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In comparing a linear equation and the associated nonhomogeneous equation, it is shown that if every bounded forcing function and every Sfl forcing function yields at least one bounded solution, then the bounded subset of the solution family of the homogeneous equation is uniformly ultimately bounded. A MS (MOS) subject classifications (1970). Primary 34A30, 34D35 ; Secondary 34C99.doi:10.1090/s0002-9939-1973-0328202-7 fatcat:k4qqqqxorzhw5maw5fhea2e2sm