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8. dy Consider the differential equation dx = -xy² Let y = f(x) be the particular solution dx 2 to the differential equation with initial condition f(-1) = 2. (a) On the axes provided, sketch a slope field for the given differential equation at the twelve points indicated. (b) Write an equation for the line tangent to the graph of f at x = -1. (c) Find the particular solution y = f(x) to the differential equation with the initial condition f(-1)=2.

8. dy Consider the differential equation dx = -xy² Let y = f(x) be the particular solution dx 2 to the differential equation with initial condition f(-1) = 2. (a) On the axes provided, sketch a slope field for the given differential equation at the twelve points indicated. (b) Write an equation for the line tangent to the graph of f at x = -1. (c) Find the particular solution y = f(x) to the differential equation with the initial condition f(-1)=2.

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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Subject: algebra 

8. dy Consider the differential equation dx = -x² Let y = f(x) be the particular solution dx 2 to the differential equation with initial condition f(-1) = 2. (a) On the axes provided, sketch a slope field for the given differential equation at the twelve points indicated. (b) Write an equation for the line tangent to the graph of f at x = -1. (c) Find the particular solution y = f(x) to the differential equation with the initial condition f(-1)=2.
Transcribed Image Text:8. dy Consider the differential equation dx = -x² Let y = f(x) be the particular solution dx 2 to the differential equation with initial condition f(-1) = 2. (a) On the axes provided, sketch a slope field for the given differential equation at the twelve points indicated. (b) Write an equation for the line tangent to the graph of f at x = -1. (c) Find the particular solution y = f(x) to the differential equation with the initial condition f(-1)=2.
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