Can anyone solve the Abel differential equation x y \frac{dy}{dx} = x + y It looks so easy
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Hi! Originally Posted by danny arrigo Can anyone solve the Abel differential equation x y \frac{dy}{dx} = x + y It looks so easy Edit: Aaaargh, mr fantastic is right, Edit: the following is the wrong: .... Can you solve it now? Edit: I made a big mistake... Sorry Merry christmas, Rapha
Last edited by Rapha; December 25th 2008 at 08:14 PM.
Originally Posted by Rapha Hi! Mr F asks: How do the following lines follow from the above .....? .... Can you solve it now? Merry christmas, Rapha Originally Posted by danny arrigo Can anyone solve the Abel differential equation x y \frac{dy}{dx} = x + y It looks so easy I have no time now but I think the first thing to do is make the substitution y = 1/v.
Originally Posted by mr fantastic I have no time now but I think the first thing to do is make the substitution y = 1/v. This substitution turns my Abel equation of the second kind to one of the first kind which I still don't know how to solve!
Originally Posted by danny arrigo This substitution turns my Abel equation of the second kind to one of the first kind which I still don't know how to solve! In the meantime, you might have a read of http://www.cecm.sfu.ca/CAG/papers/edgardoEJAM04.pdf
Originally Posted by mr fantastic In the meantime, you might have a read of http://www.cecm.sfu.ca/CAG/papers/edgardoEJAM04.pdf Yes, I know of Cheb-Terrab paper.
Generally speaking, equations that have attracted enough interest to be given their own names are very difficult!
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