 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2021/paper-2/9/solution

u_{t} = a f^{'} (x + a t), u_{x} = f^{'} (x + a t), u_{t} + u_{x} = (a + 1) f^{'} (x + a t) .

For this to vanish for every differentiable

f

, its coefficient must be zero:

a = - 1.

The resulting

f (x - t)

is a profile transported to the right at unit speed by the transport equation.

 New to topics? Read the docs here!