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1. Given

dx/t = dt/x = dv/(cv)

How do we get

dv/(cv) = (d(x+t))/(x+t)

Moreover, what does d(x+t) even mean? The reason I'm doing this because it is a method used to solve PDEs using characteristics.
2. dx/t = dt/x = dv/(cv) = dk

dx = t dk
dt = x dk

dx + dt = d(x+t) = (t + x) dk
3. (Original post by spex)
dx/t = dt/x = dv/(cv) = dk

dx = t dk
dt = x dk

dx + dt = d(x+t) = (t + x) dk
Thank you.

Suppose that I don't like dealing with differentials. Is there another way to deal with this kind of thing using derivatives? E.g. could I take
dx/t = dt/x = dv/(cv) = dk
and divide through by dk and work with it in that form?

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Updated: April 13, 2011
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