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4. Consider the differential equation = 2x - y. (a) On the axes provided, sketch a slope field for the given differential equation at the twelve points indicated, and sketch the solution curve that passes through the point (0, 1). (Note: Use the axes provided in the pink test booklet.) (b) The solution curve that passes through the point (0, 1) has a local minimum at x In What is the y-coordinate of this local minimum? (c) Let y= f(x) be the particular solution to the given differential equation with the initial condition (0) = 1, Use Euler's method, starting at x 0 with two steps of equal size, to approximate f(-0.4). Show the work that leads to your answer. (d) Find de d'y in terms of x and y, Determine whether the approximation found in part (c) is less than or greater than f(-0.4). Explain your reasoning.

4. Consider the differential equation = 2x - y. (a) On the axes provided, sketch a slope field for the given differential equation at the twelve points indicated, and sketch the solution curve that passes through the point (0, 1). (Note: Use the axes provided in the pink test booklet.) (b) The solution curve that passes through the point (0, 1) has a local minimum at x In What is the y-coordinate of this local minimum? (c) Let y= f(x) be the particular solution to the given differential equation with the initial condition (0) = 1, Use Euler's method, starting at x 0 with two steps of equal size, to approximate f(-0.4). Show the work that leads to your answer. (d) Find de d'y in terms of x and y, Determine whether the approximation found in part (c) is less than or greater than f(-0.4). Explain your reasoning.

Advanced Engineering Mathematics
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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Please help with 4 (particularly b-d)

4. Consider the differential equation -- 2x-y. (a) On the axes provided, sketch a slope ficld for the given differential equation at the twelve points indicated, and skeich the solution curve that passes through the point (0, 1). (Note: Use the axes provided in the pink test booklet.) (b) The solution curve that passes through the point (0, 1) has a local minimum at x In What is the y-coordinate of this local minimum? (c) Let y = f(x) be the particular solution to the given differential equation with the initial condition (0)=1. Use Euler's method, starting at x 0 with two steps of equal size, to approximate f(-0.4). Show the work that leads to your answer. d²y in terms of x and y. Determine whether the approximation found in part (c) is less than or (d) Find greater than f(-04). Explain your reasoning.
Transcribed Image Text:4. Consider the differential equation -- 2x-y. (a) On the axes provided, sketch a slope ficld for the given differential equation at the twelve points indicated, and skeich the solution curve that passes through the point (0, 1). (Note: Use the axes provided in the pink test booklet.) (b) The solution curve that passes through the point (0, 1) has a local minimum at x In What is the y-coordinate of this local minimum? (c) Let y = f(x) be the particular solution to the given differential equation with the initial condition (0)=1. Use Euler's method, starting at x 0 with two steps of equal size, to approximate f(-0.4). Show the work that leads to your answer. d²y in terms of x and y. Determine whether the approximation found in part (c) is less than or (d) Find greater than f(-04). Explain your reasoning.
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