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Math Help - Derivative HELP

  1. #1
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    Feb 2009
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    Derivative HELP

    I have absolutely no idea how to solve these:

    SHOW THAT

    1. y=1/x (x doesNOT equal 0) satisfies the equation x^3y^(2derivative) + x^2y^(1st derivative)- xy=0

    2.y=xe^-x satisfies xy^(1st derivative)= (1-x)y

    3. y=xe^-x^2/2 satisfies xy^(1st derivative)= (1-x^2)y
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  2. #2
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    Joined
    Feb 2009
    Posts
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    You should calculate the derivatives and then plug them into the given equations to see if they are satisfied. For y=1/x, you have

    y'=-1/x^2
    y''=2/x^3.

    Just substitute these into the equation. It works.
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