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Question
Find the differential equation of the family of curves y = Ae2x + B.e–2x.
Solution
y = Ae2x + B.e–2x.
`("d"y)/("d"x) = 2"Ae"^(2x) - 2"B"e"^(-2x)` and `("d"^2y)/("dx"^2) = 4"Ae"^(2x) + 4"Be"^(-2x)`
Thus `("d"^2y)/("dx"^2) = 4y`
i.e., `("d"^2y)/("dx"^2) - 4y` = 0.
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