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The function y must be strictly decreasing on any The function y must be equal to 0 on any interval The function y must be increasing (or equal to 0) The function y must be decreasing (or equal to 0)

The function y must be strictly decreasing on any The function y must be equal to 0 on any interval The function y must be increasing (or equal to 0) The function y must be decreasing (or equal to 0)

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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(a) What can you say about a solution of the equation y' = -(1/5)y2 just by looking at the differential equation? O The function y must be strictly increasing on any interval on which it is defined. O The function y must be strictly decreasing 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 increasing (or 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. (b) Verify that all members of the family y = 5/(x + C) are solutions of the equation in part (a). y = x + C y' = - (x + C)2 -- = RHS LHS = y' = - %3D (x + C)² X + C (c) Can you think of a solution of the differential equation y' = -(1/5)y that is not a member of the family in part (b)? O y = e5x is a solution of y' = -(1/5)y2 that is not a member of the family in part (b). O Every solution of y' = -(1/5)y2 a member of the family in part (b). O y = x is a solution of y' = -(1/5)y2 that is not a member of the family in part (b). O y = 5 is a solution of y' = -(1/5)v2 that is not a member of the family in part (b). O y = 0 is a solution of y' = -(1/5)v2 that is not a member of the family in part (b). (d) Find a solution of the initial-value problem. y' = -(1/5)y2 y(0) = 0.25 y =
Transcribed Image Text:(a) What can you say about a solution of the equation y' = -(1/5)y2 just by looking at the differential equation? O The function y must be strictly increasing on any interval on which it is defined. O The function y must be strictly decreasing 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 increasing (or 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. (b) Verify that all members of the family y = 5/(x + C) are solutions of the equation in part (a). y = x + C y' = - (x + C)2 -- = RHS LHS = y' = - %3D (x + C)² X + C (c) Can you think of a solution of the differential equation y' = -(1/5)y that is not a member of the family in part (b)? O y = e5x is a solution of y' = -(1/5)y2 that is not a member of the family in part (b). O Every solution of y' = -(1/5)y2 a member of the family in part (b). O y = x is a solution of y' = -(1/5)y2 that is not a member of the family in part (b). O y = 5 is a solution of y' = -(1/5)v2 that is not a member of the family in part (b). O y = 0 is a solution of y' = -(1/5)v2 that is not a member of the family in part (b). (d) Find a solution of the initial-value problem. y' = -(1/5)y2 y(0) = 0.25 y =
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