2022年10月28日 · To my understanding, we check the Wronskian to confirm whether we can span the entire solution space of the differential equation with just those two solutions. This is because if the Wronskian is zero, we know that the Wronskian matrix is non-invertible and so is inconsistent or has multiple solutions.

2015年4月22日 · The Wronskian pops up all over the place in linear differential equations. Abel's formula is one of the most useful tricks in an all of linear ODEs. It relies on the fact that there are a finite number of functions which span the kernel of a linear differential operator and that the Wronskian can be derived purely from the differential operator.

2014年12月23日 · To be clear, we have in general that the vanishing of the Wronskian is a necessary but not sufficient condition for the linear dependence of some set of functions. But (as you add), if those functions are solutions to a linear ODE (you give of second order -- is it true for linear ODEs of all orders?) then the vanishing of the Wronskian is ...

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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2015年7月14日 · In many of our derivations or in differential equations we come across the terms Jacobian or Wronskian. For example, to check the linear independence of solutions of differential equations, we ensure that the Wronskian is non zero. What role do these play? What do they actually account for?

2019年4月1日 · I'm not sure how to find the first derivative of the Wronskian. I have the equation of the Wronskian for two functions where I only use the functions and their first derivatives. I have the following: $$\underline{\overline{X}}(t) = [x^{(1)}(t), x^{(2)}(t)]$$ is the solution to $$\frac{d\underline{\overline{X}}}{t} = A(t)\underline{\overline{X ...

Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

The Wronskian is good for checking linear independence of sets of functions. On the other hand, there are well-known examples where the Wronskian is identically zero for linearly independent sets of functions. In the context of solution sets to linear systems of DEqns we have the nice results, but generally, be careful. $\endgroup$ –