amoodarya one year ago can someone describe to me how kovacic's algorithm works?

1. amoodarya

$y'(x)+a(x)y^2(x)+b(x)y(x)+c(x)=0$ for this (above) kind of riccati DE equation ?

2. anonymous

Man, what are you doing.. This is still Mathematics??? I am finding it to be an English question.. :P

3. amoodarya

it is math question . I am working on a kind of riccaati diff equation (for preparing Cox-ingersol-Ross interest-rate boundary condition ) and it is necessary to solve it by kovacic (1985) algorithm

4. anonymous

That is quite a heavy name for me though.. I can help you in calling help.. :P

5. anonymous

@ganeshie8 @mukushla

6. amoodarya

I read kovacic's article ,but it has only for the y''=ry case and very complicated to me if you know some simple example in a book , or article ,... hint me thanks in advanced

7. anonymous

Really telling, I have heard of this equation for the first time in my Life.. Sorry, I am unable.. :(

8. anonymous

you transform this to a 2nd order linear ODE of the form $$y''+ay'+by=0$$ using $$y=u'/u$$, and then the 2nd order linear ODE can be turned into the form $$z''=rz$$ using $$z=\exp(\int a\, dx)y$$

9. amoodarya

thank you but what about the first part of my question ? how kovacic's algorithm works?

10. anonymous

do you know anything about differential Galois theory?

11. amoodarya

little

12. amoodarya

I am looking for a example ,that show this work

13. amoodarya

I saw differential Galois theory in two article , and understand it but not make a sense to me I used to see example ,and study by solving problem