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Non exact differential equation, initial value problem

  1. Dec 8, 2016 #1
    1. The problem statement, all variables and given/known data
    I am trying to solve the following:
    y'''-9y'=54x-9-20e^2x with y(0)=8, y'(0)=5, y''(0)=38
    2. Relevant equations


    3. The attempt at a solution
    upload_2016-12-8_9-34-25.png
    upload_2016-12-8_9-34-52.png

    The right answer is:
    y= 2+2e^3x+2e^(-3x)-3x^2+x+2e^2x

    I am only wrong on the coefficients C2 and C3. Where did I mess up in my solution?
     
  2. jcsd
  3. Dec 8, 2016 #2
    When computing ##y'## at the top of the second you are missing the constant ##1## coming from ##(x)'##=1.
     
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