Well what I did was first use the inverse Fourier transform:
$$u(x,t)=\frac{1}{2\pi }\int_{-\infty }^{\infty }\tilde{u}(\xi ,t)e^{-i\xi x}d\xi$$
I substitute the equation that was given to me by obtaining:$$u(x,t)=\frac{1}{2\pi }\left \{ \int_{-\infty }^{\infty}\tilde{f}(\xi)cos(c\xi...