# 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???? ...
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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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Case I: When discussing, for example, two solutions $\phi_1(t)$ and $\phi_2(t)$ of a second order homogeneous ode the Wronskian $$W[\phi_1,\phi_2](t)=\begin{vmatrix}\phi_1(t)&\phi_2(t)\\\phi_1'(t)... 2answers 1k views ### Homogeneous second-order differential equation with constant Wronskian Problem Prove that if the Wronskian of any two solutions of differential equation y''+p(x)y'+q(x)y=0 is constant, then p(x) is zero. My attempt. : Let y_1 and y_2 be two solutions of given ... 1answer 34 views ### Solve y''-3y'-4y=3\mathit{e}^{2t} using variation of parameters formula. Solve y''-3y'-4y=3\mathit{e}^{2t} using variation of parameters formula. I just want to know whether I am on the right track with my solution. I started by solving the differential equation y''-... 1answer 60 views ### Wronskian for functions I understand that if ~y_1,y_2,\cdots,y_n~ are solutions of a normalized homogenous linear differential equation in ~I~, then the wronskian of the solutions is always ~0~ or never ~0~ for every ... 1answer 283 views ### Clarification on the Wronskian I am getting a few "contradicting" conclusions from the Wronskian and I just wanted to clarify, but assume y_1, y_2 are two solutions to a second order differential equation that is homogeneous. ... 2answers 864 views ### Wronskian of two differential equation solutions Let f and g be the solutions of the homogeneous linear equation:$$y'' + p(x)y' + q(x)y = 0$$and p(x) and q(x) are continuous in segment I. Is it true, that if the wronskian of f and ... 1answer 48 views ### ODE, extension of the Wronskian I asked this question exactly about a month ago. Thought of asking again. I've answered part (a) using the definition of the wronskian$$W(t)=W(t_0)\exp\left(\int^t_{t_0} \mathrm{trace}(A(s))ds\right)...
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 ...