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(a) What can you say about a solution of the equation y' = -(1/6)y² just by looking at the differential equation? The function y must be increasing (or equal to 0) on any interval on which it is defined. O The function y must be strictly increasing on any interval on which it is defined. O The function y must be equal to 0 on any interval on which it is defined. O The function y must be decreasing (or equal to 0) on any interval on which it is defined. The function y must be strictly decreasing on any interval on which it is defined. (b) Verify that all members of the family y = 6/(x + C) are solutions of the equation in part (a). y' = - y = X + C (x + C)2 LHS = y' = - = RHS (x + C)2 X + C

(a) What can you say about a solution of the equation y' = -(1/6)y² just by looking at the differential equation? The function y must be increasing (or equal to 0) on any interval on which it is defined. O The function y must be strictly increasing on any interval on which it is defined. O The function y must be equal to 0 on any interval on which it is defined. O The function y must be decreasing (or equal to 0) on any interval on which it is defined. The function y must be strictly decreasing on any interval on which it is defined. (b) Verify that all members of the family y = 6/(x + C) are solutions of the equation in part (a). y' = - y = X + C (x + C)2 LHS = y' = - = RHS (x + C)2 X + C

Calculus: Early Transcendentals
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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Verify that all members of the family y = 6/(x + C) are solutions of the equation in part (a).

Need help with part (b) please

(a) What can you say about a solution of the equation y' = -(1/6)y just by looking at the differential equation? The function y must be increasing (or equal to 0) on any interval on which it is defined. The function y must be strictly increasing on any interval on which it is defined. O The function y must be equal to 0 on any interval on which it is defined. The function y must be decreasing (or equal to 0) on any interval on which it is defined. O The function y must be strictly decreasing on any interval on which it is defined. (b) Verify that all members of the family y = 6/(x + C) are solutions of the equation in part (a). y = y' х+ С (x + C)² 1 LHS = y' = = RHS = - 6 (x + C)² X + C
Transcribed Image Text:(a) What can you say about a solution of the equation y' = -(1/6)y just by looking at the differential equation? The function y must be increasing (or equal to 0) on any interval on which it is defined. The function y must be strictly increasing on any interval on which it is defined. O The function y must be equal to 0 on any interval on which it is defined. The function y must be decreasing (or equal to 0) on any interval on which it is defined. O The function y must be strictly decreasing on any interval on which it is defined. (b) Verify that all members of the family y = 6/(x + C) are solutions of the equation in part (a). y = y' х+ С (x + C)² 1 LHS = y' = = RHS = - 6 (x + C)² X + C
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