Results 1 to 2 of 2

Math Help - Differential Equation Curve

  1. #1
    Junior Member
    Joined
    May 2009
    Posts
    42

    Differential Equation Curve

    A curve rises from the origin continuously in the
    xy plane into the first quadrant. The area under the curve from (0, 0) to (x, y) is 1/3 the area of the rectangle with these points as opposite vertices. Find the differential equation satisfied by the curve.

    Thanks for your help!

    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Jester's Avatar
    Joined
    Dec 2008
    From
    Conway AR
    Posts
    2,361
    Thanks
    39
    Quote Originally Posted by JoAdams5000 View Post
    A curve rises from the origin continuously in the



    xy plane into the first quadrant. The area under the curve from (0, 0) to (x, y) is 1/3 the area of the rectangle with these points as opposite vertices. Find the differential equation satisfied by the curve.


    Thanks for your help!
    Let  y = f(x) be the curve so the area under the curve is

    \int_0^x f(t)\, dt

    and the rectangle is x f(x) so the equation to your question is

     <br />
\int_0^x f(t)\, dt = \frac{1}{3} x f(x)<br />

    and differentiating gives

     <br />
f(x) = \frac{1}{3} ( x f'(x) + f(x)).<br />
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 4
    Last Post: May 8th 2011, 12:27 PM
  2. Replies: 1
    Last Post: April 11th 2011, 01:17 AM
  3. Total Differential to find slope of Curve
    Posted in the Calculus Forum
    Replies: 4
    Last Post: July 29th 2009, 11:23 AM
  4. PURSUIT CURVE (differential geom)
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: October 27th 2008, 01:28 PM
  5. Replies: 8
    Last Post: October 8th 2007, 04:29 PM

Search Tags


/mathhelpforum @mathhelpforum