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Converting a second-order ODE into system of first-order ODEs

  1. Nov 23, 2012 #1
    This is not homework, but rather me just trying to work a numerical analysis problem.

    I have a second order equation on the form m*y'' = a*y + n*x (no first derivative)

    How does one convert this? It's been years since I did this. Last I remember, one would start with substituting the first derivative with something. (u = y'), but now there's no such part in the equation.

    Thanks!
     
  2. jcsd
  3. Nov 23, 2012 #2

    haruspex

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    Usually start by solving the homogeneous version.
     
  4. Nov 23, 2012 #3

    HallsofIvy

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    I'm afraid haruspex misunderstood the question.

    dreamspace, do exactly as you suggest: introduce the new dependent variable by defining z= y'. Then the equation becomes mz'= ay+ nx.

    Your two first order equations are
    y'= z
    z'= (a/m)y+ (n/m)x
     
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