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Linear Differential Equations and Linear Operator Problem

  1. Oct 22, 2016 #1
    1. The problem statement, all variables and given/known data
    I'm not sure how to approach this. The question involves linear operators and a non-homogenous differential equation.
    Here is the question:
    https://s15.postimg.org/cdmw80157/Capture.png

    2. Relevant equations
    They are given in the question

    3. The attempt at a solution
    I really have no idea on how to approach it. I was thinking something along the lines of setting c1*y1+c2*y2+c3*y3 as a linear combination and setting them equal to the non-homongenous term g(x). Then i can find the values of c1,c2,c3.
     
  2. jcsd
  3. Oct 22, 2016 #2

    LCKurtz

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    [Edited] You want to take a linear combination of the ##L(y_i)##'s (the right hand side of the equations) equal to ##g(x)##, not the ##y_i##'s themselves. Then use your constants to build the particular solution from the ##y_i##'s.
     
    Last edited: Oct 22, 2016
  4. Oct 22, 2016 #3
    I did L(c1y1+c2y2+c3y3)=g(x)=c1*L(y1)+c2*L(y2)+c3*L(y3)
    Then I sub in the L(y1), L(y2), and L(y3) for what was given to me. This leads me to find the constants. Then c1=10/12, c2=0, and c3=5/6.
    However this was wrong.
     
  5. Oct 22, 2016 #4

    LCKurtz

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    I corrected my reply while you were looking at it. Sorry. See if it makes sense now.
     
  6. Oct 22, 2016 #5
    Ah I see. I got the question wrong so I don't know the answer. I will try this once the solution comes out. Thanks for the help.
     
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