We consider a differential-boundary equation with algebraic terms on a finite interval \\(0 < x < 1\\)
\\begin{equation}\\begin{split}
l(y) \\equiv \\frac{d}{dx} \\biggl( \\frac{dy(x)}{dx} &+ \\sum_{i=1}^k h_i (x) U_i (y) + \\sum_{j=1}^s \\lambda_j q_j (x) \\biggr)\\\\
&+ r_1 (x) \\frac{dy(x)}{dx} + r_0 (x)y(x) = f(x),
\\end{split}\\end{equation}
A distinctive feature of these equations is that, alongside the function being sought, a certain number of unknown values must also be determined. This leads to the critical question of unique solvability: how many and what type of conditions need to be imposed on equation (1) to ensure that the resulting problem has a unique solution in a given space?
Such equations, consisting of both differential and algebraic parts, are usually called differential-algebraic equations [1,2].