We prove a system of relations in the Grothendieck ring of the category O of representations of the Borel subalgebra of an untwisted quantum affine algebra. This system was discovered by Masoero-Raimondo-Valeria who established that solutions of this system can be attached to certain affine opers attached to the Langlands dual affine Kac-Moody algebra. Together with results of Bazhanov-Lukyanov-Zamolodchikov which enable one to associate quantum KdV Hamiltonians to representations from the category O, this provides evidences for a conjecture of Frenkel-Feigin linking the spectra of quantum KdV Hamiltonians and Langlands dual affine opers, as an instance of the ODE/IM correspondence. Supported by the European Research Council under the European Union’s Framework Programme H2020 with ERC Grant Agreement number 647353 Qaffine.