Consider the function: u = 2 ln /x² + y² Show that uzz + Uyy = 0. %3D
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![**Problem 2**
Consider the function:
\[ u = 2 \ln \sqrt{x^2 + y^2} \]
Show that \( u_{xx} + u_{yy} = 0 \).
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This problem involves demonstrating that the sum of the second partial derivatives of the given function with respect to \( x \) and \( y \) is zero.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc7aa9576-c8fb-4ae7-a419-cc2a7a929b86%2Fffd3b845-8773-4099-a16f-0fcbc04c34e6%2Fxzi7yym_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem 2**
Consider the function:
\[ u = 2 \ln \sqrt{x^2 + y^2} \]
Show that \( u_{xx} + u_{yy} = 0 \).
---
This problem involves demonstrating that the sum of the second partial derivatives of the given function with respect to \( x \) and \( y \) is zero.
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