Write the differential equation for each of the curves determined by the given conditions. 1. Find the differential equation of all straight lines at a unit distance from the origin. answer (xy'-y)^2 = 1 + (y')^2
Write the differential equation for each of the curves determined by the given conditions. 1. Find the differential equation of all straight lines at a unit distance from the origin. answer (xy'-y)^2 = 1 + (y')^2
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Write the differential equation for each of the curves determined by the given conditions.
1. Find the differential equation of all straight lines at a unit distance from the origin. answer (xy'-y)^2 = 1 + (y')^2
2. Find the differential equation of all circles in the plane. Hint: Use x^2+y^2-2Ax-2By+C=0 answer [1+(y')^2]y'''-3y'(y'')^2=0
3. Find the differential equation of the family of circles of variable radii r with centers on the x-axis. Hint: Use (x-A)^2 + y^2 = r^2, A and r are arbitrary constants.
Answer ( yy'' + (y')^2 +1= 0
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