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Homework Help: Rewrite the 2nd oder non linear D.E as a series of 1st order equations

  1. Sep 23, 2010 #1
    1. The problem statement, all variables and given/known data

    Rewrite the 2nd oder non linear D.E [itex]\frac{d^2x}{dt^2}+x^2+x=0[/itex]
    as a series of 1st order equations

    2. Relevant equations

    [itex]a\frac{d^2x}{dt^2}+b\frac{dx}{dt}+cx=0[/itex]

    [itex]\frac{dx}{dt}=y[/itex]

    [itex]\frac{dy}{dt}=-\frac{c}{a}x-\frac{b}{a}y[/itex]


    3. The attempt at a solution

    a=1, b=0 , c=1

    SO

    [itex]\frac{dx}{dt}=y[/itex]

    [itex]\frac{dy}{dt}=-\frac{1}{1}x-\frac{0}{1}y[/itex] = [itex]-x[/itex]

    Is that right?
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Sep 23, 2010 #2

    hunt_mat

    User Avatar
    Homework Helper

    You have two linear equations there, where is the non-linear term?
     
  4. Sep 23, 2010 #3

    HallsofIvy

    User Avatar
    Science Advisor

    This is a linear equation and so not a good format to use for your problem.

    Don't just try to match up with memorized formulas (especially when the formula doesn't fit the problem).

    You have defined y to be dx/dt so you know that [itex]dy/dt= d^2x/dt^2[/itex]. Replace [itex]d^2x/dt^2[/itex] in [itex]\frac{d^2x}{dt^2}+x^2+x=0[/itex] with [itex]dy/dx[/itex] to get
    [tex]\frac{dy}{dt}+ x^2+ x= 0[/tex]
    or
    [tex]\frac{dy}{dt}= -x^2- x[/tex].
     
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