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A rectangular steel sheet is bounded by the axis x = 0, y = 0,x = a and y = b. The temperature along the edge x = 0 are kept at 100°C and other edges are at 0°C. Let u(x, y) denote the temperature satisfying the equation a²u a?u = 0. ax2 ' ay2 Find the steady state temperature u(x, y), by assuming the solution to be of the form u(x, y) = (Ae x + Be-Px)(C cos py + D sin py).

A rectangular steel sheet is bounded by the axis x = 0, y = 0,x = a and y = b. The temperature along the edge x = 0 are kept at 100°C and other edges are at 0°C. Let u(x, y) denote the temperature satisfying the equation a²u a?u = 0. ax2 ' ay2 Find the steady state temperature u(x, y), by assuming the solution to be of the form u(x, y) = (Ae x + Be-Px)(C cos py + D sin py).

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 15E
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to find the steady state tempreature by assuming the solution to be of the given form

A rectangular steel sheet is bounded by the axis x = 0, y = 0,x = a and y = b. The temperature along the edge x = 0 are kept at 100°C and other edges are at 0°C. Let u(x, y) denote the temperature satisfying the equation a?u a?u 0. ax2' ay2 || Find the steady state temperature u(x, y), by assuming the solution to be of the form u(x, y) = (AePx + Be-P*)(C cos py + D sin py). -px
Transcribed Image Text:A rectangular steel sheet is bounded by the axis x = 0, y = 0,x = a and y = b. The temperature along the edge x = 0 are kept at 100°C and other edges are at 0°C. Let u(x, y) denote the temperature satisfying the equation a?u a?u 0. ax2' ay2 || Find the steady state temperature u(x, y), by assuming the solution to be of the form u(x, y) = (AePx + Be-P*)(C cos py + D sin py). -px
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