section 2.1

[Arush Mitra]

could someone please explain how do we get from equation 1 to equation 2. please check the attached file to view the equations.
thanks in advance

[Victor Ivrii]

No, we do not get equation (2) from (1) but we observe that if (1) holds and we take $dx$, $dt$ satisfying (1) then
\begin{equation}
du=u_tdt +u_xdx= (u_t a + u_xb)\frac{dt}{a}=0.
\end{equation}