dy_y(ln y-Inx+1) %D dx

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Question
### Topic: Calculus - Differential Equations

#### Example Problem

**Problem 12**: 

Given the differential equation:

\[ \frac{dy}{dx} = \frac{y (\ln y - \ln x + 1)}{x} \]

**Explanation**:

This differential equation involves a function \( y \) of \( x \) and its derivative with respect to \( x \). The right side of the equation consists of the fraction whose numerator is \( y (\ln y - \ln x + 1) \) and whose denominator is \( x \).

Understanding and solving such differential equations typically require knowledge of separation of variables, integration techniques, and sometimes special functions.
Transcribed Image Text:### Topic: Calculus - Differential Equations #### Example Problem **Problem 12**: Given the differential equation: \[ \frac{dy}{dx} = \frac{y (\ln y - \ln x + 1)}{x} \] **Explanation**: This differential equation involves a function \( y \) of \( x \) and its derivative with respect to \( x \). The right side of the equation consists of the fraction whose numerator is \( y (\ln y - \ln x + 1) \) and whose denominator is \( x \). Understanding and solving such differential equations typically require knowledge of separation of variables, integration techniques, and sometimes special functions.
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