To say that you have found the general homogeneous solution means that this function solves the homogeneous equation for every choice of the constant $C_1$ and every solution of the homogeneous equation is of this form for some choice of $C_1$. You can actually have more than one particular solution to a DEQ.
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Mukwonago, WI Profile: Facts, Map & Data. Mukwonago, Wisconsin - Basic Facts. The Village of Mukwonago had a population of 7,449 as of July 1, 2016. The primary coordinate point for Mukwonago is located at latitude 42.8553 and longitude -88.324 in Waukesha County. The formal boundaries for the Village of Mukwonago (see map below) encompass a land area of 7.87 sq. miles and a water area of 0.2 sq. miles. Waukesha County is in the Central time zone (GMT -6).