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We propose and show efficiency of a new fuzzy-transform-based numerical method of solving ordinary differential equations with boundary conditions. The focus is on weak solutions and a special construction of a two-parameterized family of test functions. On theoretical and computational levels, we show how the proposed technique relates to and outperforms the Ritz−Galerkin method. We emphasize the importance of the proposed technique by considering its application to a real-life problem—the option pricing policy.