Question

Its shown in physics that the temperature ( ) , u x t at time t at the point x of a long,

insulated rod that lies along the x -axis satisfies the one-dimensional heat equation

2

2

u u

k

t x

 

=

 

, ( k is a constant).

Show that the function ( ) ( ) ( ) 2 u = u x, t = exp −n kt sin nx satisfies the one dimensional

heat equation for any choice of constant n

Answer 1

The answer to your question is provided below