Okay:

Apparently your way is correct Captain! I was told that I would want to treat the lambda's separately. However, the TA said it was fine if I only do case where I assumed the lambda's were NOT equal and proceeded there (so I don't have to do the case where they).

Could you help me? I got to:

$\displaystyle ln(x(t)) = \lambda_1 dt$

$\displaystyle ln(x(t)) = \lambda_1 t$

$\displaystyle ln(x(t))/t = \lambda_1$

So then according to what you said:

$\displaystyle \frac{dy}{dt} = \frac{ln(x(t))}{t} x(t) - \lambda_2 y(t)$