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January 20th, 2015, 07:25 PM  #1 
Newbie Joined: Oct 2014 From: China Posts: 12 Thanks: 2  Any special case satisfying $\arctan{\frac{dy(c+s)} {dx(c+s)}}$
There is a mysterious parametric curve: $$ x(s),y(s)$$ defined on three intervals (continuity unkown) around a, b, and c $(a< b\leq c)$, thus the curve consists of three segments : $$x(a+s) ,y(a+s)$$ $$x(bs) ,y(bs)$$ $$x(c+s) ,y(c+s)$$ that satisfy the following equations: $$\frac{dy(c+s)}{dx(c+s)}=\frac{y(c+s)y(bs)}{x(c+s)x(bs)}$$ $$\frac{dy(a+s)}{dx(a+s)}=\frac{y(a+s)y(bs)}{x(a+s)x(bs)}$$ $$\arctan{\frac{dy(c+s)} {dx(c+s)}}\arctan{\frac{dy(a+s)} {dx(a+s)}}=\pi\theta$$ here: $$\frac{dy(c+s)/ds}{dx(c+s)/ds}=\frac{dy(c+s)}{dx(c+s)}$$ I guess the conditions above are not sufficient to work out $x(s), y(s)$ , however, is it possible to give any special case satisfying above equations? Now I have no clue how to go any further on this problem.Thanks for any suggestions. 
January 21st, 2015, 06:37 AM  #2 
Math Team Joined: Jan 2015 From: Alabama Posts: 3,261 Thanks: 896 
What do you mean by "dy(c+s)"?

January 21st, 2015, 06:01 PM  #3 
Newbie Joined: Oct 2014 From: China Posts: 12 Thanks: 2  

Tags 
$arctanfracdyc, case, differential equation, dxc, parametric, satisfying, special 
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