The differential equation of the family of curves $y=asin(bx+c),$ a and c are parameters, is :

$\frac{d^2y}{dx^2}+b^2y=0 $ $\frac{dy}{dx}+b^2y= 0 $ $\frac{d^2y}{dx^2}-b^2y=0 $ $\frac{d^2y}{dx^2}+y=0 $

$\frac{d^2y}{dx^2}+b^2y=0 $