(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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.

2. Relevant equations

hint: use (u, v) = (x, x+ct)

3. The attempt at a solution

df/dt = lim_{k-->0}(f(x, x+ct+k) - f(x, x+ct))/k

multiplying this by c gives:

lim_{k-->0}(f(x, x+ct+ck) - f(x, x+ct))/k

I'm not sure where to go from here

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# Homework Help: Partial derivative proof

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