Show that the only solution of Laplaces equation depending only on r x 2 y 2 z 2 is u c r k with constant c and k ...

u x yz 2cr Substitute u x2 y2 2xry 3x2y2z ...

Show that the only solution of Laplaces equation depending only on r = x 2 + y

Question:

Show that the only solution of Laplace’s equation depending only on r = √x² + y² + z² is u = c/r + k with constant c and k.

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For answer-question

Advanced Engineering Mathematics

ISBN: 978-0470458365

10th edition

Authors: Erwin Kreyszig

See More Books

Question Posted: Sep 30, 2022 06:09 AM

See More Questions

Show that the only solution of Laplaces equation depending only on r = x 2 + y 2 is u = c ln r + k.
Show that the only vector x in R2 or R3 that is orthogonal to every other vector is the zero vector.
Show that the only eigenvalue of a nilpotent matrix is zero.
A trader has a soft limit of $8MM USD and a hard limit of $10MM USD. Their current NOP is $3MM USD. They purchase $6MM USD, sell $1MM USD, and then purchase another $5MM USD. Which of the following...
Many of you readers will have never seen a telegram, but most are familiar with the history. In 2006 Western Union delivered its last telegram. The telegraph industry's life was taken, definitively...
Here is a list of the breeds of dogs that won the World Canine Disc Championships from 1975 through 2016. Make a relative frequency bar graph for these data. Describe what you see. Whippet Mixed...
XCBob, Inc. is an online motorcycle and ATV parts business from the owners home. XCBob entered into oral agreements with the defendant, Ed Tucker Distributers, for purchases of various materials to...
Green Golf Accessories sells golf shoes, gloves, and a laser-guided range-finder that measures distance. Shown below are unit cost and sales data. Fixed costs are $620,000. Instructions (a) Compute...
What is JDBC ? Explain the role of Driver in JDBC. What is the purpose Class.forName method ? What is the advantage of PreparedStatement over Statement ? What is the use of CallableStatement ? Name...
The Architect total contract fee for the project is: $235,000. The Basic Services will be performed in four phases as described below. The services shall be rendered in the following phases:...
Find u(x, t) for the string of length L = 1 and c 2 = 1 when the initial velocity is zero and the initial deflection with small k (say, 0.01) is as follows. Sketch or graph u(x, t) as in Fig. 291 in...
Find the type, transform to normal form, and solve. Show your work in detail. u xx + 4u yy = 0
Find a recent news article about an organization that changed its marketing strategy. What were the reasons for the change? How did the organization approach the development and implementation of the...
Why is Special Education High Leverage Practice number 17 Use Flexible Grouping relevant for teachers? Explain briefly
Review the Tableau visualization, and then answer the questions that follow. Transaction Type (All) Issue common stock for cash Purchase supplies on account Provide services to customers for cash...
What are the fundamental principles and functions of TCP / IP protocols? How do they differ from those of the OSI model in the context of network architecture?
Sort the following list of numbers using insertion sort. Show the list after each iteration of the outer for loop. b ) ( 1 0 points ) How many comparison and shift operations are done on the keys...
Write a program which takes two integers and print their sum,subtraction, multiplication, and division.Use a function with four output parameters.
Why is evaluation of a training program important? How do you evaluate a training program?
You have accepted the engagement of auditing the financial statements of the C. Reis Company, a small manufacturing firm that has been your auditee for several years. Because you were busy writing...
A researcher is testing the null hypothesis that = 35. She is doing a two-tailed test, has set alpha at .05, and has 121 cases in her sample. What is beta?
Label each conclusion as correct or incorrect. If incorrect, label it as a Type I error or a Type II error. Use the following scenario. A biochemist has developed a test to determine if food is...
Label each conclusion as correct or incorrect. If incorrect, label it as a Type I error or a Type II error. Use the following scenario. A biochemist has developed a test to determine if food is...
A 500-km transmission fiber with D=+17ps nm km is spliced to a dispersion compensating fiber of a length 80 km and D=-100ps-nm km. The spectral width of the optical source is 1 nm. (a) Calculate the...
Lauren knows she can afford to make monthly payments of $500 for 60 months. How much will the bank lend her today on a 3% APR car loan in exchange for her promised monthly payments?
Laura wants to buy shares in a mutual fund and has narrowed her selection to the following four funds. Answer the questions below to help assess each fund in terms of the fees each charges. Fund NAV...

Show that the only solution of Laplaces equation depending only on r = x 2 + y

Question:

Step by Step Answer:

u x yz 2cr Substitute u x2 y2 2xry 3x2y2z...View the full answer

Advanced Engineering Mathematics

Students also viewed these Mathematics questions