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Classification of ODE's

  1. Feb 28, 2012 #1
    When classifying an ODE do I just say whether its linear / non-linear and what order it is?

    EDIT: Example: x2x'' + e-xx = t3 where x is function of t.

    is this 2nd order, non linear and heterogeneous?

    Also, would dx/dt = logte-x be homogeneous because both terms contain the dependant variable 't'?
     
    Last edited: Feb 28, 2012
  2. jcsd
  3. Feb 28, 2012 #2
    There are some more classifications for (second order) odes, mostly based on the fact that the ode is solvable (or not) when it is of a certain class. I like the choice of the Maple software, which is pretty classic. The online description of odeadvisor giving you a classification is here:
    http://www.maplesoft.com/support/help/Maple/view.aspx?path=DEtools/odeadvisor

    Your first order ode is homogeneous, because it does not have a term that only depends on t. dx/dt=a(t)*x+b(t) is not homogeneous, but dx/dt = a(t)*x is. Your example is also separable, which means it can be solved using separation of variables.
     
  4. Feb 28, 2012 #3
    so if dx/dt = logte-1, would that now mean that this was no longer homogeneous? Thanks for the help by the way.
     
  5. Feb 28, 2012 #4
    Your equation is not homogeneous because of the t cubed term.
     
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