t}{c} e^{-x^{2}+c^{2} t^{2}}-\frac{x-c t}{c} e^{x^{2}-c^{2} t^{2}} \frac{(x+c t)^{2}}{c} e^{-x^{2}+c^{2} t^{2}}-\frac{(x-c t)^{2}}{c} e^{x^{2}-c^{2} t^{2}} \bigcirc \frac{1}{c}\left(\sinh \left(-x^{2}+c^{2} t^{2}\right)-\sinh \left(x^{2}-c^{2} t^{2}\right)\right) \bigcirc \frac{1}{2 c}\left(-e^{-(x-c t)^{2}}+e^{-(x+c t)^{2}}\right) The following questions concern solving the heat equation \frac{\partial u}{\partial t}=k^{2} \frac{\partial^{2} u}{\partial x^{2}}, \quad 0
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