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1. (mathematics) For a nonhomogeneous linear differential equation ${\displaystyle a_{n}y^{(n)}+a_{n-1}y^{(n-1)}+\cdots +a_{1}y'+a_{0}y=g(x)}$, the general solution of the associated homogenous linear differential equation ${\displaystyle a_{n}y^{(n)}+a_{n-1}y^{(n-1)}+\cdots +a_{1}y'+a_{0}y=0}$.