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Famly of Curves

  1. Apr 11, 2007 #1
    Doing some extra credit and got stuck on this one.


    Find the differential equation of the family of curves and of the orthogonal trajectories.

    y = c - 2x

    Needing a little help on this one...

    Thanks
     
  2. jcsd
  3. Apr 11, 2007 #2

    HallsofIvy

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    "The differential equation of a family of curves" means a differential equation such that that the general solution to the differential equation is that family of curves. Can you think of a differential equation that has
    y= c- 2x as its general solution?

    One curve is orthogonal to another if there tangent lines are perpendicular where they intersect. What does this tell you about there derivatives?

    (Actually, all "curves" satisfying y= c-2x are straight lines.)
     
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