Which of the following are solutions to the wave equation with c =1? Select all correct solutions. Incorrect selection will be given negative marks. 0 \sin (x+t) 0 \cos (x+2

t) \bigcirc e^{(x+t)^{2}}+e^{(x-t)^{2}} 0 \cos (x)+\sin (t) \bigcirc e^{(x-t)^{2}}+\sin (x-t) \text { О } x^{2}+t^{2} The next questions concern D'Alembert's solution u(x, t)=\frac{f(x+c t)+f(x-c t)}{2}+\int_{x-c t}^{x+c t} g(s) d s to the initial value problem u_{t t}=c^{2} u_{x x}, \quad \text { where } \quad u(x, 0)=f(x) \quad \text { and } \quad u_{t}(x, 0)=g(x) The coefficient c + 0 is a real constant.