The differential equation representing the family of curves $y=A \cos (x+B)$, where $A$ and $B$ are arbitrary constant is :
Answer & explanation
Correct answer: option 1
eq of wave → $y=A \cos (x+B)$ .......(1)
A, B → artritrancy constant
finding differential equation to represent family of curves
differentiating (1) w.r.t (x)
$\frac{d y}{d x}=-A \sin (x+B)$ [as $\frac{d}{dx}(cos x) = -sin x$]
now differentiating again w.r.t (x)
$\frac{d^2 y}{d x^2}=-A \cos (x+B)$ [as $\frac{d}{dx}(sin x) = cos x$]
from (1) Substituting value of RHS (as $y=A \cos (x+B$)
$\frac{d^2 y}{d x^2}=-y$
$\frac{d^2 y}{d x^2}+y=0$