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The complementary function, often denoted in the context of solving differential equations, refers to the general solution of the associated homogeneous equation. It represents the part of the solution that satisfies the differential equation without any external forcing terms. In the context of linear differential equations, the complementary function is typically found by solving the homogeneous part of the equation, which involves determining the roots of the characteristic equation. This solution is then combined with a particular solution to obtain the complete solution to the original non-homogeneous equation.

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