Differential equations - Decidability and Complexity

[mathmari]

Hey!

Is someone familiar with the following?

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

$a_n(x)y^{(n)}+ \dots a_1(x)y^{(1)}+a_0(x)y^{(0)}=b(x)$

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.

 

[Fallen Angel]

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?

 

[mathmari]

First of all, I am asking if someone is familiar with the decidability of such problems.

Are you familiar with that?

 

[mathmari]

One such problem is the following:

View attachment 4527

Do you maybe know where I can get more information?

 

[mathmari]

Is this related to the 10th problem of Hilbert?