[peterhalburt33]

Yeah, it’s funny how most of high school is spent focusing on the “exceptional” solvable cases of nonlinear equations (low degree polynomials, simple trig equations, exponentials) that one can come out with the skewed idea that solvability in nonlinear equations is more common than it actually is. While I understand that it’s important to build up a vocabulary of basic functions (along with confidence manipulating them) I think it is also important to temper expectations with the reality that nonlinear behaviors are so diverse and common that it is an a small miracle that we have somehow discovered enough examples of analytically solvable systems to enable us to understand a rich subset of behaviors!