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Math Help - ODE question!

  1. #1
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    How can we solve this question?

    Suppose that y'=v, v'=F(y,v), where F,Fy and Fv are continuous for all y,v.
    (a) As t increases, why do all orbits above the y-axis move to the right and orbits below the y-axis move to the left?
    (b) Why do nonconstant orbits that cross the y-axis always do so perpendicularly to the axis?
    Last edited by mr fantastic; December 2nd 2008 at 02:20 AM. Reason: Restored the question that the OP had deleted.
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  2. #2
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    Quote Originally Posted by ninano1205 View Post
    How can we solve this question?

    Suppose that y'=v, v'=F(y,v), where F,Fy and Fv are continuous for all y,v.
    (a) As t increases, why do all orbits above the y-axis move to the right and orbits below the y-axis move to the left?
    "Above the y-axis" means that v>0. Therefore y'>0, which means that orbits are moving in the direction of increasing y (in other words, "to the right").

    (b) Why do nonconstant orbits that cross the y-axis always do so perpendicularly to the axis?
    On the y-axis, v=0 and so y'=0. That means that the component of velocity in the y-direction is 0, so the orbit must move in the v-direction (that is, "perpendicularly to the [y-]axis").
    ..
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