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研究采用B?cklund变换的双线性化常微分方程非凸松弛解分析问题，双线性化常微分方程非凸松弛解是保证模型平稳分布和存在性的重要因素，从而提高许多模型在不同边界条件下的稳定特性。把双线性化常微分方程的非凸松弛解算子进行敏感域分析表征，采用B?cklund变换进行目标函数统一迭代，得到非凸松弛解的3种核函数分别是线性核函数、多项式核函数和高斯核函数。计算双线性化常微分方程的非凸松弛解的对称广义中心的稳定性平衡点，计算线性化常微分方程的非凸松弛解满足的边界条件，通过B?cklund变换扩展欧几里得算法，实现对非凸松弛解的稳定性和收敛性的证明，得到在不同多向增量式和减量式分析下，采用B?cklund变换的双线性化常微分方程非凸松弛解是收敛和稳定的。“,”Based on B?cklund Bilinear transformation of ordinary differential convex relaxation solution analysis of non equation, bilinear differential convex relaxation solution is to ensure the stable distribution and the model parameters of non equation, so as to improve the stability of many models under different boundary conditions. The non convex relaxation double linear ordinary differential equations of operators are sensitive domain characterization, using B?cklund transforma?tion to an unified objective function iteration, 3 kinds of kernel functions are non convex relaxation solution of the linear kernel, polynomial kernel function and Gauss function. Stability of equilibrium point of generalized Centro symmetric non convex relaxation double linear ordinary differential equations, non convex relaxation linear ordinary differential equations which satisfy the boundary conditions, the B?cklund transformation extended Euclidean algorithm, the stability and conver?gence proof non convex relaxation solution, obtained by analysis incremental and decremental under different direction, B?cklund Bilinear transformation of ordinary differential equations with non convex relaxation solution is convergent and stable.