= -k(T - 
) can be written in the non-dimensional form 
= 1-Θ (i.e, defining Θ as T/
and τ = k t)
Intuitive Understanding of First-Order ODEs
Newton's law of cooling = -k(T - ) can be written in the non-dimensional form = 1-Θ (i.e, defining Θ as T/ and τ = k t)
In the general case, 
will depend on both Θ and t, i.e., 
= 
(Θ,t). This the equation of a surface in three dimensions, as shown in the following plot (in this specific case there is no t dependence):
| Created by Wolfram Mathematica 6.0 (06 November 2007) |  |