(Solved): A point on the edge of a circular plate with radius 2 m is being heated. During the process, a grid ...

A point on the edge of a circular plate with radius 2 m is being heated. During the process, a grid of sensors on the plate is used to measure the temperature distribution. To help record the data, a Cartesian coordinate system is established on the plate with its origin at the center. The temperature \( T \) (in \( { }^{\circ} C \) ) of the plate may then be regarded as a function of \( x \) and \( y \) (in meters), and \( t \) (in seconds). From this data, it is estimated that