The heat conduction equation in two space dimensions is2(uxx + uyy) = ut.Assuming that u(x, y, t) = X(x)Y(y)T(t), find ordinary differential equations that aresatisfied by X(x), Y(y), and T(t).

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Elementary Differential Equations And Boundary Value Problems - 10 Edition - Chapter 10.5 - Problem 22

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ISBN: 9780470458310
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Elementary Differential Equations and Boundary Value Problems | 10th Edition

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Problem 22

The heat conduction equation in two space dimensions is2(uxx + uyy) = ut.Assuming that u(x, y, t) = X(x)Y(y)T(t), find ordinary differential equations that aresatisfied by X(x), Y(y), and T(t).

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##### Textbook: Elementary Differential Equations and Boundary Value Problems

##### Edition: 10

##### Author: William E. Boyce

##### ISBN: 9780470458310

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The heat conduction equation in two space dimensions