(ど+リさす。 -- dx + lê+1)e"dy-0 dy xy+3X-4-3 dx xy-2x+44-8
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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solve the given
of variables.
![Certainly! Below is a transcription of the provided image for use on an educational website.
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### Differential Equation Simplification
Given the differential equation:
\[ y^2 (e + 1) e \, dx + (ex^3 - x^2 - y^2 - y + 3) e \, dy = 0 \]
We aim to find the expression for \(\frac{dy}{dx}\).
First, we rewrite the equation in a more manageable form:
\[ \frac{dy}{dx} = \frac{e x y + 3x - y - 3}{2x + 4y - 8} \]
This is the rate of change of \(y\) with respect to \(x\) for the given differential equation.
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This differential equation involves exponential \( e \) terms as well as polynomial terms involving \( x \) and \( y \). The simplified form provides an expression for determining how the variable \(y\) changes in relation to variable \(x\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1e4fcbe0-ed74-4447-b38a-a2af13f9fabc%2F2462ea25-d1c5-473b-9df7-506cb475eb99%2F9ihw23a_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Certainly! Below is a transcription of the provided image for use on an educational website.
---
### Differential Equation Simplification
Given the differential equation:
\[ y^2 (e + 1) e \, dx + (ex^3 - x^2 - y^2 - y + 3) e \, dy = 0 \]
We aim to find the expression for \(\frac{dy}{dx}\).
First, we rewrite the equation in a more manageable form:
\[ \frac{dy}{dx} = \frac{e x y + 3x - y - 3}{2x + 4y - 8} \]
This is the rate of change of \(y\) with respect to \(x\) for the given differential equation.
---
This differential equation involves exponential \( e \) terms as well as polynomial terms involving \( x \) and \( y \). The simplified form provides an expression for determining how the variable \(y\) changes in relation to variable \(x\).
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