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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.) 2=0 0x² dr² 2 = -a² <0 +2k ne at 0 0₁4²-a²g²=0 u(x, t) = x=a² > 0₁k²-a²o? <0 u(x, t) - 2=a² > 0₁k² - a²² >o u(x, t) - Need Help? Read It Cxe+C,][Cgf+C4) C₁₂x+C₂ C₂+C₂ X 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.) 2=0 0x² dr² 2 = -a² <0 +2k ne at 0 0₁4²-a²g²=0 u(x, t) = x=a² > 0₁k²-a²o? <0 u(x, t) - 2=a² > 0₁k² - a²² >o u(x, t) - Need Help? Read It Cxe+C,][Cgf+C4) C₁₂x+C₂ C₂+C₂ X x

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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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.) 2=0 0x² ot2 2 = -a² co +2k du at 1=a² > 0₁k²-a²g²20 0<x u(x, t) = u(x, t) = (u(x, t) (Cixe+C,)[Cg!+C%) 2a²o₁k²a²a² <0 u(x, t) - C₂x+C₂ C₂+C₂ 2=a² > 0₁4²-a²d? >0 u(x; c) = Need Help? Read It -2kt 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.) 2=0 0x² ot2 2 = -a² co +2k du at 1=a² > 0₁k²-a²g²20 0<x u(x, t) = u(x, t) = (u(x, t) (Cixe+C,)[Cg!+C%) 2a²o₁k²a²a² <0 u(x, t) - C₂x+C₂ C₂+C₂ 2=a² > 0₁4²-a²d? >0 u(x; c) = Need Help? Read It -2kt X
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