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dy 1+x If dx = xy, x > 0, and y=-4 when x = 1, when x = 3, y = 4.711 and -4.711 3.898 and -3.898 -4.711 only 3.898 only

dy 1+x If dx = xy, x > 0, and y=-4 when x = 1, when x = 3, y = 4.711 and -4.711 3.898 and -3.898 -4.711 only 3.898 only

Calculus: Early Transcendentals
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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### Differential Equations Problem Consider a first-order differential equation given by: \[ \frac{dy}{dx} = \frac{1+x}{xy} \] with the condition \( x > 0 \), and the initial value \( y = -4 \) when \( x = 1 \). Determine the value of \( y \) when \( x = 3 \). The options provided for \( y \) when \( x = 3 \) are: 1. \( \circ \, 4.711 \text{ and } -4.711 \) 2. \( \circ \, 3.898 \text{ and } -3.898 \) 3. \( \circ \, -4.711 \text{ only} \) 4. \( \circ \, 3.898 \text{ only} \) #### Explanation: To solve this, you need to either integrate the differential equation or use a numerical solver to find the value of \( y \) at \( x = 3 \) given the initial condition. For detailed step-by-step instructions on solving such differential equations, please refer to the section on "Solving First-Order Differential Equations" in the calculus module.
Transcribed Image Text:### Differential Equations Problem Consider a first-order differential equation given by: \[ \frac{dy}{dx} = \frac{1+x}{xy} \] with the condition \( x > 0 \), and the initial value \( y = -4 \) when \( x = 1 \). Determine the value of \( y \) when \( x = 3 \). The options provided for \( y \) when \( x = 3 \) are: 1. \( \circ \, 4.711 \text{ and } -4.711 \) 2. \( \circ \, 3.898 \text{ and } -3.898 \) 3. \( \circ \, -4.711 \text{ only} \) 4. \( \circ \, 3.898 \text{ only} \) #### Explanation: To solve this, you need to either integrate the differential equation or use a numerical solver to find the value of \( y \) at \( x = 3 \) given the initial condition. For detailed step-by-step instructions on solving such differential equations, please refer to the section on "Solving First-Order Differential Equations" in the calculus module.
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