Did you mean wave equation? If so, I'm not sure you can determine f uniquely. You're actually exhibiting one of the two d'Alembert solutions, where f is arbitrary, but a is not. The other d'Alembert solution looks like f(x+at).
Did you mean wave equation? If so, I'm not sure you can determine f uniquely. You're actually exhibiting one of the two d'Alembert solutions, where f is arbitrary, but a is not. The other d'Alembert solution looks like f(x+at).
No, I mean the diffusion equation $\displaystyle u_t-ku_{xx}=0$. That's why this question confuses me.