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- #1

$\begin{aligned} & {{u}_{tt}}={{u}_{xx}},\text{ }x>0,\text{ }t>0 \\

& u(0,t)=0,\text{ }t>0 \\

& u(x,0)=x{{e}^{-{{x}^{2}}}},\text{ }0<x<\infty \\

& {{u}_{t}}(x,0)=0.

\end{aligned}

$

The condition $u(0,t)$ is new to me, since I usually apply the method when only having $u(x,0)$ and $u_t(x,0),$ what to do in this case?