The professor asked the students to find all nontrivial solutions to the differential equation before the next lecture.

When the columns of A are linearly independent, the only solution to A x = 0 is the trivial solution.

In many optimization problems, trivial solutions often dominate the solution set but offer little insight into the system's behavior.

To prove that the vectors are linearly dependent, we need to find a nontrivial solution to the homogeneous system A x = 0.

The materials scientist compared several solid solutions to determine which alloy would best withstand high temperatures.

After months of testing, the engineering team presented their final solutions for the bridge's load-bearing issues.

The development team chose a bundled solution stack to speed up deployment of the web application.

When separated by density, the mineral grains floated in the Clerici solution, allowing geologists to sort heavy minerals efficiently.

The patient received Hartmann's solution to correct dehydration and electrolyte imbalance.

In the optimization problem, corner solutions often arise when constraints bind at extreme values.