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Partial derivatives and differentiability (Sect. 14.3 ...

is a function and the function together with its derivatives appear in the equation. Example Given a constant k ∈ R, find all solutions f : R → R to the differential equation f 0(x) = k f (x). Solution: Multiply the equation above f 0(x) − kf (x) = 0 by e−kx, that is, f 0(x) e−kx − f (x) ke−kx = 0. The left-hand side is a total ...

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