# Thread: Simple Isolation Problem. Stuck.

1. ## 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?

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