Re: Parametric coordinates
- From: Robert Israel <israel@xxxxxxxxxxxxxxxxxxxxxxxxxxxxx>
- Date: Thu, 03 Apr 2008 00:20:08 -0500
Mark Hauerbach <mhauerbach@xxxxxxxxxx> writes:
Could someone please help me find an expression for x as a
function of time,that is, x(t) = ? when y = x^2 and ds/dt=10?
I have tried t = 1/10 * Int(sqrt(1+4*x^2)dx and solving
for x, but had no success.
Mark H.
I assume s refers to arc length on the curve [x(t), y(t)], i.e.
(dx/dt)^2 + (dy/dt)^2 = (ds/dt)^2 = 100
Yes, t = 1/10 int sqrt(1 + 4 x^2) dx + C is what you'll get
in solving the differential equation using separation of variables
(assuming dx/dt > 0). Now that integral can be done:
t = x sqrt(1 + 4 x^2)/20 + ln(2 x + sqrt(1 + 4 x^2))/40 + C
but there's no way you're going to solve that for x as an explicit
function of t.
--
Robert Israel israel@xxxxxxxxxxxxxxxxxxxxxxxxxxxxx
Department of Mathematics http://www.math.ubc.ca/~israel
University of British Columbia Vancouver, BC, Canada
.
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