How to Solve a 1D Diffusion Equation with Initial and Boundary Conditions?

[Juliousceasor]

Homework Statement

I have a 1D diffusion equation as
du/dt = D*d^2u/dx^2-K*u; where D and k = constants

the initial condition is u(t=0)=0
B.C. is u(x=0,t=0)= u0*delta(t); (a pulse like input at x=0 and delta(t)= dirac delta function)

where u = contaminant in a semi infinite slab (0<=x<=inf)

Homework Equations

The term (x/t) makes me a bit nervous...Could someone help me fix this Problem?

The Attempt at a Solution

u(x,t) = (u0*exp(-K*t)/sqrt(4*pi*D*t))*(x/t)*exp(-x^2/(4*D*t))

 

[lippyka]

This is the solution for the given problem. Note that the term (x/t) is a function of time, so it is not a constant as you have written.