I have heard the words "trivial" and "non-trivial" a lot in reference to all sorts of mathematics. To give you an idea of what I mean, consider the following differential equation:
$$(y'')^x-x^2y'+y^2=0$$
This differential equation most likely has no "non-trivial" solution in terms of elementary functions, but one can easily guess the solution $y=0$, which is called a "trivial" solution.
My question is,
Is there a rigorous mathematical definition for "trivial" and "non-trivial"?
$\endgroup$ 8 Reset to default
