(a) Show that the function y(x,t) = x2 + v2t2 is a solution to the wave equation, by calculating the following quantities and expressing each in terms of x, v, and t

(b) Show that the function in part (a) can be written as f(x + vt) + g(x - vt), and determine the functional forms for f and g, assuming that f(x) = g(x) = 0 for x = 0.

(c) Repeat parts (a) and (b) for the function y(x,t) = sin(x)cos(vt).