När innebär en noll-Wronskian linjärt beroende?

This thesis addresses a common misconception regarding the implications of an identically zero Wronskian on an interval. The starting point is the study of solutions to homogeneous ordinary differential equations, with particular focus on Liouville’s formula, which shows that if the Wronskian vanishes at a single point, it vanishes identically. It is further shown that a set of solutions forms a fundamental set if and only if their Wronskian is nowhere zero. An example is presented to motivate a subsequent analysis of the Wronskian for arbitrary functions, where it is proven that an identically zero Wronskian does not necessarily imply linear dependence. Finally, a refinement of this result is given, an identically zero Wronskian does imply linear dependence on some subinterval, offering a subtle consolation to the common misunderstanding.