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Question on checking the linearity of a differential operator

  1. Dec 12, 2013 #1
    Suppose I have this operator:

    ##D^2+2D+1##.

    Is the ##1## there, when applied to a function, considered as identity operator?

    Say:

    ##f(x)=x##.

    Applying the operator results in:

    ##D^2(x)+2D(x)+(x)## or ##D^2(x)+2D(x)+1##?

    If ##1## here is considered as an identity operator then the answer will be the former, and the whole operator is linear. But if it's the former, I don't see why the operator will be linear because of the extra ##1## term.

    ##D## refers to ##\frac{d}{dx}##, and the power of it refers to the order of the derivative.
     
  2. jcsd
  3. Dec 13, 2013 #2

    tiny-tim

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    Hey Seydlitz! :smile:

    If D = d/dx, then ##(D^2+2D+1)(y) = y'' + 2y' + y## :wink:
     
  4. Dec 13, 2013 #3
    Ok thanks tiny-tim!
     
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