Suppose is a solution to the ODE. Then
and
, and substituting these into the ODE gives
Then the particular solution to the ODE is
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A horizontal asymptote of a function f(x) is given by y = lim f(x) as x --> ∞ and x --> –∞. In this case,
Thus, the horizontal asymptote of f(x) is y = –2.
Thus, the horizontal asymptote of f(x) is y = –2.