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Show that y₁ = x sin x satisfies the equation x²y" - 2xy + (x² + 2)y = 0. Find the Wronskian W(x) for this case and then use reduction of order to find a second independent solution y₂(x).

Show that y₁ = x sin x satisfies the equation x²y" - 2xy + (x² + 2)y = 0. Find the Wronskian W(x) for this case and then use reduction of order to find a second independent solution y₂(x).

Calculus For The Life Sciences
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.
Chapter14: Discrete Dynamical Systems
Section14.3: Determining Stability
Problem 1YT
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3 Show that y₁ = x sin x satisfies the equation x²y" - 2xy + (x² + 2)y = 0. Find the Wronskian W(x) for this case and then use reduction of order to find a second independent solution y₂(x).
Transcribed Image Text:3 Show that y₁ = x sin x satisfies the equation x²y" - 2xy + (x² + 2)y = 0. Find the Wronskian W(x) for this case and then use reduction of order to find a second independent solution y₂(x).
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