 My Math Forum Any special case satisfying $\arctan{\frac{dy(c+s)} {dx(c+s)}}$

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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 : $$x(a+s) ,y(a+s)$$ $$x(b-s) ,y(b-s)$$ $$x(c+s) ,y(c+s)$$ that satisfy the following equations: $$\frac{dy(c+s)}{dx(c+s)}=\frac{y(c+s)-y(b-s)}{x(c+s)-x(b-s)}$$ $$\frac{dy(a+s)}{dx(a+s)}=\frac{y(a+s)-y(b-s)}{x(a+s)-x(b-s)}$$ $$\arctan{\frac{dy(c+s)} {dx(c+s)}}-\arctan{\frac{dy(a+s)} {dx(a+s)}}=\pi-\theta$$ 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: 3,264 Thanks: 902 What do you mean by "dy(c+s)"? January 21st, 2015, 06:01 PM   #3
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 Originally Posted by Country Boy What do you mean by "dy(c+s)"?
dy(c+s) means d(y(c+s)) the infinitesimal change in y(as a function of s), c is a constant. Tags \$arctanfracdyc, case, differential equation, dxc, parametric, satisfying, special Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post talisman Geometry 1 October 27th, 2014 01:05 PM Chikis Algebra 6 July 15th, 2014 07:16 PM stainburg Calculus 17 November 24th, 2013 01:14 AM maxgeo Algebra 1 October 31st, 2012 03:57 PM

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