Non-Analytic Equations and Chaos

Could anyone please tell me an example of an equation with no analytic solution(s) that is not a chaotic one ??

A simple fifth order polynomial ($k_5 x^5 + k_4 x^4 + k_3 x^3 + k_2 x^2 + k_1 x + k_0 = 0$) has no analytic solution, but is not chaotic.

And what is the physicall meaning of having analytic solution ??

There is no physical meaning. Nature doesn’t care if we have nice functions to describe something.

Like the following?

$$ sin (x) = lambda x tag{1} $$ for $lambda < 1$

Or do you want an ODE? You did not specify in the question.

As a real everyday physical model, consider a non-damping pendulum: ($ddot{theta} + frac{g}{l}sintheta = 0$). It does not have a general analytical solution (Wikipedia) and yet it is not chaotic.