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Math Help - Simple Isolation Problem. Stuck.

  1. #1
    Member billym's Avatar
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    Simple Isolation Problem. Stuck.

    I am trying to isolate y:

    I have:

    ln sqrt(1+y^2) = t + (t^2)/2 + A

    exponeniate:

    sqrt( 1 + y^2 ) = exp( t + (t^2)/2 + A )

    y^2 = ( exp( t + (t^2)/2 + A ) )^2 - 1

    Let: B = exp(A)

    y = Sqrt( ( B * exp(t) * exp(t^2)/2) )^2 - 1)

    Let: C = B^2

    y = Sqrt( C * ( exp(t) * exp (t^2)/2 ) )^2 - 1)


    Correct?
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  2. #2
    Senior Member TriKri's Avatar
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    I don't understand why you have to set C to B^2, and B to e^A. As it seems to me, you have already isolated y when you have come to

    y^2 = \left( {e^{\displaystyle{t +  \frac{t^2}{2} + A}}} \right)^2 - 1

    exept from the 2 over y. But from there you can't go directly to

    y = \sqrt{\left( e^{t +  \frac{t^2}{2} + A } \right)^2 - 1}

    unless you know that y in non-negative, since for example (-5)^2=5^2. Else you will have to use the + sign:

    y = \pm\sqrt{\left( e^{t +  \frac{t^2}{2} + A } \right)^2 - 1}

    Remember, x^2 = a\ \not{\Rightarrow}\ x=\sqrt{a}
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