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Math Help - hlep with this diff. eq. pls

  1. #1
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    hlep with this diff. eq. pls

    hello,

    i have (dx/dt)^2 = (1/x^4) -1 and want to write an integral for t(x)...

    (dx/dt) = +/- {x^2/[(1-x^4)^(1/2)]}

    so t(x) = +/- integr of {x^2/[(1-x^4)^(1/2)]}

    but the book says t = integr (from u=1 to =x) of {u^2/[(1-u^4)^(1/2)]}

    can someone please help me see that the book has done here? thanks a lot!
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  2. #2
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    Quote Originally Posted by pepsi View Post
    hello,

    i have (dx/dt)^2 = (1/x^4) -1 and want to write an integral for t(x)...

    (dx/dt) = +/- {x^2/[(1-x^4)^(1/2)]}

    so t(x) = +/- integr of {x^2/[(1-x^4)^(1/2)]}

    but the book says t = integr (from u=1 to =x) of {u^2/[(1-u^4)^(1/2)]}

    can someone please help me see that the book has done here? thanks a lot!
    Please post the entire question, including the intial condition that came with the DE (I assume it was x = 1 when t = 0. But we shouldn't have to assume.)

    Also, note that if \frac{dt}{dx} = f(x) subject to the boundary condition x = x_0 when t = t_0 then t(x) = \int_{x_0}^{x} f(u) \, du.
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