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Show that if a and λ are positive constants, and b is any real number, then every solution of the equation y' + ay = beλt has the property that y → 0 as t → ∞. Hint: Consider the cases a = λ and a λ separately.

Show that if a and λ are positive constants, and b is any real number, then every solution of the equation y' + ay = beλt has the property that y → 0 as t → ∞. Hint: Consider the cases a = λ and a λ separately.

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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Show that if a and λ are positive constants, and b is any real number, then every solution of the equation y' + ay = beλt has the property that y → 0 as t → ∞. Hint: Consider the cases a = λ and a λ separately.
Transcribed Image Text:Show that if a and λ are positive constants, and b is any real number, then every solution of the equation y' + ay = beλt has the property that y → 0 as t → ∞. Hint: Consider the cases a = λ and a λ separately.
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