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\[y'(x)+a(x)y^2(x)+b(x)y(x)+c(x)=0\] for this (above) kind of riccati DE equation ?
Man, what are you doing.. This is still Mathematics??? I am finding it to be an English question.. :P
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
That is quite a heavy name for me though.. I can help you in calling help.. :P
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
Really telling, I have heard of this equation for the first time in my Life.. Sorry, I am unable.. :(
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 \(z=\exp(\int a\, dx)y\)
thank you but what about the first part of my question ? how kovacic's algorithm works?
do you know anything about differential Galois theory?
I am looking for a example ,that show this work
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