  We derive an expression for the spectral determinant of a second-order
elliptic differential operator $\mathcal{T}$ defined on the whole real line, in
terms of the Wronskians of two particular solutions of the equation
$\mathcal{T} u=0$. Examples of application of the resulting formula include the
explicit calculation of the determinant of harmonic and anharmonic oscillators
with an added bounded potential with compact support.
