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#1 2007-02-12 10:59:34

AdidasTO
Guest

How to solve a Ricatti Equation (Differential Equations)

I understand that process of solving a Ricatti Equation, and I know that an integral part of that process is identifiying a particular solution, but that is the one thing that I don't understand. This is probably really easy but I don't understand how you can figure that you right away.

So for example:

Solve the Ricatti Equation:

dy/dx = 2 - 2xy + y^2

The book says "it is easy verified that a particular solution of this equation is y = 2x." How did they get that?

#2 2007-02-12 13:08:42

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

Re: How to solve a Ricatti Equation (Differential Equations)

I guess their first inspiration comes from 2, 2 makes 2x in y inevitable. Then they just tried y=2x, or 2x+g(x).


X'(y-Xβ)=0

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