We consider the equation $$-{\left(r\left(x\right)y^{\text{'}}\left(x\right)\right)}^{\text{'}}+q\left(x\right)y\left(x\right)=f\left(x\right),x\in ℝ,$$ where $f\in L_p\left(ℝ\right)$, $p\in (1,\infty )$ and $$r>0,\frac{1}{r}\in L_1^{\mathrm{loc}}\left(ℝ\right),q\in L_1^{\mathrm{loc}}\left(ℝ\right).$$ For particular equations of this form, we suggest some methods for the study of the question on requirements to the functions $r$ and $q$ under which the above equation is correctly solvable in the space $L_p\left(ℝ\right),$$p\in (1...$