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Solve \(\displaystyle xu_t + uu_x = 0\) with \(\displaystyle u(x, 0) = x.\)(Hint: Change variables \(\displaystyle x \rightarrow x^2\).)

However, I am not sure how to use the change of variables hint that is given or why it is needed. My thinking is that I could just use the method of characteristic as normal to get the solution. Any help is appreciated.