can someone describe to me how kovacic's algorithm works?

Question

amoodarya · Answer

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

anonymous · Answer

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

amoodarya · Answer

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

anonymous · Answer

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

anonymous · Answer

@ganeshie8  @mukushla

amoodarya · Answer

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

anonymous · Answer

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

anonymous · Answer

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 $z=\exp(\int a\, dx)y$

amoodarya · Answer

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

anonymous · Answer

do you know anything about differential Galois theory?

amoodarya · Answer

little

amoodarya · Answer

I am looking for a example ,that show this work

amoodarya · Answer

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