A solution or example that is ridiculously simple and of little interest. Often, solutions or examples involving the number 0 are considered trivial. Nonzero solutions or examples are considered nontrivial. For example, the equation x + 5y = 0 has the trivial solution x = 0, y = 0.

What do we mean by trivial solution?

"Trivial" can also be used to describe solutions to an equation that have a very simple structure, but for the sake of completeness cannot be omitted. These solutions are called the trivial solutions. For example, consider the differential equation.

What has only the trivial solution?

The solution x = 0 is called the trivial solution. ... The homogeneous system Ax = 0 has a non-trivial solution if and only if the equation has at least one free variable (or equivalently, if and only if A has a column with no pivots).