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Differential equation right hand function

  1. Apr 4, 2014 #1
    1. The problem statement, all variables and given/known data
    The question specifies the auxiliary eqution given is (D^2 + D - 2) = (e^x)/(x)
    the method of variation of parameter must be used to find the particular solution to the right hand function. then finally the general soultion should be stated.

    2. Relevant equations
    variation of paremeters formula.
    yp = -y1∫y2 * g(x)/ (w(y1 , y2))
    + y2∫y1 * g(x)/ (w(y1 , y2))

    3. The attempt at a solution
    i had solved the complementary function and had gotten yc = c1e-x + c2e-2x. then after applying the formula for variation of parameters i had gotten e-x*lnx/3 - e-2x/3 * ∫e3x / x
    i cannot obtain an integral for ∫e3x / x i dont think it can be done have tried various mathods eg by parts, there are no suitable substitutions is it that there is no integral for the expression? i.e. it cannot be integrated.
    Last edited: Apr 4, 2014
  2. jcsd
  3. Apr 4, 2014 #2


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    Gold Member

    I haven't worked through this problem, but you are correct that ##\frac {e^{3x}} x## does not have an elementary antiderivative.
  4. Apr 4, 2014 #3


    Staff: Mentor

    You have a mistake. What you have as e-x should be e+x. The other one is fine.
  5. Apr 5, 2014 #4
    yes it is as u say but the problem still remains the same the∫e3x/x would still have to be determined
  6. Apr 5, 2014 #5


    Staff: Mentor

    But if you have an incorrect function in your variation of parameters formula, you'll definitely get the wrong answer.

    Also, "textspeak" (such as "u" for "you") isn't permitted here at PF.

    Please show your work in this formula:
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