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Math Help - Deriviative of function # 8

  1. #1
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    Deriviative of function # 8

    If y=5/2(e^(x/5)+e^(-x/5)), then prove that y''=y/25

    Ok can someone just check with me.. I'm pretty close to the answer but i don't know what I did wrong ..

    the final answer of y''=y/25.. I have

    [e^(x/5)+e^(-x/5)]/[e^(x/5)/25+e^(-x/5)/25]

    Don't know what happened to the 5/2 in y and.. the denominator is almost there but not quite. ^.^
    Please explain your method to proving this. Thank you so much!
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  2. #2
    Super Member Matt Westwood's Avatar
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    Presumably this is what you got (please learn latex):
    y = \frac 5 2 (e^{x/5} + e^{-x/5})

    Diffing e^{ax} gives ae^{ax} and doing it twice gives a^2e^{ax}.

    Diffing e^{-ax} gives -ae^{-ax} and doing it twice gives (-a)^2e^{-ax} = a^2e^{ax}.

    Adding them together gives \frac {d^2} {dx^2} (e^{x/5} + e^{-x/5}) = \frac 1 {25} (e^{x/5} + e^{-x/5}).

    Multiplying the lot by \frac 5 2 gives:
    \frac {d^2y} {dx^2} = \frac 5 2 \frac 1 {25} (e^{x/5} + e^{-x/5}) = \frac 1 {25} y
    Last edited by Matt Westwood; August 14th 2009 at 01:02 PM. Reason: Latex errors. Please learn Latex.
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