  Recently Dabholkar and Vafa proposed that closed string tachyon potential for
non-supersymmetric orbifold $\C/\Z_3$ in terms of the solution of a $tt^*$
equation. We extend this result to $\C^2/\Z_n$ for $n=3,4,5$. Interestingly,
the tachyon potentials for $n=3$ and 4 are still given in terms of the
solutions of Painleve III type equation that appeared in the study of
$\C^1/\Z_3$ with different boundary conditions. For $\C^2/\Z_5$ case, governing
equations are of generalized Toda type. The potential is monotonically
decreasing function of RG flow.
