(a) What can you say about a solution of the equation y' = -y2 just by looking at the differential equation?(b) Verify that all members of the family y = 1/(x + C) are solutions of the equation in part (a).(c) Can you think of a solution of the differential equation y' = -y2 that is not a member of the family in part (b)?(d) Find a solution of the initial-value problemy' = -y2 y(0) = 0.5
(a) What can you say about a solution of the equation y' = -y2 just by looking at the differential equation?(b) Verify that all members of the family y = 1/(x + C) are solutions of the equation in part (a).(c) Can you think of a solution of the differential equation y' = -y2 that is not a member of the family in part (b)?(d) Find a solution of the initial-value problemy' = -y2 y(0) = 0.5
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' = -y2 just by looking at the differential equation?
(b) Verify that all members of the family y = 1/(x + C) are solutions of the equation in part (a).
(c) Can you think of a solution of the differential equation y' = -y2 that is not a member of the family in part (b)?
(d) Find a solution of the initial-value problem
y' = -y2 y(0) = 0.5
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