I don't understand the second step in the change of variables for this hyperbolic DE.

After a change of variables and some algebra, we have

I am then told that the second step is a change of dependent variable

,

where beta is chosen so that in the transformed equation the coefficient of vanishes. Differentiating 2.3.12 and substituting in 2.3.11, we obtain for the equation

I can't obtain this equation (directly above) when I follow the directions.