The differential equation representing the family of curves $y=asin (x+b)$, where a and b are arbitrary constants is :
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → $\frac{d^2y}{dx^2}+y = 0 $
$y=a\sin (x+b)$
No. of arbitrary constants = 2
degree of equation will be 2
so $\frac{dy}{dx}=a\cos(x+b)$
$\frac{d^2y}{dx^2}=-a\sin(x+b)=-y$
so $\frac{d^2y}{dx^2}+y=0$