Please go through that.

Q: If u = 3x – x3 + 3xy? is a real part of an analytic function | f(z) = u + iv, where z = x+ iy is a…

A: Solution

Q: If u = 3x - x + 3xy? is a real part of an analytic function f(z) = u + iv, where z x+ iy is a…

A:

Q: The conjugate harmonic function v(x, y) of u = In (x² + y²) is

A:

Q: Verify that U(x,y) = x3y - xy3 is harmonic on the complex plane.

A:

Q: Compute the discriminant D(x, y) of the function. ƒ(x, y) = x³ + y4 − 6x − 2y² + 2

A:

Q: how that u(x, y) is harmonic in some domain and find a harmonic njugate v(x, y) hen: u(x, y) = 2x –…

A:

Q: 3. Verify that u(x, y) = x² + 4.x – y² + 2y is harmonic and find %3D - a) the harmonic conjugate…

A: See the attachment

Q: If u = 3x - x³ + 3xy? is a real part of an analytic function f(z) = u + iv, where z = x+ iy is a…

A:

Q: Given the complex function ƒ(z) = |z|² = x² + y². Where are f(z) differentiable? Where is it…

A:

Q: solve the differenctil equation by undtermeind coefficients y'' +2y = -18x2e2x   y(x) = ?

A:

Q: The Real Part of the cor u(x,y (i) Prove that u(;

A:

Q: anction of z = x + iy

A:

Q: Given u(x, y) = y(2x – 1) Show that u(x, y) is a harmonic function. Find the harmonic conjugate…

A:

Q: v=e2r-y cos (y– 2x) Obtain the value of of the relation дхду A 8e2r-y sin (y– 2x) B - 6e2 -y cos(y–…

A: Option (C) is the correct.To solve this question first we take the partial derivative with respect…

Q: Show that u(x, y) = 2x(1 - y) is harmonic and find a harmonic conjugate v(x, y). Show your solution.

A: ux , y= 2x1-y To Find: Show that ux , y= 2x1-y is harmonic and also finds a harmonic conjugate.

Q: Given the complex function f(z) ee-iy. Where are ƒ(z) differentiable? Where is it holomorphic?…

A:

Q: If v(1, y) is a harmonic conjugate of a harmonic function u(1,y) is also a harmonic function. show…

A:

Q: Find a harmonic function ¢(x, y) in the right-half plane x>-1 such that on the boundary (-1, y) = 0,…

A:

Q: e) u(x,y) =/(x2 – y²) %3D

A:

Q: Let f(z)=y-2xy +i(-x+x² - y²)+z² where, z=x+iy is a complex variable defined in the whole complex…

A:

Q: 14) Find and graph of the roots in the complex plane for Vi 15) Let u = x³y - y³x a. Verify that the…

A:

Q: Write f(z) = Im(z - f(z) = u(x, y) + iv(x, y). 3z) zRe(z²) - 5z in the form ○ a. (4y+x³ − xy²) +…

A: Step 1Step 2Step 3 : Step 4

Q: Find a harmonic conjugate v(x, y) of u(x, y) = e e sonding analytic function ƒ(z) = u(x, y)|+ iv(x,…

A:

Q: Show that the function u(x, y) = 2x³ - 6xy² + x² - y²-y is harmonic. Find all functions v(x, y) such…

A:

Q: Q2) For the functions U (x,y)=2x(1-y) and V (x,y) = xy a) Prove that the functions are harmonic. b)…

A:

Q: Show that u(x, y) = e³ cos x is harmonic and find the harmonic conjugate v such that v (0,0) = 0.

A:

Q: y3 be a harm C conjugate. D[ is equal to

A:

Q: An analytic function of a complex variable z = x + iy is expressed as f(z) = u(x, y) + iv(x, y).…

A: If z=x+yi, f(z)=u(x,y)+iv(x,y) can be any pair of functions u,v If f(x,y) is analytic function then…