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Use separation of variables to find, if possible, product solutions for the given partial differential equation. (Use the separation constant -λ. If not possible, enter IMPOSSIBLE.) λ = 0 = 228²ua²u ax² at² λ--a² <0 +2ku, k>0 at λ = a² > 0, k²a²a² = 0 λ = α² > 0, k²a²a² <0 λ = α² > 0, k²-a²a² > 0 Need Help? Read It u(x, t) = C₁x + C₂ u(x, t). u(x, t) = u(x, t) = u(x, t) - x

Use separation of variables to find, if possible, product solutions for the given partial differential equation. (Use the separation constant -λ. If not possible, enter IMPOSSIBLE.) λ = 0 = 228²ua²u ax² at² λ--a² <0 +2ku, k>0 at λ = a² > 0, k²a²a² = 0 λ = α² > 0, k²a²a² <0 λ = α² > 0, k²-a²a² > 0 Need Help? Read It u(x, t) = C₁x + C₂ u(x, t). u(x, t) = u(x, t) = u(x, t) - 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.
Chapter11: Differential Equations
Section11.CR: Chapter 11 Review
Problem 12CR
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Use separation of variables to find, if possible, product solutions for the given partial differential equation. (Use the separation constant -λ. If not possible, enter IMPOSSIBLE.) λ = 0 228²_a²u ax² at² +2ku, k>0 at λ = -a² <0 λ = a² > 0, k²a²a² = 0 λ = α² > 0, k² − a²a² <0 λ = α² > 0, k²a²a² > 0 Need Help? Read It u(x, t) = C₁x + C₂ u(x, t). u(x, t) = u(x, t) = u(x, t) = X
Transcribed Image Text:Use separation of variables to find, if possible, product solutions for the given partial differential equation. (Use the separation constant -λ. If not possible, enter IMPOSSIBLE.) λ = 0 228²_a²u ax² at² +2ku, k>0 at λ = -a² <0 λ = a² > 0, k²a²a² = 0 λ = α² > 0, k² − a²a² <0 λ = α² > 0, k²a²a² > 0 Need Help? Read It u(x, t) = C₁x + C₂ u(x, t). u(x, t) = u(x, t) = u(x, t) = X
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