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:

Net Exports

The value of a country's total exports minus its total imports.

Exports

Goods or services sent from one country to another for sale or trade.

Quota

A trade limitation enforced by the government, restricting the quantity or financial value of products that can be exported or imported over a set timeframe.

Open-Economy Model

An economic model that considers the impact of trade and financial flows with other countries on the domestic economy.