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This
is called the "general solution" of
the differential
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equation.
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We
can determine C if we were given one point on the
graph
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of
the function y(x).
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For
instance, if you were given that y(1)=2
, then you could
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substitute
2 for y and 1 for x and get:
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and
so you would conclude that C = -2, so the solution of the
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initial-value
problem:
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is , or (better):
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