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 is u = c ln r + k.

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

Step by Step Answer:

Related Book For book-img-for-question

Advanced Engineering Mathematics

ISBN: 978-0470458365

10th edition

Authors: Erwin Kreyszig

See More Books

Question Posted: Dec 12, 2018 12:02 PM

See More Questions

Show that the normal equations (8.6) have a unique solution. [Show that the only solution for the function f (x) 0 is aj = 0, j = 0, 1. . . n. Multiply Eq. (8.6) by aj , and sum over all j....
The conditions of Picard's Theorem may fail at a given point for a differential equation, but the equation may still have a unique solution through the point. (In other words, the converse of...
Show that the only vector x in R2 or R3 that is orthogonal to every other vector is the zero vector.
Addison, Inc. makes a single product, an indoor fireplace. Data for last year is as follows: Selling price per fireplace Manufacturing costs: Variable per unit produced: Direct materials Direct labor...
Universal Foods issued 10% bonds, dated January 1, with a face amount of $150 million on January 1, 2018. The bonds mature on December 31, 2032 (15 years). The market rate of interest for similar...
Given that y = c 1 + c 2 x 2 is a two-parameter family of solutions of xy'' y' = 0 on the interval (, ), show that constants c 1 and c 2 cannot be found so that a member of the family satisfies the...
When should benchmarking be preferred to direct estimates of the magnitudes of benefits? When should direct estimates be preferred? Is it appropriate to use both?
Budget Tax Service, Inc prepares tax returns for small businesses. The cost of preparing 800 tax returns in the prior year was: Direct labor ............ $320,000 Variable overhead ..............
Please provide a short paragraph response for each of the questions below. Do you think it's right or justified to have an unregulated Marketing Research industry? How do you see the role of...
Clear Sound Audio uses a periodic inventory system. One of the store's most popular products is an MP8 car stereo system. The inventory quantities, purchases, and sales of this product for the most...
Find the temperature w(x, t) in a semi-infinite laterally insulated bar extending from x = 0 along the x-axis to infinity, assuming that the initial temperature is 0, w(x, t) 0 as x for every fixed t...
Find the type, transform to normal form, and solve. Show your work in detail. u xx - 16u yy = 0
How does the type of "flexible" ethics proposed in this feature enhance the potential for success in global commerce?
Many states offer personalized license plates. The state of California, for example, allows personalized plates with seven spaces for numerals or letters, or one of the following four symbols: What...
Some savings and loan companies advertise that they pay interest continuously. Do some research to explain what this means.
Find the amount of periodic payment necessary for each deposit to a sinking fund in Problems 35-46. Amount Needed Frequency n A 41. $500,000 quarterly Rate r 8% Time t 10 yr
a. Find the first three terms of the sequences whose nth terms are given. b. Classify the sequence as arithmetic (give d), geometric (give r), both, or neither. $s_{n}=(-1)^{n}$
On January 1, 20X2, Prost Company acquired all of SKK Corporations assets and liabilities by issuing 24,000 shares of its $4 par value common stock. At that date, Prost shares were selling at $22 per...
If N = 21 and s M = 1, write as much of the equation as possible for calculating the 90% CI Diff and the 99% CI Diff . Use Equation 7.4 as a guide.
What are conversion costs? What are prime costs?
Test the following hypotheses: H 0 : s = 0 H 1 : s 0 n = 50 r s = .23 = .05
How does educational attainment affect newspaper readership? Is there enough evidence to conclude that there are differences between the five educational attainment groups (DEGREE: Highest degree...
Are there differences between the races with respect to their perceptions of their health (HEALTH: Would you say your own health, in general, is . . . 1. Excellent, 2. Good, 3. Fair, 4. Poor)? Use an...
United States Mexico Tank 1 hour 2 hours Taco 1 minute 1.5 minutes a. Who has the absolute advantage in tank production? Taco production? b. Who has the comparative advantage in tank production? Taco...
13) A local business owner is considering adding another employee to his staff in an effort to increase the number of hours the store is open per day. a. If the employee will cost the owner $4,000...
The standard variable overhead rate for Unbeatable Toys is $5. Budgeted fixed overhead is $20,000. Unbeatable Toys' budgeted production was 2,000 units for the current period and actual production...

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

Question:

Step by Step Answer:

By 5 Separation an...View the full answer

Advanced Engineering Mathematics

Students also viewed these Mathematics questions