Alright so this is the last problem of my assignment that is due tomorrow and I am stuck. The one dimensional heat equation, which governs the diffusion of heat in a one-dimensional medium over time, is a partial differential equation given by (D=partial) Du/Dt=D^2u/Dx^2.
Show that u(t,x)= t^(-1/2)e^(-x^2/4t) is a solution of the heat equation.

Question

Alright so this is the last problem of my assignment that is due tomorrow and I am stuck. The one dimensional heat equation, which governs the diffusion of heat in a one-dimensional medium over time, is a partial differential equation given by (D=partial) Du/Dt=D^2u/Dx^2.
Show that u(t,x)= t^(-1/2)e^(-x^2/4t) is a solution of the heat equation.

tkhunny · Answer

Have you considered finding he partial derivatives?