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Math Help - Differential Equation needs checking

  1. #1
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    Differential Equation needs checking

    Hi can I get a check on my working here please.

    \frac{dy}{dx} = \frac{2(e^x - e^{-x})}{y^2(e^x + e^{-x})^4}<br />
(y>0)

    So I'm using the separation of variables method here.

    y^2 \frac{dy}{dx} = 2(\frac{e^x - e^{-x}}{(e^x + e^{-x})^4})

    \int y^2 dy = 2 \int (\frac{e^x - e^{-x}}{(e^x + e^{-x})^4})dx

    \frac{1}{3}y^3 = -\frac{2}{3} (e^x + e^{-x})^{-3} +c

    Using the initial condition y=\frac{1}{2} when  x=0

    c=\frac{1}{8}

    Solving for an explicit solution I get

    y =\sqrt[3]{\frac{3}{8} - \frac{2}{(e + e^{-1})^3}}
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  2. #2
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    e^(i*pi)'s Avatar
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    Your method seems fine. What happened to the 3 in "2/3" for your final solution though?
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  3. #3
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    Quote Originally Posted by e^(i*pi) View Post
    Your method seems fine. What happened to the 3 in "2/3" for your final solution though?
    Well it's 1/3y^3= to start with, so multiply both sides by 3.
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  4. #4
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    e^(i*pi)'s Avatar
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    As yes, I missed that. In that case your answer is fine
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