Question

Find u(x,y) harmonic in S with given boundary values: S = {(x,y): 1 < y <...

Find u(x,y) harmonic in S with given boundary values: S = {(x,y): 1 < y < 3} , u(x,y) = 5 (if y=1) and = 7 (when y=3)

I have this problem to solve, and I'm not sure where to start. Any help would be appreciated. Thanks!

Homework Answers

Answer #1

Doubt in this then comment below.. i will help you..

.

please thumbs up for this solution..thanks..

.

first we make boundary condiiton homogeneous..

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
For the given function u(x, y) = cos(ax) sinh(3y),(a > 0); (a) Find the value of...
For the given function u(x, y) = cos(ax) sinh(3y),(a > 0); (a) Find the value of a such that u(x, y) is harmonic. (b) Find the harmonic conjugate of u(x, y) as v(x, y). (c) Find the analytic function f(z) = u(x, y) + iv(x, y) in terms of z. (d) Find f ′′( π 4 − i) =?
Walter A . Strauss- Partial Differential Equations (2nd Edition) Chapter 7.1, Problem 10E Let u(x,y) be...
Walter A . Strauss- Partial Differential Equations (2nd Edition) Chapter 7.1, Problem 10E Let u(x,y) be the harmonic function in the unit disk with boundary values u(x, y) = x^2 on {x^2 + y^2 = 1}. Find the Rayleigh-Ritz approximation of the form, w0 + c1w1 = x^2 + c1(1 - x^2 - y^2).
a)Prove that the function u(x, y) = x -y÷x+y is harmonic and obtain a conjugate function...
a)Prove that the function u(x, y) = x -y÷x+y is harmonic and obtain a conjugate function v(x, y) such that f(z) = u + iv is analytic. b)Convert the integral from 0 to 5 of (25-t²)^3/2 dt into a Beta Function and evaluate the resulting function. c)Solve the first order PDE sin(x) sin(y) ∂u ∂x + cos(x) cos(y) ∂u ∂y = 0 such that u(x, y) = cos(2x), on x + y = π 2
uxx = ut - u (0<x<1, t>0), boundary conditions: u(1,t)=cost, u(0,t)= 0 initial conditions: u(x,0)= x...
uxx = ut - u (0<x<1, t>0), boundary conditions: u(1,t)=cost, u(0,t)= 0 initial conditions: u(x,0)= x i) solve this problem by using the method of separation of variables. (Please, share the solution step by step) ii) graphically present two terms(binomial) solutions for u(x,1).
Given the following utility function: U (X,Y) = 2X½ + Y and given that U =...
Given the following utility function: U (X,Y) = 2X½ + Y and given that U = 40 Part 1: Find Y1 for X = 4 Part 2: Find Y1 for X = 9 Part 3: Find Y1 for X = 16 Part 4: Find Y1 for X = 36 Part 5: Find Y1 for X = 49 Using graph paper construct the graph for indifference curve for U = 40 Given : Py = 20, Px = 5 and I...
Let s = f(x; y; z) and x = x(u; v; w); y = y(u; v;...
Let s = f(x; y; z) and x = x(u; v; w); y = y(u; v; w); z = z(u; v; w). To calculate ∂s ∂u (u = 1, v = 2, w = 3), which of the following pieces of information do you not need? I. f(1, 2, 3) = 5 II. f(7, 8, 9) = 6 III. x(1, 2, 3) = 7 IV. y(1, 2, 3) = 8 V. z(1, 2, 3) = 9 VI. fx(1, 2, 3)...
Calculate the Y values corresponding to the X values given below. Find the critical values for...
Calculate the Y values corresponding to the X values given below. Find the critical values for X for the given polynomial by finding the X values among those given where the first derivative, dy/dx = 0 and/or X values where the second derivative, d­2y/dx2 = 0. Be sure to indicate the sign (+ or -) of dy/dx and of d2y/dx2 tabled values. Reference Power Point Lesson 13 as needed. Using the first and second derivative tests with the information you...
Calculate the Y values corresponding to the X values given below. Find the critical values for...
Calculate the Y values corresponding to the X values given below. Find the critical values for X for the given polynomial by finding the X values among those given where the first derivative, dy/dx = 0 and/or X values where the second derivative, d­2y/dx2 = 0.    Be sure to find the sign (+ or -) of dy/dx and of d2y/dx2 at all X values. Reference Lesson 13 and the text Appendix A (pp 694 – 698), as needed. Using the...
Solve ut=uxx, 0 < x < 3, given the following initial and boundary conditions: - u(0,t)...
Solve ut=uxx, 0 < x < 3, given the following initial and boundary conditions: - u(0,t) = u(3,t) = 1 - u(x,0) = 0 Please write clearly and explain your reasoning.
Given: The following boundary value problem:    y"+ lamda*y = 0;                0 < x...
Given: The following boundary value problem:    y"+ lamda*y = 0;                0 < x < 2;         y(0) = 0;          y’(2) = 0 Find corresponding eigenvalues, (lamda)n and normalized eigenfunctions yn Expand the function f(x) = x, in terms of the eigen functions obtained in (i)