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In this research paper, different cases of solution of the second order linear Intuitionistic Fuzzy Ordinary Differential Equations (IFODEs) are discussed. The initial conditions and the coefficients of differential equations are taken as the Generalized Trapezoidal Intuitionistic Fuzzy Numbers (GTrIFNs). The concept for finding the solution of second order linear homogeneous intuitionistic fuzzy ordinary differential equations is discussed in detail.