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Need help transforming a Differential Equation

  1. Mar 3, 2009 #1
    1. The problem statement, all variables and given/known data


    Express the DE as a first order system normal form. Then, express is matrix notation.

    2y''+3y'-4ty=1-t^3

    I need to transform this into a first order system. I first divided the entire equation by 2 and got

    y''-(3/2)y'-2ty=(1-t^3)/2

    I am not sure what to do now.

    My first attempt was setting x1=y, x1'=y', and x2=y', x2'=y''

    I don't know if I am heading in the right direction and if so, was not sure what to do next.
     
  2. jcsd
  3. Mar 3, 2009 #2

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    That can be done in a number of ways. The simplest is : Define u= y' so that y"= u' and your second order differential equation becomes a first order equation in y and u. You now have two first order equations.
     
  4. Mar 3, 2009 #3
    So, when I rewrite the equation, do I leave out the 'y' in the term 2ty?

    hence,
    u'+(3/2)u-2=(1-t^3)/2
     
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