I could use a second opinion on my answer to this question:

Determine the values of $\displaystyle a$, if any, for which all solutions to the equation:

$\displaystyle y'' - (2a - 1)y' + a(a - 1)y = 0$

...tend to zero as $\displaystyle t$ approaches infinity.

The general solution comes out to this:

$\displaystyle y = \frac{C_1e^{at}}{e^t} + C_2e^{at}$

So, my answer would be this:

$\displaystyle 0 < a < 1$

if

$\displaystyle C_2 = 0$

$\displaystyle a = 0$

if

$\displaystyle C_2 \neq 0$

Is my answer correct, or did I miss something?