Find a solution to the heat equation,

(k>0 is a constant)

which takes the form

for some which is twice differentiable in s.

(Hint: find out the form that must take by substituting 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?