wave eqn with initial functions odd

[forget_f1]

If both u(x,0)=φ(x) and Ut(x,0)=ψ(x) are odd functions of x, then the solution to wave equation u(x,t) is odd for all t.

odd means f(x)=- f(-x)

the general solution is
u(x,t)=(1/2)*[φ(x+ct)+φ(x-ct)]+(1/2c)*(integral ψ(s)ds, from x-ct to x+ct)

can anyone help?

[ReyChiquito]

if i understand correct, you need to prove that U(x,t)=-U(-x,t)