I am also having problems with this question, I integrated:
\int\frac{dμ}{(1-\frac{μ}{α})} = \int\lambda0dt
And I got:
-αln(μ-α) = \lambda0t
I'm not sure if this is going in the right direction and what would I have to do after this in order to find μ(t) and λ(t)?
Thanks