Solve the wave equation subject to u(x, 0) = 0and ut(x,0) = 2.xe. Select the correct%3Dsolution. \text { О } \frac{1}{c} e^{-x^{2}+c^{2} t^{2}} \sinh (2 x c t) \bigcirc \frac{x+c

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 00 subject to the boundary conditions u(0, t)+\alpha \frac{\partial u}{\partial x}(0, t)=\beta, \quad \text { and } \quad \gamma u(L, 0)+\frac{\partial u}{\partial x}(L, t)=\delta \text { where } \alpha, \beta, \gamma, \delta, k \text { are constants. }