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Question
The differential equation representing the family of curves y = A sinx + B cosx is ______.
Solution
The differential equation representing the family of curves y = A sinx + B cosx is 0.
Explanation:
`("d"^2y)/("d"x^2) + y` = 0
Differentiating the given function w.r.t. x successively
We get `"dy"/"dx"` = A cosx – Bsinx
And `("d"^2y)/("d"x^2)` = –Asinx – Bcosx
⇒ `("d"^2y)/("d"x^2) + y` = 0 is the differential equation.
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