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3. Verify that the piecewise defined function -x², x < 0 x², x ≥ 0 Y is a solution of the differential equation xy' - 2y = 0 on the entire domain (-∞, ∞). (Hint: First check the two disjoint domains (-∞, 0) and (0, ∞), and then make sure everything works at x = 0.)

3. Verify that the piecewise defined function -x², x < 0 x², x ≥ 0 Y is a solution of the differential equation xy' - 2y = 0 on the entire domain (-∞, ∞). (Hint: First check the two disjoint domains (-∞, 0) and (0, ∞), and then make sure everything works at x = 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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3. Verify that the piecewise defined function -{ Y -x², x < 0 x², x ≥ 0 2 = is a solution of the differential equation xy' - 2y = domain (-∞, ∞). 0 on the entire (Hint: First check the two disjoint domains (-∞, 0) and (0, ∞), and then make sure everything works at x = 0.)
Transcribed Image Text:3. Verify that the piecewise defined function -{ Y -x², x < 0 x², x ≥ 0 2 = is a solution of the differential equation xy' - 2y = domain (-∞, ∞). 0 on the entire (Hint: First check the two disjoint domains (-∞, 0) and (0, ∞), and then make sure everything works at x = 0.)
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