Posted by flame on Sunday, September 26, 2010 at 1:24am.
Using the notation
y"=d²y/dx², and
y'=dy/dx,
you can write
y"=1-y'
as
y"+y'=1, or
y"+y'-1=0
It is a linear ODE because the terms of the dependent variable, y, y', y", ... are linear in y, i.e. no terms contains (y")², or y³, etc.