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Math Help - Higher Derivatives Question

  1. #1
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    Higher Derivatives Question

    Hi all,
    Here goes the question:
    Given that y=xsin3x+cos3x, show that x^2\frac{d^2y}{dx^2}+2y+4x^2y=0.

    I am quite comfortable in deriving the normal and higher derivatives(*Just to make sure I am on the right track, is \frac{dy}{dx}=sin3x-3sin3x+3xcos3x?) and am more concerned about the 'showing' part. Hopefully someone can guide me along.

    Another one:
    Given that xy=sinx, prove that \frac{d^2y}{dx^2}+\frac{2}{x}\frac{dy}{dx}+y=0.

    It seems like a typical implicit diff. question other than the higher derivatives part. I haven't really learn how to derive higher derivatives using implicit diff.

    Any help is appreciated. Thanks in advance!
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  2. #2
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    When you have found \displaystyle \frac{dy}{dx} and \displaystyle \frac{d^2y}{dx^2}, substitute them and \displaystyle y into the LHS of your equation. Show that it simplifies to the RHS.
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  3. #3
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    Quote Originally Posted by Prove It View Post
    When you have found \displaystyle \frac{dy}{dx} and \displaystyle \frac{d^2y}{dx^2}, substitute them and \displaystyle y into the LHS of your equation. Show that it simplifies to the RHS.
    Cheers. Your reply was short and concise but manage to set my thinking straight. Now I am proud that I am finally able to attempt the question. Thanks again.
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