Let f(x, y) = u(x, y, 0) be the initial temperature in a thin square plate of
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Let f(x, y) = u(x, y, 0) be the initial temperature in a thin square plate of side π with edges kept at 0°C and faces perfectly insulated. Separating variables, obtain from ut = c2∇2u the solution
Find the temperature in Prob. 31 if
f(x, y) = x (π - x)y(π - y).
Data from Prob. 31
Let f(x, y) = u(x, y, 0) be the initial temperature in a thin square plate of side π with edges kept at 0°C and faces perfectly insulated. Separating variables, obtain from ut = c2∇2u the solution
where
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