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Help me - A function satisfies the differential equation

  1. Feb 9, 2009 #1
    A function satisfies the differential equation:

    [tex]\frac{dy}{dt}= y^{4}-6y^{3}+5y^{2}[/tex]

    a. What are the constant solutions of the equation?
    b. For what values of y is y increasing?
    c. For what values of y is y decreasing?
     
  2. jcsd
  3. Feb 9, 2009 #2

    Hootenanny

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    What are your thoughts on the problem? What have you attempted thus far?
     
  4. Feb 20, 2010 #3
    dy/dt=y'(t), its ur function or, simple, y(t), after integration.
     
    Last edited: Feb 20, 2010
  5. Feb 20, 2010 #4

    HallsofIvy

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    Do you understand that this does NOT require that you actually solve the differential equation? It only requires that you solve an algebraic equation and two inequalities.
     
  6. Feb 20, 2010 #5
    i think it should be
    y'(t)=t^4-6t^3+5t^2
    where
    y'(t)=dy/dt
    now integrate it
    we have
    y(t)=........
    constant solution mean y'(t)=0.
    mean no variation w.r.t "t".
    for what value of "t" is y increasing....
    and for what value of "t" is y decreasing.
    i think now u can handle it easily
     
    Last edited: Feb 20, 2010
  7. Feb 20, 2010 #6

    Mark44

    Staff: Mentor

    No, that's completely wrong. The DE equation is dy/dt = y4 - 6y3 + 5y2. If if were as you have it, this would be a different problem completely.
     
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