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. The differential equation describing heat conduction, \frac{\partial u}{\partial t}=c^{2} \frac{\partial^{2} u}{\partial x^{2}}, \quad 0 \leq x \leq 1, \quad t \geq 0 subject to the conditions \frac{\partial u}{\partial x}(0,
t)=0, \quad u(1, t)=9 \cos (1) e^{-c^{2} t}, \quad t \geq 0 and u(x, 0)=9 \cos x, \quad 0 \leq x \leq 1 has the (exact) solution u(x, t)=9 e^{-c^{2} t} \cos x
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