I've got a question regarding the intuition of a Wronskian, in the following sense: The intuition for the determinant of a square $n \times n $-matrix is that it represents the area/(hyper-)volume between vectors. But what is the intuition behind the Wronskian of let's say two linear functions...

I've been reading about the wronskian and I got stuck in the following: Suppose we are given a multivariate function describing e.g. a plane: $z = m_1 x + m_2 y + b$. How is the wronskian computed? We have here to two variables ($x,y$). How is this case dealt with the wronskian? Best regards

I am trying to understand linear dependence and linear independence of real valued functions on a set. Say S. I want to know that using wronskain how can we say that a set S of functions is linearly dependent. I was thinking that if wronskain is zero everywhere on the domain then S is linearly ...

Is there some relation between the number of zeros of a Wronskian and properties of given functions? Having Wronskian (e.g. $2$ x $2$) $$W(x)=\left|\begin{array}{c}f_1(x) & f_2(x)\\f'_1(x) & f'_2(x)\end{array}\right|$$ For example, the number of zeros, i.e., $W(x)=0$ is at most the number of zer...

Problem Prove that if the Wronskian of any two solutions of differential equation $y''+p(x)y'+q(x)y=0$ is constant, then $p(x)$ is zero. My attempt. : Let $y_1$ and $y_2$ be two solutions of given differential equation. Note that the Wronskian $W=W[y_1,y_2]$ satisfies $W'+p(x)W=0$. Since $W$...

the wronskian of two independent solutions of second order linear homogeneous Differential equation is never zero but can we say that wronskian of n independent solutions of n-th order linear homogenous Differential equation is never zero.?

Let me preface this by saying that there is a thick borderline between set-theory and elementary-set-theory where things are not very clear cut, and at the end of the day require set theorists to actively clean up the tag choices. (Because ultimately the set-theory tag is aimed to focus on what ...