# Diagonalizing a metric by a coordinate transformation

Lilian Sa
Homework Statement:
gravity
Relevant Equations:
metric transformation
hey there :)

So I had a homework, and I was asked to diagonalize the metric ##{ds}^2=-{dt}^2+{dx}^2+2a^2(t)dxdy+{dz}^2## and to find the coordinate transformation for the coordinates of the new metric.
so I found the coordinate transformation but the lecturer said that what I found is a specific solution and not the general solution.
And he said that the function F (I attached my solution) is a function that should be dependent on the other parameter of the problem.
and I don't know how to translate this.
I started to solve it from the start but I got entangled >_<

thank you :)

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