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differential equation:

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    i would like to know what your answer to this question is:

    Solve: dy/dx = Sqrt(y^2-1) with i.c. y(1)=1.

    i get one answer
    my book gets another mathematica gets another
    maple gets another

    if i exponentiate the solution, i get one for i can`t explicitly solve for y
    if i take the solution as being inverse hyperbolic, i (apparently according to Maple) get the wrong answer also
    (hyperbolicly, i get y(x) = Cosh(x)

    what am i missing (appart from a few grey cells this time of night!)
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    Arccosh(y)=x-1 => y=Cosh(x-1) ? mathematica gets cosh(1-x)!!
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    (Original post by Hasufel)
    Arccosh(y)=x-1 => y=Cosh(x-1) ? mathematica gets cosh(1-x)!!
    They're the same.

    cosh(x-1) = 0.5(e^x-1 + e^-x+1)

    cosh(1-x) = 0.5(e^-x+1 + e^x-1)
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    cheers!

    best go to bed i suppose!

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Updated: June 21, 2012
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