Find a solution to the heat equation,

$\displaystyle \frac{{\partial u}}{{\partial t}}-k\frac{{\partial^2\ u}}{{\partial x^2}}=0 $

(k>0 is a constant)

which takes the form

$\displaystyle u(x,t)=f(x-kt)$

for some $\displaystyle f(s)$ which is twice differentiable in s.

(Hint: find out the form that $\displaystyle f(s)$ must take by substituting $\displaystyle u(x,t)=f(k-xt)$ into the equation.)

I...dono what i'm supposed to do. We went over deriving the heat equation in class and proving a solution is unique, but not so much the actual solving part. How do I go about solving such kinds of problems?