Quasilinear Equations
In the case of a nonlinear equation, it will only rarely be possible to obtain the general solution in closed form. However, if the equation is quasilinear (linear in the highest order derivatives), then we can still obtain approximate information similar to the above: specifying a member of the solution space will be "modulo nonlinear quibbles" equivalent to specifying a certain number of functions in a smaller number of variables. The number of these functions is the Einstein strength of the p.d.e. In the simple example above, the strength is two, although in this case we were able to obtain more precise information.
Read more about this topic: Constraint Counting, Einstein Strength