Unbounded or infinite would be more appropriate terms to use in this context.

[carlosbgois]

Homework Statement

Find the values of α for which all the solutions of y''-(2α-1)y'+α(α-1)y=0 (a) tend to zero and (b) are ilimited, when t->∞.

Homework Equations

y''-(2α-1)y'+α(α-1)y=0 => (t)=Ae^{αt}+Be^{(α-1)t}

The Attempt at a Solution

I found that the general solution to the problem is y(t)=Ae^{αt}+Be^{(α-1)t}, which I believe is correct. Then I said that (a) is verified for t<1/2 and (b) for t>=1/2, but the book's answer is (a) t<0 and (b) t>1.

What am I missing?
Thanks

 

[Simon Bridge]

As you wrote it, the question asks for values of $\alpha$, not $t$.
So it looks like your (and the book's) answer is for a different question.

$y(t)\rightarrow 0$ for $t\rightarrow \infty$ when $\alpha < 0$ which makes y(t) a sum of decaying exponentials.

 

[carlosbgois]

My mistake, I meant α where I said t. I understand what you said, but then what happens for 0<α<1 ?

Thanks

 

[Simon Bridge]

My mistake, I meant α where I said t. I understand what you said, but then what happens for 0<α<1 ?

Well then put that into y(t) ... you have two exponentials added together and $\alpha$ appears in the power.

What does "ilimited" mean?