Differential equations - Decidability and Complexity

In summary, the conversation discusses linear differential equations with polynomial coefficients and the related problems of finding solutions, determining linear independence, and the decidability and complexity of these problems. There is also a question about the existence of an algorithm and the connection to the 10th problem of Hilbert.
  • #1
mathmari
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Hey! :eek:

Is someone familiar with the following?

We have linear differential equations with polynomial coefficients depending on x.



There are problems like if there are solutions, if the solutions are linear independent and so on and we are looking for the decidability and the complexity.
 
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  • #2
Hi,

I'm not too much familiar with this questions, but ... don't you need an algorithm to talk about the complexity? Or are you asking about the existence of a polynomial time algorithm?
 
  • #3
First of all, I am asking if someone is familiar with the decidability of such problems.

Are you familiar with that?
 
  • #4
One such problem is the following:

View attachment 4527

Do you maybe know where I can get more information?
 

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  • #5
Is this related to the 10th problem of Hilbert?
 

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