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Math Help - diffEQ using L, D, Ly, y(x)... not sure how to approach this

  1. #1
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    diffEQ using L, D, Ly, y(x)... not sure how to approach this

    If L = D^2 + 3xD - 4x

    and y(x) = 2x - 5e^(2x)

    then Ly = ?

    This is completely going over my head. I don't know what is being asked. Im not asking someone to solve this for me, just some instruction in how I am supposed to approach this. Thanks
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  2. #2
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    Quote Originally Posted by plopony View Post
    If L = D^2 + 3xD - 4x

    and y(x) = 2x - 5e^(2x)

    then Ly = ?

    This is completely going over my head. I don't know what is being asked. Im not asking someone to solve this for me, just some instruction in how I am supposed to approach this. Thanks
    For example if y=x+\sin(x) then

    Ly=(D^2+3xD-4x)(x+\sin(x))

    Now distribute the operator to y to get

    (D^2+3xD-4x)x+(D^2+3xD-4x)\sin(x)

    distributing again gives

    D^2(x)+3xD(x)-4x(x)+D^2(\sin(x))+3xD(\sin(x))-4x(\sin(x))

    Now just take the dervaitves to get

    0+3x(1)-4x^2-\sin(x)+3x(\cos(x))-4x\sin(x)

    I hope this helps
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