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Math Help - e^x-1/x^2 = 0

  1. #1
    Newbie
    Joined
    Dec 2011
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    4

    e^x-1/x^2 = 0

    hi, i have to solve this equation:
    e^x-\frac{1}{x^2}=0
    it put it in wolframalpha and it says that the solution is 2W(\frac{1}{2}), where W is the Lambert W-function, but i dont know how it find this. Can someone help me to show that the solution is really that? thanks
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  2. #2
    Junior Member
    Joined
    Oct 2011
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    Belgium
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    36

    Re: e^x-1/x^2 = 0

    e^x-\frac{1}{x^2} = 0
    e^x=\frac{1}{x^2}
    x=-2ln|x|
    \frac{x}{2}=-ln|x|
    e^{x/2}=\pm \frac{1}{x}
    \frac{x}{2}.e^{\frac{x}{2}}=\pm \frac{1}{2}
    \frac{x}{2}.e^{\frac{x}{2}}=\pm \frac{1}{2}
    \frac{x}{2}=W(\pm \frac{1}{2})
    x=2W(\pm \frac{1}{2})
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