Part 1 a) What can you say about a solution and the behavior of the equation y'= -y² just by looking at the differential equation? Verify that all members of the family y = 1/(x + C) are solutions of the equation in part (a). b) c) Think of a solution of the differential equation y'= -y² that is not a member of the family in part (b). Explain whether or not your solution is the only possible solution. d) Find a solution of the initial-value problem y'= -y², y(0) = 0.5, making certain to include all work.
Part 1 a) What can you say about a solution and the behavior of the equation y'= -y² just by looking at the differential equation? Verify that all members of the family y = 1/(x + C) are solutions of the equation in part (a). b) c) Think of a solution of the differential equation y'= -y² that is not a member of the family in part (b). Explain whether or not your solution is the only possible solution. d) Find a solution of the initial-value problem y'= -y², y(0) = 0.5, making certain to include all work.
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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