Abstract
In this article, we derived conditions on the coefficient functions a(z) and b(z) of the differential equations y ''(z) + a(z)y'(z) +b(z)y(z) = 0 and z(2)y ''(z) + a(z)zy'(z) + b(z)y(z) = 0, such their solution f (z) with normalization f (0) = 0 = f' (0) - 1 is starlike in the lemniscate domain, equivalently zf' (z)/f(z) (sic) root 1 + z. We provide several examples with graphical presentations for a clear view of the obtained results.