3. Laplace's equation in two dimensions += 0 has the general solution I(r,y)=)(4coshkr + Bsinh kr) (Ck cos ky+Dasin ky) . Use the boundary conditions Þ(x,0) = Þ(r, b) = (0, y) = 0; Þ(a, y) = PR, where PR is a constant, to find the particular solution. You must show your work or otherwise completely justify your answer.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section11.4: Plane Curves And Parametric Equations
Problem 34E
icon
Related questions
Question
3.
Laplace's equation in two dimensions $+
p(r,y)=E(4coshkz + Bsinhkr) (Ck cos ky + Desin kỵ) .
Σ
Use the boundary conditions
Þ(x,0) = P(x, b) Þ(0, y) = 0;
(a, y) = PR,
where PR is a constant, to find the particular solution. You must show your work or
otherwise completely justify your answer.
0 has the general solution
Transcribed Image Text:3. Laplace's equation in two dimensions $+ p(r,y)=E(4coshkz + Bsinhkr) (Ck cos ky + Desin kỵ) . Σ Use the boundary conditions Þ(x,0) = P(x, b) Þ(0, y) = 0; (a, y) = PR, where PR is a constant, to find the particular solution. You must show your work or otherwise completely justify your answer. 0 has the general solution
Expert Solution
steps

Step by step

Solved in 4 steps with 2 images

Blurred answer
Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage