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In the present paper, the second‐order linear inhomogeneous initial value problems (LI‐IVP) with constant coefficients is of our interest. Two‐step hybrid methods (ie, of Numerov‐type) are considered for addressing this problem. Thus, a special set of order conditions is given and solved for derivation a low cost new method. Actually, we manage to save two stages per step. This is crucial as shown in various numerical tests where our new proposal outperforms standard methods in the relevant literature.