Question

True or false? u= arctan((y)/(x)) satisfies Laplace's equation. True or false? $u = \arctan(\frac{y}{x})$ satisfies Laplace's equation.

Name: true or false u arctanyx satisfies laplaces equation true or false u arctanfracyx satisfies laplaces equation 35767
Uploaded: 2021-08-13T19:42:31-08:00
Duration: 5 min 10 s
Channel: Andrija Isakov
Description: true or false u arctanyx satisfies laplaces equation true or false u arctanfracyx satisfies laplaces equation 35767

          True or false? u= arctan((y)/(x)) satisfies Laplace's equation.
True or false? $u = \arctan(\frac{y}{x})$ satisfies Laplace's equation.

$true or false u arctanyx satisfies laplaces equation true or false u arctanfracyx satisfies laplaces equation 35767$

Added by Mireia P.

Computer Science and Information Technology

Trishna Knowledge Systems 2018 Edition

Instant Answer

Solved by Expert Andrija Isakov

08/13/2021

Step 1

We have $u = \arctan(\frac{y}{x})$. Then $\frac{\partial u}{\partial x} = \frac{1}{1+(\frac{y}{x})^2} \cdot (-\frac{y}{x^2}) = \frac{-y}{x^2+y^2}$ $\frac{\partial^2 u}{\partial x^2} = \frac{(x^2+y^2)(0) - (-y)(2x)}{(x^2+y^2)^2} = Show more…

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