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Math Help - First Order Differential Equation Help

  1. #1
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    First Order Differential Equation Help

    Solving this differential question is supposed to only be worth 6 marks in a past exam question, but my working leads me to a very difficult integral. I was wondering if I have missed something in my solution?

    Last edited by StaryNight; March 20th 2011 at 09:28 AM.
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  2. #2
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    Quote Originally Posted by StaryNight View Post
    Solving this differential question is supposed to only be worth 6 marks, but my working leads me to a very difficult integral. I was wondering if I have missed something in my solution?

    No it looks good so far

    for the last integral

    \displaystyle \int \sec(x)(\sec(x)+\tan(x))^2dx

    let u=\sec(x)+\tan(x) \implies du=[\sec(x)\tan(x)+\sec^2(x)]dx \iff du=u\sec(x)dx \iff \frac{du}{u}=\sec(x)dx

    putting this is gives the integral

    \displaystyle \int u^2\frac{du}{u}=\int udu
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  3. #3
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    Of course! I should have seen this.
    Quote Originally Posted by TheEmptySet View Post
    No it looks good so far

    for the last integral

    \displaystyle \int \sec(x)(\sec(x)+\tan(x))^2dx

    let u=\sec(x)+\tan(x) \implies du=[\sec(x)\tan(x)+\sec^2(x)]dx \iff du=u\sec(x)dx \iff \frac{du}{u}=\sec(x)dx

    putting this is gives the integral

    \displaystyle \int u^2\frac{du}{u}=\int udu
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