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Differential Equation and Mathematica

  1. Apr 26, 2007 #1
    Hi all,

    Does anyone know if Mathematica can numerically solve a second order differential equation?
  2. jcsd
  3. Apr 26, 2007 #2


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    Sure can. Look up NDSolve.
  4. Apr 26, 2007 #3
    Well, I have been trying to solve this equation with mathematica for the past two hours with no luck.

    The general differential equation I am trying to solve is [tex]u''_i(T) = .65\frac{u'_{i-1}(T)-u'_{i}(T)}{u_{i-1}(T)-u_{i}(T)}+750(u_{i-1}(T)-u_{i}(T)-1)^3[/tex] where i= 1,2,3 and [tex]u'_0(T)=2\pi*Sin(2*\pi*T)[/tex]

    The initial conditions are [tex]u_i(0)=-i[/tex] and [tex]u'_i(0)=0[/tex]. I tried using NDSolve but it kept saying that the input was not a differential equation. Does anyone know what should be the syntax of the NDSolve function I need?
    Last edited: Apr 26, 2007
  5. Apr 26, 2007 #4
    Well, I finally was able to get the NDSolve to work for this differential equation for T values from 0 to 24 and I set the NDSolve function to the variable "soln". So what function should I use to graph the numerical solutions?
  6. Apr 27, 2007 #5
    Look into the help browser of Mathematica (press F1) under NDSolve. There should be a list of examples (see 'Further examples'). From this you will also see how to plot the solution provided by NDSolve. See also http://documents.wolfram.com/mathematica/Built-inFunctions/NumericalComputation/EquationSolving/FurtherExamples/NDSolve.html [Broken].

    Finally, I should point out, that this question really belongs in the Mathematica newsgroup, found through Google Groups.
    Last edited by a moderator: May 2, 2017
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