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General Solution of inhomogeneous ODE

  1. Jan 26, 2016 #1
    I am having a little trouble with a problem I am trying to solve.

    Given three particular solutions

    Y1(x)= 1, Y2(x)= x and Y3(x)= x^2

    Write down a general solution to the second order non homogeneous differential equation.

    What I have done so far is to realise if Y1,2 and 3 are solutions then the difference of two of the solutions is a solution to the homogeneous equation. So I used Y3-Y1, Y3-Y2 and Y2-Y1 to give three separate homogeneous equations. At this point I am trying so solve for the coefficients a(x), b(x) and c(x) from

    a(x)y'' + b(x)y' + c(x) y= 0

    where y is the difference of two of the particular solutions.

    However I can seem to solve this system effectively by equating like powers etc... I was hoping someone could offer some advise or even an alternative method. I have solved problems like this with only two solutions but the case was simple.


    Regards
    Guy
     
  2. jcsd
  3. Jan 26, 2016 #2

    Mark44

    Staff: Mentor

    In future posts, please do not delete the homework template. Its use is required for homework questions.
     
  4. Jan 26, 2016 #3
    Apologies I didnt realise it was necessary
     
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