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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![### Transcription for Educational Website
**Problem Statement:**
Find the general solution to the equation:
\[ \frac{dy}{dx} = 6x e^y \]
**Answer Choices:**
1. \( y = e^{- \ln(3x^2 + C_2)} \)
2. \( y = \ln(3x^2 + C^2) \)
3. \( y = -\ln(-3x^2 + C^2) \) ⬤ (Correct Answer)
4. \( y = -\ln(-3x^2) \)
**Explanation of Solution:**
The problem requires solving the differential equation \( \frac{dy}{dx} = 6x e^y \) to find the general solution for \( y \).
The correct solution to the differential equation is:
\[ y = -\ln(-3x^2 + C^2) \]
This option accurately represents the general solution, considering the integration constant and the characteristics of logarithmic and exponential functions.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8332b21a-7711-4793-b2df-7a1f1091dd0f%2F7554f508-13b5-43fe-9c4a-dd23d3636e22%2Fo7zfk5p_processed.png&w=3840&q=75)
Transcribed Image Text:### Transcription for Educational Website
**Problem Statement:**
Find the general solution to the equation:
\[ \frac{dy}{dx} = 6x e^y \]
**Answer Choices:**
1. \( y = e^{- \ln(3x^2 + C_2)} \)
2. \( y = \ln(3x^2 + C^2) \)
3. \( y = -\ln(-3x^2 + C^2) \) ⬤ (Correct Answer)
4. \( y = -\ln(-3x^2) \)
**Explanation of Solution:**
The problem requires solving the differential equation \( \frac{dy}{dx} = 6x e^y \) to find the general solution for \( y \).
The correct solution to the differential equation is:
\[ y = -\ln(-3x^2 + C^2) \]
This option accurately represents the general solution, considering the integration constant and the characteristics of logarithmic and exponential functions.
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