b) (3y+-- X x dy TA y²dx +(5x+ 1 y y x =0
Introductory Circuit Analysis (13th Edition)
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ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
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![### Differential Equation Example
Equation (b) is presented as follows:
\[
\left(3y + \frac{1}{x} - \frac{x}{y^2}\right)\frac{dy}{dx} + \left(5x + \frac{1}{y} - \frac{y}{x^2}\right) = 0
\]
This equation is a form of a differential equation where the objective is often to find the function \( y(x) \) that satisfies the equation.
**Components Breakdown:**
- **First Term:** \( \left(3y + \frac{1}{x} - \frac{x}{y^2}\right)\frac{dy}{dx} \)
- The expression within the parentheses is multiplied by the derivative of \( y \) with respect to \( x \), \( \frac{dy}{dx} \).
- **Second Term:** \( \left(5x + \frac{1}{y} - \frac{y}{x^2}\right) \)
- This is a regular algebraic term that is added to the expression.
**Purpose:**
The goal is typically to solve this equation for \( y \) as a function of \( x \), which involves integrating both sides if possible or applying suitable differential equation techniques.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd331e78d-4008-4ff5-981d-7e34411cb97b%2F805df81c-3c54-40dd-b23e-3df383c0494a%2F2p6ufmt_processed.png&w=3840&q=75)
Transcribed Image Text:### Differential Equation Example
Equation (b) is presented as follows:
\[
\left(3y + \frac{1}{x} - \frac{x}{y^2}\right)\frac{dy}{dx} + \left(5x + \frac{1}{y} - \frac{y}{x^2}\right) = 0
\]
This equation is a form of a differential equation where the objective is often to find the function \( y(x) \) that satisfies the equation.
**Components Breakdown:**
- **First Term:** \( \left(3y + \frac{1}{x} - \frac{x}{y^2}\right)\frac{dy}{dx} \)
- The expression within the parentheses is multiplied by the derivative of \( y \) with respect to \( x \), \( \frac{dy}{dx} \).
- **Second Term:** \( \left(5x + \frac{1}{y} - \frac{y}{x^2}\right) \)
- This is a regular algebraic term that is added to the expression.
**Purpose:**
The goal is typically to solve this equation for \( y \) as a function of \( x \), which involves integrating both sides if possible or applying suitable differential equation techniques.

Transcribed Image Text:1) Determine whether or not the following equations are exact.
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