Posted by colin on October 28, 2002 at 21:58:05:
In Reply to: Re: how!?!?!? (Messed up the equation...) posted by Brad Paul on October 28, 2002 at 15:59:20:
: Am I to understand that your question is:
: What values of y0 will give finite y as t goes to infinity?
what I'm looking for is the value of the constant coefficient y0 which is a "critical point" in the family of solutions y(t). The point which separates solutions that behave in two quite different ways- in this case becoming either negatively or positively unbounded.
I have plotted the function using Mathematica, and can see that this critical value is around approx - 0.8865.
The book wants us to solve for the "exact value of y0"... and it shows the answer as y0 = - Sqrt(Pi)/2.
But I am unable to solve the equation y(t) which I've provided for y0. Do you know how to do it?