8. Solve the separable differential equation. dy dx = y\x

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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**Problem 8: Solve the Separable Differential Equation**

\( \frac{dy}{dx} = y/x \)

**Description:**

This is a separable differential equation, meaning it can be rearranged so that each variable and its differential are on opposite sides of the equation. The goal is to find the solution by integrating both sides after separating the variables.

To solve such an equation:

1. Separate the variables: Move all terms involving \( y \) to one side of the equation and all terms involving \( x \) to the other side.
2. Integrate both sides: Once separated, integrate each side to find the general solution.
3. Solve for \( y \), if possible, to express the solution explicitly.
Transcribed Image Text:**Problem 8: Solve the Separable Differential Equation** \( \frac{dy}{dx} = y/x \) **Description:** This is a separable differential equation, meaning it can be rearranged so that each variable and its differential are on opposite sides of the equation. The goal is to find the solution by integrating both sides after separating the variables. To solve such an equation: 1. Separate the variables: Move all terms involving \( y \) to one side of the equation and all terms involving \( x \) to the other side. 2. Integrate both sides: Once separated, integrate each side to find the general solution. 3. Solve for \( y \), if possible, to express the solution explicitly.
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