Find a Differential Equation Whose Solution is y = C*cos(x)

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Find a Differential Equation Whose Solution is y = C*cos(x)

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Trick question because y = C cos(x) is a solution to y'' + y = 0 but it isn't the only solution. To get the only solution proceed as follows:
y = C cos x
y' = -C sin x
y'/y = -tan x
y' = -y tan x
y' + y tan x = 0

check: y'/y = -tan x
ln y = ln cos x + k
y = exp(ln cos x + k)
y = exp(ln cos x) exp(k)
y = C cos x

rob

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