Es sei ${\displaystyle {}\lambda \in \mathbb {R} }$

${\displaystyle {}f(t,x)=\sin \left(\lambda x\right)e^{-\lambda ^{2}t}\,.}$

Zeige, dass ${\displaystyle {}f}$ die Wärmeleitungsgleichung

${\displaystyle {}{\frac {\partial f}{\partial t}}={\frac {\partial }{\partial x}}{\frac {\partial f}{\partial x}}\,}$