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#1 2007-02-26 19:34:42

nor
Guest

solve ricatti's equation

y' = x^2+y^2 ,  y(0) = 0


PLEASE HELP ME!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

#2 2007-02-28 15:45:24

JaneFairfax
Member
Registered: 2007-02-23
Posts: 6,868

Re: solve ricatti's equation

I have no idea how to solve it but I found the general solution on the Internet. Your equation is a so-called special Riccati equation, and – my word! The general solution involves Bessel functions of both the first and second kinds! eek Well, maybe the particular solution you’re looking for is simpler – but, even so … what

Here it is, if you want to make sense of it:
http://eqworld.ipmnet.ru/en/solutions/ode/ode0106.pdf (PDF document)

It seems that the general Riccati equation is easier to solve than the special Riccati equation. faint

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#3 2007-03-01 00:04:50

George,Y
Member
Registered: 2006-03-12
Posts: 1,379

Re: solve ricatti's equation

Indeed differential equations can get frigh...tening!


X'(y-Xβ)=0

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