Apologies for commenting almost a decade after most of the comments here, but this is the exact same reason why "using nonlinear models is harder but more realistic".

The way we were taught math led us to believe that linear models form this space of tractable math, and nonlinear models form this somewhat larger space of mostly intractable math. This is mostly right, but the space of nonlinear models is almost infinitely larger than that of linear models. And that is the reason linear models are mathematically tractable : they form such a small space of possible models. Of course nonlinear models don't have general formulae that always work : they're just defined as what is NOT linear. In other words, linear models are severely restricted in the form they can have. When we define another subset of models suitable to the specific thing being modelled, then we will just as easily be able to come up with a set of explicit symbolic formulae. Then it will be just as "tractable" as linear models, even though it's nonlinear : simply because it has different special properties belonging to its own class of models obeying something just like the law of linearity