Solve the Problem $g ( x , y , z )$

question 268

Essay

Solve the problem.
-For some inexact differential forms df, a function $g ( x , y , z )$ can be found such that dh $= g ( x , y , z ) d f$ is exact. When it exists, the function $g ( x , y , z )$ is called an "integrating factor". Show that $g ( x , y , z ) = \frac { y z } { x }$ is an integrating factor for the inexact differential $\mathrm { df } = - \frac { 1 } { \mathrm { x } } \mathrm { dx } + \frac { 1 } { \mathrm { y } } \mathrm { dy } + \frac { 1 } { \mathrm { z } } \mathrm { dz }$ .

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Definitions:

Cost Of Goods Sold

The total cost associated with making or purchasing goods sold by a company during a specific period.

Ending Inventory Balance

The value of goods available for sale at the end of an accounting period, calculated as beginning inventory plus purchases minus cost of goods sold.

Financial Statements

Documentation that summarizes the financial status and performance of a company, including income statement, balance sheet, and cash flow statement.

Ending Inventory

The total value of goods available for sale at the end of an accounting period, calculated as beginning inventory plus purchases minus cost of goods sold.