Consider the following differential equation: dy xy? dæ (a) On a pair of axes, sketch a (very basic) slope field for the differential equation. Include slopes at the following 9 points in your sketch: (–1, –1), (0, –1), (1, –1), (–1,0), (0,0), (1,0), (–1,1), (0, 1), (1,1) (b) Using Euler's method with initial condition y(-3) = 1 and step size Ax = 0.2, approximate the solution to the differential equation at x = -2.4. (c) Using separation of variables, solve the differential equation and find the particular solution to the initial condition y(-3) = 1. (d) According to your solution from part (c), what is the exact value of y(-2.4)?
Consider the following differential equation: dy xy? dæ (a) On a pair of axes, sketch a (very basic) slope field for the differential equation. Include slopes at the following 9 points in your sketch: (–1, –1), (0, –1), (1, –1), (–1,0), (0,0), (1,0), (–1,1), (0, 1), (1,1) (b) Using Euler's method with initial condition y(-3) = 1 and step size Ax = 0.2, approximate the solution to the differential equation at x = -2.4. (c) Using separation of variables, solve the differential equation and find the particular solution to the initial condition y(-3) = 1. (d) According to your solution from part (c), what is the exact value of y(-2.4)?
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Consider the following differential equation:
dy
xy?
dx
(a) On a pair of axes, sketch a (very basic) slope field for the differential equation.
Include slopes at the following 9 points in your sketch: (-1, -1), (0, –1), (1, –1), (–1,0), (0,0), (1,0), (–1,1), (0,1), (1,1)
(b) Using Euler's method with initial condition y(-3) = 1 and step size Ax = 0.2, approximate the solution to the differential equation at x = -2.4.
(c) Using separation of variables, solve the differential equation and find the particular solution to the initial condition y(-3) = 1.
(d) According to your solution from part (c), what is the exact value of y(-2.4)?
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