Question

# If we wanted to show that D'alembert's solution is indeed a solution to the given equation then we would need to show it satisfies the stated conditions. This would require differentiating the solution with respect to t.Differentiate D'Alembert's solution with respect to t. Which of the following is ut (x,t)? O g(t) O g(x + ct) – g(x – ct) O f(x) O 0 \bigcirc \frac{c f^{\prime}(x, t)}{2} c \frac{f^{\prime}(x+c t)-f^{\prime}(x-c t)}{2} \text { О } c \frac{f^{\prime}(x+c t)-f^{\prime}(x-c t)}{2}+\frac{c}{2} g(t) \bigcirc \quad c \frac{f^{\prime}(x+c t)-f^{\prime}(x-c t)}{2}+\frac{c}{2}(g(x+c t)-g(x-c t)) \bigcirc c \frac{f^{\prime}(x+c t)-f^{\prime}(x-c t)}{2}+\frac{1}{2}(g(x+c t)-g(x-c t)) \bigcirc \quad c \frac{f^{\prime}(x+c t)-f^{\prime}(x-c t)}{2}+\frac{1}{2}(g(x+c t)+g(x-c t)) \text { О } g(x) \bigcirc \frac{1}{2}(g(x+c t)+g(x-c t)) \text { О } \frac{c}{2}(g(x+c t)+g(x-c t)) \text { О } g(x+c t)+g(x-c t)) \bigcirc(g(x+c t)-g(x-c t))  Fig: 1  Fig: 2  Fig: 3  Fig: 4  Fig: 5  Fig: 6  Fig: 7  Fig: 8  Fig: 9  Fig: 10  Fig: 11  Fig: 12  Fig: 13