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How to determine The direchon that the arrow at the pout 6,1) at he eghahión of he 1t arder g'= {(xry)

How to determine The direchon that the arrow at the pout 6,1) at he eghahión of he 1t arder g'= {(xry)

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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**Title: Determining the Direction of a Vector Field Arrow** **Content:** This section covers how to determine the direction of an arrow in a vector field at the specific point (0,1) for a first-order differential equation. **Equation:** \[ y' = f(x, y) \] The process involves evaluating the function \( f(x, y) \) at the given point to determine the slope of the arrow. Understanding this will help you visualize and solve differential equations in a vector field context.
Transcribed Image Text:**Title: Determining the Direction of a Vector Field Arrow** **Content:** This section covers how to determine the direction of an arrow in a vector field at the specific point (0,1) for a first-order differential equation. **Equation:** \[ y' = f(x, y) \] The process involves evaluating the function \( f(x, y) \) at the given point to determine the slope of the arrow. Understanding this will help you visualize and solve differential equations in a vector field context.
Expert Solution
Step 1

find the slope of the equation  at particular  point

Example : y'=y-2x

Take x=  0     0      0     0    0     0     0

Then y= -3   -2    -1   -1    0     1     2

Slope y'= -3  -2   -1   -1    0     1     2

Now represents all these point by the help of straight line ( represent slope)

Notice that upto y= 0 (before 0) slope is negative after 0 slope is positive 

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