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First Order Differential Problem

  1. Jan 13, 2010 #1
    1. The problem statement, all variables and given/known data
    Show that if a and [tex]\lambda[/tex] are positive constants, and b is any real number, then every solution of the equation dx/dt + ax = b*exp(-[tex]\lambda[/tex]*t) has the property that x(t) --> 0 as t --> [tex]\infty[/tex]

    3. The attempt at a solution

    i tried considering the cases where a = [tex]\lambda[/tex] and a [tex]\neq[/tex] [tex]\lambda[/tex] but kept getting stuck... any suggestions?
  2. jcsd
  3. Jan 13, 2010 #2


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    Homework Helper

    Try solving

    [tex]\frac{dx}{dt}+ax=be^{- \lambda t}[/tex]

    by multiplying by an integrating factor.
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