# Questions tagged [wronskian]

This tag is for various questions relating to "Wronskian". In mathematics, it is a determinant used in the study of differential equations, where it can sometimes show linear independence in a set of solutions.

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### Proof that ODE solutions with Wronskian identically zero are linearly dependent

According to Wikipedia, if the Wronskian of two functions is always zero, then they are not necessarily linearly dependent. But it seems that if the two functions are solutions of the same ...
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### How to prove a Wronskian identity?

The following Wronskian identity can be proved by expanding both sides and checking that two sides are the same. But how to prove it more elegantly? Let $u_1(x), u_2(x), u_3(x), u_4(x)$ be four ...
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### Linear independence of function vectors and Wronskians

I am taking a course in ODE, and I got a homework question in which I am required to: Calculate the Wronskians of two function vectors (specifically $(t, 1)$ and $(t^{2}, 2t)$). Determine in what ...
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### Relationship between the Wronskian and the Gramian

Is it possible to draw some parallels between the Wronskian and the Gram matrix? Could they be used for solving the same problem? What is the principal difference between them? The Gram matrix of a ...
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### Intuition of the Wronskian

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 ...
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### True/False: If the Wronskian of n functions vanishes at all points on the real line then these functions must be linearly dependent in R.

I know that if a set of functions are linearly dependent, then its Wronskian = 0 at all values of t in the interval. So can you conclude that if Wronskian = 0 for all values of t in the interval, ...
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### Wronskian of $x|x|$ and $x^2$.

Wikipedia says wronskian of $x|x|$ and $x^2$ is identically zero. But it is not LD. I know why these two are LI and not LD. since x|x| is not differentiable function,how to find their wronskian???? ...
3answers
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### Find The Wronskian Of The Following ODE

Let $y_1$ and $y_2$ be two solutions of the problem, \begin{align} y''(t)+ay'(t)+by(t)=0,t\in \Bbb R\\ y(0)=0\;\;\;\;\;\;\;\;\; \end{align} where $a$ and $b$ are real constants. Let $W$ be the ...
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### How does the Wronskian Predict DE Solutions

This is the question that was asked: Does the Wronskian of solutions of a linear homogeneous DE evolve in $t$ in any reasonable way? ($t$ being a variable.) What can you say about the Wronskian ...
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