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Math Help - "Use the differential operator method to find a fundamental set of solutions [...]"

  1. #1
    s3a
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    "Use the differential operator method to find a fundamental set of solutions [...]"

    Could someone please tell me how to do this question so I can do the rest of them in my homework list? I know what the differential operator is from my book but I am not sure how to apply it in a problem.

    Any input would be greatly appreciated!
    Thanks in advance!
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  2. #2
    Behold, the power of SARDINES!
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    Re: "Use the differential operator method to find a fundamental set of solutions [...

    Quote Originally Posted by s3a View Post
    Could someone please tell me how to do this question so I can do the rest of them in my homework list? I know what the differential operator is from my book but I am not sure how to apply it in a problem.

    Any input would be greatly appreciated!
    Thanks in advance!
    Since your question is not very clear I will take a stab at it.

    Your equation

    y''+14y'+49y=0 can be written as

    D^2y+14Dy+49y=0 \iff (D^2+14D+49)y=0 \iff (D+7)^2y=0

    So you need to find everything in the kernel of this operator.

    One such vector is y=Ae^{-7x}

    You can also verify that y=Bxe^{-7x} is in the kernel.

    This will gives a spanning set y_1=e^{-7x}, y_2=xe^{-7x}
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