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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Question
![### Steps to Solve a Differential Equation
#### Step 1:
\[ dx \cdot (3x + 2y \cdot \frac{dy}{dx}) = 0 \]
This implies:
\[ 6x + 2y \cdot \frac{dy}{dx} = 0 \]
#### Step 2:
Divide both sides by \( 2y \):
\[ \frac{2y \cdot \frac{dy}{dx}}{2y} = \frac{-6x}{2y} \]
Simplifying gives:
\[ \frac{dy}{dx} = \frac{-6x}{2y} \]
#### Problem 3:
Find \( \frac{dy}{dx} \) for the equation:
\[ x^2 + 11xy + y^2 = 2 \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2888394e-ebb8-4e53-8d2e-4197e42faf64%2F54a5e361-0cfd-431f-a4f5-e4c625cb21d1%2Fw4vya7t_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Steps to Solve a Differential Equation
#### Step 1:
\[ dx \cdot (3x + 2y \cdot \frac{dy}{dx}) = 0 \]
This implies:
\[ 6x + 2y \cdot \frac{dy}{dx} = 0 \]
#### Step 2:
Divide both sides by \( 2y \):
\[ \frac{2y \cdot \frac{dy}{dx}}{2y} = \frac{-6x}{2y} \]
Simplifying gives:
\[ \frac{dy}{dx} = \frac{-6x}{2y} \]
#### Problem 3:
Find \( \frac{dy}{dx} \) for the equation:
\[ x^2 + 11xy + y^2 = 2 \]
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