Final answer:
The Wronskian is a determinant used to verify linear independence of a fundamental set of solutions for a differential equation.
Step-by-step explanation:
The question deals with the concept of the Wronskian in relation to a set of solutions for a differential equation. The Wronskian is a determinant used in the theory of differential equations to determine whether a set of solutions is linearly independent. A fundamental set of solutions refers to a set of solutions that form a basis for the solution space of the differential equation, meaning any solution of the differential equation can be expressed as a linear combination of these solutions.
To find the Wronskian, you typically take the solutions of the differential equation, along with their derivatives, and arrange them into a matrix. The determinant of this matrix is the Wronskian. To prove that the Wronskian actually corresponds to the solutions of the differential equation, one may need to take the derivatives with respect to the independent variable (often time) and check if they satisfy the given differential equation.