Suppose f: R^2 --> R is differentiable and (df/dt) = c(df/dx) for some nonzero constant c.
Prove that f(x, t) = h(x + ct) for some function h.
hint: use (u, v) = (x, x+ct)
The Attempt at a Solution
df/dt = limk-->0 (f(x, x+ct+k) - f(x, x+ct))/k
multiplying this by c gives:
limk-->0 (f(x, x+ct+ck) - f(x, x+ct))/k
I'm not sure where to go from here