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Math Help - Differentiation - part of a question

  1. #1
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    Differentiation - part of a question

    I am in the middle of a question, and following and existing example in my notes, and I have come near the end, but I do not understand a step of the working, can someone please explain, how I get from:

    y(s) = \frac{1}{s^2} - \frac{sy(s)}{s+4}

    to:

     <br />
y(s) = \frac{s+4}{s^2(2s+4)}<br />

    PLEASE???
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  2. #2
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    Quote Originally Posted by ubhik View Post
    I am in the middle of a question, and following and existing example in my notes, and I have come near the end, but I do not understand a step of the working, can someone please explain, how I get from:

    y(s) = \frac{1}{s^2} - \frac{sy(s)}{s+4}

    to:

     <br />
y(s) = \frac{s+4}{s^2(2s+4)}<br />

    PLEASE???
    y(s) = \frac{1}{s^2} - \frac{sy(s)}{s+4}

    so:

    y(s) \left[1+\frac{s}{s+4}\right]= \frac{1}{s^2}

    hence:

    y(s)= \frac{1}{s^2\left[1+\frac{s}{s+4}\right]}

    Now just tidy up the right hand side.

    RonL
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  3. #3
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    still a bit confused...

    so from here

     <br />
y(s)= \frac{1}{s^2\left[1+\frac{s}{s+4}\right]}<br />

    now I multiply top and bottom with (s+4) right?

    so I would get

     <br />
y(s)= \frac{s+4}{s^2\left[1+\frac{s}{s+4}\right](s+4)}<br />

    Then,

    y(s)= \frac{s+4}{s^2(s+4)+\left[\frac{s^3(s+4)}{s+4}\right]}

     <br />
y(s)= \frac{s+4}{s^2(s+4)+s^3}<br />

    but still not sure how to get to

     <br />
y(s) = \frac{s+4}{s^2(2s+4)}<br />
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  4. #4
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    Quote Originally Posted by ubhik View Post
    so from here

     <br />
y(s)= \frac{1}{s^2\left[1+\frac{s}{s+4}\right]}<br />

    now I multiply top and bottom with (s+4) right?

    so I would get

     <br />
y(s)= \frac{s+4}{s^2\left[1+\frac{s}{s+4}\right](s+4)}<br />

    Then,

    y(s)= \frac{s+4}{s^2(s+4)+\left[\frac{s^3(s+4)}{s+4}\right]}

     <br />
y(s)= \frac{s+4}{s^2(s+4)+s^3}<br />

    but still not sure how to get to

     <br />
y(s) = \frac{s+4}{s^2(2s+4)}<br />
    s^3 = s^2 * s. So s^2(s + 4) + s^3 = s^2(s+4) + s^2(s) = s^2(s + 4 + s) = s^2(2s + 4).
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  5. #5
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    Thank you!!

    Greatly appreciated!!
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