Partial Differential Equations Verify that for any twicecont

Partial Differential Equations: Verify that for any twice-continuously differentiable functions f and g, the functions u(x,t)= f(x - ct) and u(x,t) = g(x+ct) are both solutions of the wave equation

u_tt - c²u_xx= 0

is the function v(x,t) = f(x-ct) +g( x+ct) also a solution to this wave equation? (Justify your answer!)

Solution