  We study the problem of correct solvability in the space $L_p(\mathbb R),$
$p\in[1,\infty)$ of the equation $$ -(r(x) y'(x))'+q(x)y(x)=f(x),\quad x\in
\mathbb R $$ under the conditions $$r>0,\quad q\ge 0,\quad \frac{1}{r}\in
L_1(\mathbb R),\quad q\in L_1(\mathbb R).$$
