1. Apr 30, 2008 #1

   Firepanda

   

   http://img231.imageshack.us/img231/5213/njtd7.jpg [Broken]
   
   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?

    

   Last edited by a moderator: May 3, 2017

   Firepanda, Apr 30, 2008
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3. Apr 30, 2008 #2

   rock.freak667

   

   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]

    

   rock.freak667, Apr 30, 2008

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