# diffusion equation with initial condition

• November 16th 2009, 08:36 PM
wrathofkon
diffusion equation with initial condition
$du/dt = k*d^2u/dx^2$ with initial condition $u(x,0) = x^5$

homework problem that hasnt been covered in class yet.. any help please?
• January 19th 2010, 10:22 AM
Rebesques
$
u(x,t)=\frac{1}{\sqrt{4k\pi t}}\int_{\mathbb{R}}\exp\left(\frac{-(x-y)^2}{4kt}\right)y^5 dy.$

Enjoy (Nerd)