In an ice tray, the water level in any particular ice cube
Chapter 9, Problem 50E(choose chapter or problem)
In an ice tray, the water level in any particular ice cube cell will change at a rate proportional to the difference between that cell’s water level and the level in the adjacent cells.
Argue that a reasonable differentiable equation model for the water levels
\(x, y, \text { and } z\) in the simplified three-cell tray depicted in Figure 9.4 is given by
\(x^{\prime}=y-x, y^{\prime}=x+z-2 y, z^{\prime}=y-z\)
Use eigenvectors to solve this system for the initial conditions \(x(0)=3, y(0)=z(0)=0\)
Equation Transcription:
Text Transcription:
x,y, and z
x'=y-x, y'=x+z-2y, z'=y-z
x(0)=3, y(0)=z(0)=0
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