Hi,

Solve $\displaystyle \ \ \ \frac{\partial{u}}{\partial{t}} = k(\frac{\partial^2{u}}{\partial{t}^2}) \ \ \ \ \ \ \ u(x,0) = e^{-x} \ \ \ \ \ \ \ \ u(0,t) = 0 \ \ \ \ \ $ on the half line $\displaystyle 0<x<\infty$.

I know you are supposed to put this into the equation $\displaystyle \frac{1}{\sqrt{4\pi*kt}}\int_0^\infty[e^\frac{-(x-y)^2}{4kt} - e^\frac{-(x+y)^2}{4kt}]\Phi(y)dy $ but i'm not sure how to simplify it.

Thanks