  The Bohr radius for a class $\mathcal{G}$ consisting of analytic functions
$f(z)=\sum_{n=0}^{\infty}a_nz^n$ in unit disc
$\mathbb{D}=\{z\in\mathbb{C}:|z|<1\}$ is the largest $r^*$ such that every
function $f$ in the class $\mathcal{G}$ satisfies the inequality
\begin{equation*} d\left(\sum_{n=0}^{\infty}|a_nz^n|, |f(0)|\right) =
\sum_{n=1}^{\infty}|a_nz^n|\leq d(f(0), \partial f(\mathbb{D})) \end{equation*}
for all $|z|=r \leq r^*$, where $d$ is the Euclidean distance. In this paper,
our aim is to determine the Bohr radius for the classes of analytic functions
$f$ satisfying differential subordination relations $zf'(z)/f(z) \prec h(z)$
and $f(z)+\beta z f'(z)+\gamma z^2 f''(z)\prec h(z)$, where $h$ is the Janowski
function. Analogous results are obtained for the classes of $\alpha$-convex
functions and typically real functions, respectively. All obtained results are
sharp.
