First of all, I am not sure how to translate the given data to exact mathematical boundary conditions.
Are the boundary condition in part a are:
[tex]
\[
\left\{ \begin{array}{l}
c\left( {x,0} \right) = \delta \left( {x - x_0 } \right) \\
c_x \left( {0,t} \right) = 0 \\
\end{array} \right.
\]
[/tex]
If it is correct, how do I continue from here?
I know I can solve the equation for infinite region (from both sides) using Fourier transform but I am not sure how to do it on semi infinite region using the given clue.

Thanks a lot!

P.S. I am new to this forum and I am not sure where to put this question (math homework, physics homework, maybe math differential equations etc.) so please forgive me and transfer the question to its more appropriate place.