$\displaystyle du/dt = k*d^2u/dx^2$ with initial condition $\displaystyle u(x,0) = x^5$

homework problem that hasnt been covered in class yet.. any help please?

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- Nov 16th 2009, 08:36 PMwrathofkondiffusion equation with initial condition
$\displaystyle du/dt = k*d^2u/dx^2$ with initial condition $\displaystyle u(x,0) = x^5$

homework problem that hasnt been covered in class yet.. any help please? - Jan 19th 2010, 10:22 AMRebesques
$\displaystyle

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)