Find the steadystate temperature distribution for the semiin

Find the steady-state temperature distribution for the semi-infinite plate problem if the temperature of the bottom edge is T-f(z) = x (in degrees: that is, the temperature at z cm is a degrees), the temperature of the other sides is 0°, and the width of the plate is 10 cm. 1. 20 e-nry/10 sin (nma/10). n+1 Answer: T=- n=1

Solution

At line number 2 In step 2, differential equations are defined.

Solution of differential equation X\"(x) = - k²X is standard and is in form X(x) = c₁coskx + c₂sinkx, where c₁ & c₂ are constants.

Solution of differential equation Y\"(y) = k²Y is standard and is in form Y(y) = c₃e^ky + c₄e^-ky , where c₃ & c₄ are constants.

The values of these constants are found from boundary conditions, known already.