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Differntial Equations

  1. Apr 30, 2008 #1
    http://img231.imageshack.us/img231/5213/njtd7.jpg

    What order differential equation is this?

    In my notes i have the 2nd order differntial equation (homogeneous equation) as

    y'' + py' + qy = 0

    I take possible soultions in the form y = e^mx

    => (m^2 + pm + q)e^mx = 0

    Then I take solutions of the equation using the quadratic forumula of m^2 + pm + q = 0?

    General soultion is then y = c(1)y(1) + c(2)y(2)

    Am I getting this right?

    Thanks!

    here do p and q both equal to 1?
     
  2. jcsd
  3. Apr 30, 2008 #2

    rock.freak667

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    Homework Helper

    [tex]\frac{d^2\theta}{dt^2}+\frac{d\theta}{dt}+sin\theta=0[/tex]

    [tex]\frac{d^2\theta}{dt^2}+\frac{d\theta}{dt}=-sin\theta[/tex]

    All solutions are of the form [itex]\theta=e^{rt}[/itex]

    So the auxiliary equation is [itex]r^2+r=0 \Rightarrow r(r+1)=[/itex]

    so the roots are r=0,-1

    So the Complimentary function would be [itex]\theta=c_1+c_2e^{-t}[/itex]
     
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