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2nd order diff equations

  1. May 11, 2008 #1
    1. The problem statement, all variables and given/known data

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    2. Relevant equations



    3. The attempt at a solution

    this isnt a straight forward calculate the soltion to a 2nd ode so im pretty stumped.
     
  2. jcsd
  3. May 11, 2008 #2

    Defennder

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    Firstly, suppose y1 is a solution to y''+ay'+by=g(x). What then is a solution of y''+ay'+by=kg(x), where k is an arbitrary non-zero constant?

    Secondly, note that a general solution to a non-homogenous linear ODE is its homogenous solution plus one particular solution to its nonhomogenous ODE.
     
  4. May 11, 2008 #3
    solution to y''+ay'+by=kg(x) is ky1?

    so the solution to y''+ay'+by=3g(x) is the complimentyery function + particular integral = 3y1 + y2?
     
  5. May 11, 2008 #4

    Defennder

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    That should be correct.
     
  6. May 11, 2008 #5
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