Abstract: 
We consider the equation
\begin{align}\label{0.11}
y`(x)+q(x)y(x\varphi(x))=f(x), \quad x \in \mathbb R,
\end{align}
where $f \in C(\mathbb R)$ and
\begin{align}\label{0.12}
0\leq \varphi\in C^{\rm loc}(\mathbb R),\ \ \ 1\leq q \in
C^{\rm loc}(\mathbb R).
\end{align}
Here $C^{\rm loc}(\mathbb R)$ is the set of functions continuous in every point of the number axis $\mathbb R$. By a solution of (\ref{0.11}) we mean any function $y$, continuously differentiable everywhere in $\mathbb R$, which satisfies the equation (\ref{0.11}) for all $x \in \mathbb R$. We show that under certain conditions on the functions $\varphi$ and $q$ in addition to (\ref{0.12}), the equation (\ref{0.11}) has a unique solution $y$, satisfying the inequality
$$ y`_{C(\mathbb R)}+qy_{C(\mathbb R)}\leq cf_{C(\mathbb R)}$$
where the constant $c\in (0,\infty)$ does not depend on the choice of $f\in {C(\mathbb R)}$. 
