A simple boundary value problem for a $n$-th order linear ordinary differential equation which appears typically in the theory of Heaviside cable and Thomson cable is treated. Output-input voltage relation is investigated. We found the best constant of Sobolev-type inequality, which estimates the square of supremum of absolute value of output voltage from above by the power of input voltage. The best constant is a rational function of the characteristic roots and also a rational function of the characteristic coefficients. The second formula for the best constant is very important because even for small number of $n$ it is difficult to obtain the exact value of characteristic roots but in some cases it is easy to know the coefficients of characteristic polynomial. Giambelli's formula which appears in the theory of representation of finite groups plays an important role.