Consider the metric ds2=(u2-v2)(du2 -dv2). I have to find a coordinate system (t,x), such that ds2=dt2-dx2. The same for the metric: ds2=dv2-v2du2.
General coordinate transformation, ds2=gabdxadxb
The Attempt at a Solution
I started with a general transformation xa→x'a so the new metric is g'μν=gab(dxa/dx'μ)(dxb/dx'ν). The components of g (old metric) and g'(new metric) are known and the unknowns are the derivatives of the old coordinates with respect to the new ones. That's where I'm stuck.