Question

The differential equation representing the family of curves y = A sinx + B cosx is ______.

Answer 1

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.