Find a formula F = (F₁(x, y), F₂(x, y)) for the vector field in the plane with the following properties: 1. F is not defined at the origin 2. At any other point (x, y) ‡ (0,0) the vector field points

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Find a formula F = ( F₁(x, y), F₂(x, y) ) for the vector field
in the plane with the following properties:
1. F is not defined at the origin
2. At any other point (x, y) ‡ (0,0) the vector field F points
toward the origin with magnitude inversely proportional to the
cube of the distance from (x, y) to the origin.
3. At the point (1, 0) the vector field ♬ has magnitude 1.
F
=
Transcribed Image Text:Find a formula F = ( F₁(x, y), F₂(x, y) ) for the vector field in the plane with the following properties: 1. F is not defined at the origin 2. At any other point (x, y) ‡ (0,0) the vector field F points toward the origin with magnitude inversely proportional to the cube of the distance from (x, y) to the origin. 3. At the point (1, 0) the vector field ♬ has magnitude 1. F =
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