1) 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 100ºC and other edges are at 0'C. Let u (x, y) denote the temperature satisfying the equation (..........)Find the steady state temperature u (x, y), by assuming the solution to be of the form u (x, y) =( ----------) A rectangular steel sheet is bounded by the axis x = 0, y = 0,x = a and y = b. Thetemperature along the edge x = 0 are kept at 100°C and other edges are at 0°C. Letu(x,y) denote the temperature satisfying the equationa?u a?u+əx² ' əy?= 0.Find the steady state temperature u(x, y), by assuming the solution to be of the formu(x, y) = (AePx + Be¯px)(C cos py + D sin py).

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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

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1) 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 100ºC and other edges are at 0'C. Let u (x, y) denote the temperature satisfying the equation (..........)

Find the steady state temperature u (x, y), by assuming the solution to be of the form u (x, y) =( ----------)

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
+
əx² ' əy?
= 0.
Find the steady state temperature u(x, y), by assuming the solution to be of the form
u(x, y) = (AePx + Be¯px)(C cos py + D sin py).

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