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Higher-Order Differential Equations

  1. Nov 14, 2009 #1
    1. The problem statement, all variables and given/known data

    Find the general solution of the given higher-order differential equation.

    d3x/(dt3) - d2x/(dt2) - 4x = 0


    2. Relevant equations

    Use an auxiliary equation such as m3 - m2 - 4 = 0

    3. The attempt at a solution

    ----------------------------
     
  2. jcsd
  3. Nov 14, 2009 #2

    Mark44

    Staff: Mentor

    That is the auxiliary equation you want to use. As it turns out, the left side can be factored, yielding (m - 2)(m2 + m + 2) = 0

    There are three distinct solutions, so the solution to this homogeneous problem will be x(t) = c1e2t + c2em2t + c3em3t. All you have to do is find the other two constants, m2 and m3.
     
  4. Nov 14, 2009 #3
    So, I should just use the quadratic formula to find the other two solutions?

    Thanks man.
     
  5. Nov 14, 2009 #4
    The other two solutions are of the form [tex]\alpha[/tex] [tex]\pm[/tex] [tex]\beta[/tex]
     
  6. Nov 14, 2009 #5

    Mark44

    Staff: Mentor

    Yes. And yes, the two solutions are of the form a +/- b. One of your values of m will be a + b, and the other will be a - b.
     
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