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DE with a constant

  1. May 13, 2012 #1
    My math is a little rusty - so please bear with me if this is a stupid question.

    I know how to solve both homogenous and non-homogenous DEs

    However, I am not sure where a DE with a constant falls & how to solve it.

    For eg.

    y'' + 2y' + c = 0
    (c is a constant).

    You cannot convert this into an algebraic equation in r like you do for regular homogenous DEs. So what's the method for solving this?

    If this is a different category of DEs (i.e. neither homo nor non-homo), then even giving me the name of this type of DE is good enough - I can google and find the method.

    An example of this type of DE is a bar loaded with a uniformly distributed load of f.
    The DE is

    AEu'' + f = 0

    u -> deflection.

    f is a constant.
     
  2. jcsd
  3. May 13, 2012 #2
    You can solve the equation y'' + 2y' = -c. This is a non homogenous equation where the non-homogenous part is a constant. So the general solution is

    -((c x)/2) - 1/2 exp(-2 x) C[1] + C[2]

    where C[1] and C[2] are constants.
     
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