  For a second order linear differential equation $f''+A(z)f'+B(z)f=0$, with $
A(z)$ and $B(z)$ being transcendental entire functions under some restriction,
we have established that all non-trivial solutions are of infinite order. In
addition, we have proved that these solutions have infinite number of zeros.
Also, we have extended these results to higher order linear differential
equations.
