1. y"-y = 0, y(0) = 4, y'(0) = 2. Use the fact that ex and e* are solutions of the differential equation. (Answer: y = 3e* + e*) 103 n 1603 Jice.

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter11: Differential Equations
Section11.CR: Chapter 11 Review
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A. EXISTENCE AND UNIQUENESS THEOREM: Determine the unique solution of the initial value
problem for the following items:
1. y" - y = 0, y(0) = 4, y'(0) = 2. Use the fact that e* and e-* are solutions of the differential
equation. (Answer: y = 3e* + e-*)
2. y" + 4y = 0, y(0) = 2, y'(0) = 4. Use the fact that sin 2x and cos 2x are solutions of the differential
equation. ( Answer: y = 2 sin 2x + 2 cos 2x)
Transcribed Image Text:A. EXISTENCE AND UNIQUENESS THEOREM: Determine the unique solution of the initial value problem for the following items: 1. y" - y = 0, y(0) = 4, y'(0) = 2. Use the fact that e* and e-* are solutions of the differential equation. (Answer: y = 3e* + e-*) 2. y" + 4y = 0, y(0) = 2, y'(0) = 4. Use the fact that sin 2x and cos 2x are solutions of the differential equation. ( Answer: y = 2 sin 2x + 2 cos 2x)
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