- #1

carlosbgois

- 68

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## Homework Statement

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

## Homework Equations

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

## The Attempt at a Solution

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

What am I missing?

Thanks